arXiv Papers of Physics-Informed AI

Abstract:
Deep learning has emerged as a promising paradigm for spatio-temporal modeling of fluid dynamics. However, existing approaches often suffer from limited generalization to unseen flow conditions and typically require retraining when applied to new scenarios. In this paper, we present LLM4Fluid, a spatio-temporal prediction framework that leverages Large Language Models (LLMs) as generalizable neural solvers for fluid dynamics. The framework first compresses high-dimensional flow fields into a compact latent space via reduced-order modeling enhanced with a physics-informed disentanglement mechanism, effectively mitigating spatial feature entanglement while preserving essential flow structures. A pretrained LLM then serves as a temporal processor, autoregressively predicting the dynamics of physical sequences with time series prompts. To bridge the modality gap between prompts and physical sequences, which can otherwise degrade prediction accuracy, we propose a dedicated modality alignment strategy that resolves representational mismatch and stabilizes long-term prediction. Extensive experiments across diverse flow scenarios demonstrate that LLM4Fluid functions as a robust and generalizable neural solver without retraining, achieving state-of-the-art accuracy while exhibiting powerful zero-shot and in-context learning capabilities. Code and datasets are publicly available at https://github.com/qisongxiao/LLM4Fluid.

Paperid: 2, https://arxiv.org/pdf/2601.08719.pdf GitHub

Abstract:
Physics-informed machine learning holds great promise for solving differential equations, yet existing methods struggle with highly oscillatory, multiscale, or singularly perturbed PDEs due to spectral bias, costly backpropagation, and manually tuned kernel or Fourier frequencies. This work introduces a soft partition--based Kernel-Adaptive Physics-Informed Extreme Learning Machine (KAPI-ELM), a deterministic low-dimensional parameterization in which smooth partition lengths jointly control collocation centers and Gaussian kernel widths, enabling continuous coarse-to-fine resolution without Fourier features, random sampling, or hard domain interfaces. A signed-distance-based weighting further stabilizes least-squares learning on irregular geometries. Across eight benchmarks--including oscillatory ODEs, high-frequency Poisson equations, irregular-shaped domains, and stiff singularly perturbed convection-diffusion problems-the proposed method matches or exceeds the accuracy of state-of-the-art Physics-Informed Neural Network (PINN) and Theory of Functional Connections (TFC) variants while using only a single linear solve. Although demonstrated on steady linear PDEs, the results show that soft-partition kernel adaptation provides a fast, architecture-free approach for multiscale PDEs with broad potential for future physics-informed modeling. For reproducibility, the reference codes are available at https://github.com/vikas-dwivedi-2022/soft_kapi

Paperid: 3, https://arxiv.org/pdf/2601.04176.pdf GitHub

Abstract:
We demonstrate a deep learning framework capable of recovering physical parameters from the Nonlinear Schrodinger Equation (NLSE) under severe noise conditions. By integrating Physics-Informed Neural Networks (PINNs) with automatic differentiation, we achieve reconstruction of the nonlinear coefficient beta with less than 0.2 percent relative error using only 500 sparse, randomly sampled data points corrupted by 20 percent additive Gaussian noise, a regime where traditional finite difference methods typically fail due to noise amplification in numerical derivatives. We validate the method's generalization capabilities across different physical regimes (beta between 0.5 and 2.0) and varying data availability (between 100 and 1000 training points), demonstrating consistent sub-1 percent accuracy. Statistical analysis over multiple independent runs confirms robustness (standard deviation less than 0.15 percent for beta equals 1.0). The complete pipeline executes in approximately 80 minutes on modest cloud GPU resources (NVIDIA Tesla T4), making the approach accessible for widespread adoption. Our results indicate that physics-based regularization acts as an effective filter against high measurement uncertainty, positioning PINNs as a viable alternative to traditional optimization methods for inverse problems in spatiotemporal dynamics where experimental data is scarce and noisy. All code is made publicly available to facilitate reproducibility.

Paperid: 4, https://arxiv.org/pdf/2512.23964.pdf GitHub

Abstract:
Flood models inform strategic disaster management by simulating the spatiotemporal hydrodynamics of flooding. While physics-based numerical flood models are accurate, their substantial computational cost limits their use in operational settings where rapid predictions are essential. Models designed with graph neural networks (GNNs) provide both speed and accuracy while having the ability to process unstructured spatial domains. Given its flexible input and architecture, GNNs can be leveraged alongside physics-informed techniques with ease, significantly improving interpretability. This study introduces a novel flood GNN architecture, DUALFloodGNN, which embeds physical constraints at both global and local scales through explicit loss terms. The model jointly predicts water volume at nodes and flow along edges through a shared message-passing framework. To improve performance for autoregressive inference, model training is conducted with a multi-step loss enhanced with dynamic curriculum learning. Compared with standard GNN architectures and state-of-the-art GNN flood models, DUALFloodGNN achieves substantial improvements in predicting multiple hydrologic variables while maintaining high computational efficiency. The model is open-sourced at https://github.com/acostacos/dual_flood_gnn.

Paperid: 5, https://arxiv.org/pdf/2512.22261.pdf GitHub

Abstract:
Physics-constrained data generation is essential for machine learning in scientific domains where real data are scarce; however, existing approaches often over-constrain models without identifying which physical components are necessary. We present a systematic ablation study of a physics-informed grating coupler spectrum generator that maps five geometric parameters to 100-point spectral responses. By selectively removing explicit energy conservation enforcement, Fabry-Perot oscillations, bandwidth variation, and noise, we uncover a physics constraint paradox: explicit energy conservation enforcement is mathematically redundant when the underlying equations are physically consistent, with constrained and unconstrained variants achieving identical conservation accuracy (mean error approximately 7 x 10^-9). In contrast, Fabry-Perot oscillations dominate threshold-based bandwidth variability, accounting for a 72 percent reduction in half-maximum bandwidth spread when removed (with bandwidth spread reduced from 132.3 nm to 37.4 nm). We further identify a subtle pitfall: standard noise-addition-plus-renormalization pipelines introduce 0.5 percent unphysical negative absorption values. The generator operates at 200 samples per second, enabling high-throughput data generation and remaining orders of magnitude faster than typical full-wave solvers reported in the literature. Finally, downstream machine learning evaluation reveals a clear physics-learnability trade-off: while central wavelength prediction remains unaffected, removing Fabry-Perot oscillations improves bandwidth prediction accuracy by 31.3 percent in R-squared and reduces RMSE by 73.8 percent. These findings provide actionable guidance for physics-informed dataset design and highlight machine learning performance as a diagnostic tool for assessing constraint relevance.

Paperid: 6, https://arxiv.org/pdf/2512.22222.pdf GitHub

Abstract:
Standard neural network architectures employ fixed activation functions (ReLU, tanh, sigmoid) that are poorly suited for approximating functions with singular or fractional power behavior, a structure that arises ubiquitously in physics, including boundary layers, fracture mechanics, and corner singularities. We introduce Müntz-Szász Networks (MSN), a novel architecture that replaces fixed smooth activations with learnable fractional power bases grounded in classical approximation theory. Each MSN edge computes $ϕ(x) = \sum_k a_k |x|^{μ_k} + \sum_k b_k \mathrm{sign}(x)|x|^{λ_k}$, where the exponents $\{μ_k, λ_k\}$ are learned alongside the coefficients. We prove that MSN inherits universal approximation from the Müntz-Szász theorem and establish novel approximation rates: for functions of the form $|x|^α$, MSN achieves error $\mathcal{O}(|μ- α|^2)$ with a single learned exponent, whereas standard MLPs require $\mathcal{O}(ε^{-1/α})$ neurons for comparable accuracy. On supervised regression with singular target functions, MSN achieves 5-8x lower error than MLPs with 10x fewer parameters. Physics-informed neural networks (PINNs) represent a particularly demanding application for singular function approximation; on PINN benchmarks including a singular ODE and stiff boundary-layer problems, MSN achieves 3-6x improvement while learning interpretable exponents that match the known solution structure. Our results demonstrate that theory-guided architectural design can yield dramatic improvements for scientifically-motivated function classes.

Paperid: 7, https://arxiv.org/pdf/2512.21652.pdf GitHub

Authors:Zi Wang, Mingkai Huang, Zhang Shi, Hongjie Hu, Lan Lan, Hui Zhang, Yan Li, Xi Hu, Qing Lu, Zongming Zhu, Qiong Yao, Yuxiang Dai, Fanwen Wang, Yinzhe Wu, Jun Lyu, Qianqian Gao, Guangming Xu, Zhenxuan Zhang, Haosen Zhang, Qing Li, Guangming Wang, Tianxing He, Lizhen Lan, Siyue Li, Le Xue, Mengting Sun, Yuntong Lyu, Junpu Hu, Jiayu Zhu, Rizwan Ahmad, Zhengyu Bu, Xianling Qian, Guanke Cai, Ruiyu Cao, Weirui Cai, Chang Xu, Yuyang Ren, Feidan Yu, Siying Ma, Ziqiang Xu, Xinran Chen, Sha Hua, Daniel Kim, Yajing Zhang, Chen Ouyang, Wenjia Bai, Jing Qin, Yucheng Yang, Daniel Rueckert, He Wang, Qian Tao, Claudia Prieto, Michael Markl, Alistair Young, Lianming Wu, Shuo Wang, Chen Qin, Mengsu Zeng, Xihong Hu, Haibo Xu, Xiaobo Qu, Hao Li, Guang Yang, Chengyan Wang

Abstract:
Multimodal cardiovascular magnetic resonance (CMR) imaging provides comprehensive and non-invasive insights into cardiovascular disease (CVD) diagnosis and underlying mechanisms. Despite decades of advancements, its widespread clinical adoption remains constrained by prolonged scan times and heterogeneity across medical environments. This underscores the urgent need for a generalist reconstruction foundation model for ultra-fast CMR imaging, one capable of adapting across diverse imaging scenarios and serving as the essential substrate for all downstream analyses. To enable this goal, we curate MMCMR-427K, the largest and most comprehensive multimodal CMR k-space database to date, comprising 427,465 multi-coil k-space data paired with structured metadata across 13 international centers, 12 CMR modalities, 15 scanners, and 17 CVD categories in populations across three continents. Building on this unprecedented resource, we introduce CardioMM, a generalist reconstruction foundation model capable of dynamically adapting to heterogeneous fast CMR imaging scenarios. CardioMM unifies semantic contextual understanding with physics-informed data consistency to deliver robust reconstructions across varied scanners, protocols, and patient presentations. Comprehensive evaluations demonstrate that CardioMM achieves state-of-the-art performance in the internal centers and exhibits strong zero-shot generalization to unseen external settings. Even at imaging acceleration up to 24x, CardioMM reliably preserves key cardiac phenotypes, quantitative myocardial biomarkers, and diagnostic image quality, enabling a substantial increase in CMR examination throughput without compromising clinical integrity. Together, our open-access MMCMR-427K database and CardioMM framework establish a scalable pathway toward high-throughput, high-quality, and clinically accessible cardiovascular imaging.

Paperid: 8, https://arxiv.org/pdf/2512.12751.pdf GitHub

Abstract:
Physics-aware driving world model is essential for drive planning, out-of-distribution data synthesis, and closed-loop evaluation. However, existing methods often rely on a single diffusion model to directly map driving actions to videos, which makes learning difficult and leads to physically inconsistent outputs. To overcome these challenges, we propose GenieDrive, a novel framework designed for physics-aware driving video generation. Our approach starts by generating 4D occupancy, which serves as a physics-informed foundation for subsequent video generation. 4D occupancy contains rich physical information, including high-resolution 3D structures and dynamics. To facilitate effective compression of such high-resolution occupancy, we propose a VAE that encodes occupancy into a latent tri-plane representation, reducing the latent size to only 58% of that used in previous methods. We further introduce Mutual Control Attention (MCA) to accurately model the influence of control on occupancy evolution, and we jointly train the VAE and the subsequent prediction module in an end-to-end manner to maximize forecasting accuracy. Together, these designs yield a 7.2% improvement in forecasting mIoU at an inference speed of 41 FPS, while using only 3.47 M parameters. Additionally, a Normalized Multi-View Attention is introduced in the video generation model to generate multi-view driving videos with guidance from our 4D occupancy, significantly improving video quality with a 20.7% reduction in FVD. Experiments demonstrate that GenieDrive enables highly controllable, multi-view consistent, and physics-aware driving video generation.

Paperid: 9, https://arxiv.org/pdf/2512.12402.pdf GitHub

Abstract:
We present DeepVekua, a hybrid architecture that unifies geometric deep learning with spectral analysis to solve partial differential equations (PDEs) in sparse data regimes. By learning a diffeomorphic coordinate transformation that maps complex geometries to a latent harmonic space, our method outperforms state-of-the-art implicit representations on advection-diffusion systems. Unlike standard coordinate-based networks which struggle with spectral bias, DeepVekua separates the learning of geometry from the learning of physics, solving for optimal spectral weights in closed form. We demonstrate a 100x improvement over spectral baselines. The code is available at https://github.com/VladimerKhasia/vekuanet.

Paperid: 10, https://arxiv.org/pdf/2512.11776.pdf GitHub

Abstract:
Coordinate-based neural networks have emerged as a powerful tool for representing continuous physical fields, yet they face two fundamental pathologies: spectral bias, which hinders the learning of high-frequency dynamics, and the curse of dimensionality, which causes parameter explosion in discrete feature grids. We propose the Adaptive Vekua Cascade (AVC), a hybrid architecture that bridges deep learning and classical approximation theory. AVC decouples manifold learning from function approximation by using a deep network to learn a diffeomorphic warping of the physical domain, projecting complex spatiotemporal dynamics onto a latent manifold where the solution is represented by a basis of generalized analytic functions. Crucially, we replace the standard gradient-descent output layer with a differentiable linear solver, allowing the network to optimally resolve spectral coefficients in a closed form during the forward pass. We evaluate AVC on a suite of five rigorous physics benchmarks, including high-frequency Helmholtz wave propagation, sparse medical reconstruction, and unsteady 3D Navier-Stokes turbulence. Our results demonstrate that AVC achieves state-of-the-art accuracy while reducing parameter counts by orders of magnitude (e.g., 840 parameters vs. 4.2 million for 3D grids) and converging 2-3x faster than implicit neural representations. This work establishes a new paradigm for memory-efficient, spectrally accurate scientific machine learning. The code is available at https://github.com/VladimerKhasia/vecua.

Paperid: 11, https://arxiv.org/pdf/2512.10424.pdf GitHub

Abstract:
Representing and rendering dynamic scenes with complex motions remains challenging in computer vision and graphics. Recent dynamic view synthesis methods achieve high-quality rendering but often produce physically implausible motions. We introduce NeHaD, a neural deformation field for dynamic Gaussian Splatting governed by Hamiltonian mechanics. Our key observation is that existing methods using MLPs to predict deformation fields introduce inevitable biases, resulting in unnatural dynamics. By incorporating physics priors, we achieve robust and realistic dynamic scene rendering. Hamiltonian mechanics provides an ideal framework for modeling Gaussian deformation fields due to their shared phase-space structure, where primitives evolve along energy-conserving trajectories. We employ Hamiltonian neural networks to implicitly learn underlying physical laws governing deformation. Meanwhile, we introduce Boltzmann equilibrium decomposition, an energy-aware mechanism that adaptively separates static and dynamic Gaussians based on their spatial-temporal energy states for flexible rendering. To handle real-world dissipation, we employ second-order symplectic integration and local rigidity regularization as physics-informed constraints for robust dynamics modeling. Additionally, we extend NeHaD to adaptive streaming through scale-aware mipmapping and progressive optimization. Extensive experiments demonstrate that NeHaD achieves physically plausible results with a rendering quality-efficiency trade-off. To our knowledge, this is the first exploration leveraging Hamiltonian mechanics for neural Gaussian deformation, enabling physically realistic dynamic scene rendering with streaming capabilities.

Paperid: 12, https://arxiv.org/pdf/2512.05881.pdf GitHub

Abstract:
Traditional physics-informed neural networks (PINNs) do not always satisfy physics based constraints, especially when the constraints include differential operators. Rather, they minimize the constraint violations in a soft way. Strict satisfaction of differential-algebraic equations (DAEs) to embed domain knowledge and first-principles in data-driven models is generally challenging. This is because data-driven models consider the original functions to be black-box whose derivatives can only be obtained after evaluating the functions. We introduce DAE-HardNet, a physics-constrained (rather than simply physics-informed) neural network that learns both the functions and their derivatives simultaneously, while enforcing algebraic as well as differential constraints. This is done by projecting model predictions onto the constraint manifold using a differentiable projection layer. We apply DAE-HardNet to several systems and test problems governed by DAEs, including the dynamic Lotka-Volterra predator-prey system and transient heat conduction. We also show the ability of DAE-HardNet to estimate unknown parameters through a parameter estimation problem. Compared to multilayer perceptrons (MLPs) and PINNs, DAE-HardNet achieves orders of magnitude reduction in the physics loss while maintaining the prediction accuracy. It has the added benefits of learning the derivatives which improves the constrained learning of the backbone neural network prior to the projection layer. For specific problems, this suggests that the projection layer can be bypassed for faster inference. The current implementation and codes are available at https://github.com/SOULS-TAMU/DAE-HardNet.

Paperid: 13, https://arxiv.org/pdf/2512.05683.pdf GitHub

Abstract:
Optical aberrations significantly degrade image quality in microscopy, particularly when imaging deeper into samples. These aberrations arise from distortions in the optical wavefront and can be mathematically represented using Zernike polynomials. Existing methods often address only mild aberrations on limited sample types and modalities, typically treating the problem as a black-box mapping without leveraging the underlying optical physics of wavefront distortions. We propose ZRNet, a physics-informed framework that jointly performs Zernike coefficient prediction and optical image Restoration. We contribute a Zernike Graph module that explicitly models physical relationships between Zernike polynomials based on their azimuthal degrees-ensuring that learned corrections align with fundamental optical principles. To further enforce physical consistency between image restoration and Zernike prediction, we introduce a Frequency-Aware Alignment (FAA) loss, which better aligns Zernike coefficient prediction and image features in the Fourier domain. Extensive experiments on CytoImageNet demonstrates that our approach achieves state-of-the-art performance in both image restoration and Zernike coefficient prediction across diverse microscopy modalities and biological samples with complex, large-amplitude aberrations. Code is available at https://github.com/janetkok/ZRNet.

Paperid: 14, https://arxiv.org/pdf/2511.22793.pdf GitHub GitHub

Abstract:
Channel state information (CSI) is essential for adaptive beamforming and maintaining robust links in wireless communication systems. However, acquiring CSI incurs significant overhead, consuming up to 25\% of spectrum resources in 5G networks due to frequent pilot transmissions at sub-millisecond intervals. Recent approaches aim to reduce this burden by reconstructing CSI from spatiotemporal RF measurements, such as signal strength and direction-of-arrival. While effective in offline settings, these methods often suffer from inference latencies in the 5--100~ms range, making them impractical for real-time systems. We present GSpaRC: Gaussian Splatting for Real-time Reconstruction of RF Channels, the first algorithm to break the 1 ms latency barrier while maintaining high accuracy. GSpaRC represents the RF environment using a compact set of 3D Gaussian primitives, each parameterized by a lightweight neural model augmented with physics-informed features such as distance-based attenuation. Unlike traditional vision-based splatting pipelines, GSpaRC is tailored for RF reception: it employs an equirectangular projection onto a hemispherical surface centered at the receiver to reflect omnidirectional antenna behavior. A custom CUDA pipeline enables fully parallelized directional sorting, splatting, and rendering across frequency and spatial dimensions. Evaluated on multiple RF datasets, GSpaRC achieves similar CSI reconstruction fidelity to recent state-of-the-art methods while reducing training and inference time by over an order of magnitude. By trading modest GPU computation for a substantial reduction in pilot overhead, GSpaRC enables scalable, low-latency channel estimation suitable for deployment in 5G and future wireless systems. The code is available here: \href{https://github.com/Nbhavyasai/GSpaRC-WirelessGaussianSplatting.git}{GSpaRC}.

Paperid: 15, https://arxiv.org/pdf/2511.20501.pdf GitHub

Abstract:
Accurate extraction and segmentation of the cerebral arteries from digital subtraction angiography (DSA) sequences is essential for developing reliable clinical management models of complex cerebrovascular diseases. Conventional loss functions often rely solely on pixel-wise overlap, overlooking the geometric and physical consistency of vascular boundaries, which can lead to fragmented or unstable vessel predictions. To overcome this limitation, we propose a novel \textit{Physics-Informed Loss} (PIL) that models the interaction between the predicted and ground-truth boundaries as an elastic process inspired by dislocation theory in materials physics. This formulation introduces a physics-based regularization term that enforces smooth contour evolution and structural consistency, allowing the network to better capture fine vascular geometry. The proposed loss is integrated into several segmentation architectures, including U-Net, U-Net++, SegFormer, and MedFormer, and evaluated on two public benchmarks: DIAS and DSCA. Experimental results demonstrate that PIL consistently outperforms conventional loss functions such as Cross-Entropy, Dice, Active Contour, and Surface losses, achieving superior sensitivity, F1 score, and boundary coherence. These findings confirm that the incorporation of physics-based boundary interactions into deep neural networks improves both the precision and robustness of vascular segmentation in dynamic angiographic imaging. The implementation of the proposed method is publicly available at https://github.com/irfantahir301/Physicsis_loss.

Paperid: 16, https://arxiv.org/pdf/2511.20015.pdf GitHub

Abstract:
Radio maps (RMs) serve as environment-aware electromagnetic (EM) representations that connect scenario geometry and material properties to the spatial distribution of signal strength, enabling localization without costly in-situ measurements. However, constructing high-fidelity indoor RMs remains challenging due to the prohibitive latency of EM solvers and the limitations of learning-based methods, which often rely on sparse measurements or assumptions of homogeneous material, which are misaligned with the heterogeneous and multipath-rich nature of indoor environments. To overcome these challenges, we propose iRadioDiff, a sampling-free diffusion-based framework for indoor RM construction. iRadioDiff is conditioned on access point (AP) positions, and physics-informed prompt encoded by material reflection and transmission coefficients. It further incorporates multipath-critical priors, including diffraction points, strong transmission boundaries, and line-of-sight (LoS) contours, to guide the generative process via conditional channels and boundary-weighted objectives. This design enables accurate modeling of nonstationary field discontinuities and efficient construction of physically consistent RMs. Experiments demonstrate that iRadioDiff achieves state-of-the-art performance in indoor RM construction and received signal strength based indoor localization, which offers effective generalization across layouts and material configurations. Code is available at https://github.com/UNIC-Lab/iRadioDiff.

Paperid: 17, https://arxiv.org/pdf/2511.15530.pdf GitHub

Abstract:
In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses according to some meta-goal. For example, in physics-informed neural networks (PINNs), these weights are often adaptively chosen to improve the network's generalization error. A popular choice of adaptive weights is based on the neural tangent kernel (NTK) of the PINN, which describes the evolution of the network in predictor space during training. The convergence of such an adaptive weighting algorithm is not clear a priori. Moreover, these NTK-based weights would be updated frequently during training, further increasing the computational burden of the learning process. In this paper, we prove that under appropriate conditions, gradient descent enhanced with adaptive NTK-based weights is convergent in a suitable sense. We then address the problem of computational efficiency by developing a randomized algorithm inspired by a predictor-corrector approach and matrix sketching, which produces unbiased estimates of the NTK up to an arbitrarily small discretization error. Finally, we provide numerical experiments to support our theoretical findings and to show the efficacy of our randomized algorithm. Code Availability: https://github.com/maxhirsch/Efficient-NTK

Paperid: 18, https://arxiv.org/pdf/2511.14033.pdf GitHub

Abstract:
Flood prediction is critical for emergency planning and response to mitigate human and economic losses. Traditional physics-based hydrodynamic models generate high-resolution flood maps using numerical methods requiring fine-grid discretization; which are computationally intensive and impractical for real-time large-scale applications. While recent studies have applied convolutional neural networks for flood map super-resolution with good accuracy and speed, they suffer from limited generalizability to unseen areas. In this paper, we propose a novel approach that leverages latent diffusion models to perform super-resolution on coarse-grid flood maps, with the objective of achieving the accuracy of fine-grid flood maps while significantly reducing inference time. Experimental results demonstrate that latent diffusion models substantially decrease the computational time required to produce high-fidelity flood maps without compromising on accuracy, enabling their use in real-time flood risk management. Moreover, diffusion models exhibit superior generalizability across different physical locations, with transfer learning further accelerating adaptation to new geographic regions. Our approach also incorporates physics-informed inputs, addressing the common limitation of black-box behavior in machine learning, thereby enhancing interpretability. Code is available at https://github.com/neosunhan/flood-diff.

Paperid: 19, https://arxiv.org/pdf/2511.11077.pdf GitHub GitHub GitHub

Abstract:
Estimating the geometric and volumetric properties of transparent deformable liquids is challenging due to optical complexities and dynamic surface deformations induced by container movements. Autonomous robots performing precise liquid manipulation tasks, such as dispensing, aspiration, and mixing, must handle containers in ways that inevitably induce these deformations, complicating accurate liquid state assessment. Current datasets lack comprehensive physics-informed simulation data representing realistic liquid behaviors under diverse dynamic scenarios. To bridge this gap, we introduce Phys-Liquid, a physics-informed dataset comprising 97,200 simulation images and corresponding 3D meshes, capturing liquid dynamics across multiple laboratory scenes, lighting conditions, liquid colors, and container rotations. To validate the realism and effectiveness of Phys-Liquid, we propose a four-stage reconstruction and estimation pipeline involving liquid segmentation, multi-view mask generation, 3D mesh reconstruction, and real-world scaling. Experimental results demonstrate improved accuracy and consistency in reconstructing liquid geometry and volume, outperforming existing benchmarks. The dataset and associated validation methods facilitate future advancements in transparent liquid perception tasks. The dataset and code are available at https://dualtransparency.github.io/Phys-Liquid/.

Paperid: 20, https://arxiv.org/pdf/2511.11048.pdf GitHub

Abstract:
4D flow magnetic resonance imaging (MRI) is a reliable, non-invasive approach for estimating blood flow velocities, vital for cardiovascular diagnostics. Unlike conventional MRI focused on anatomical structures, 4D flow MRI requires high spatiotemporal resolution for early detection of critical conditions such as stenosis or aneurysms. However, achieving such resolution typically results in prolonged scan times, creating a trade-off between acquisition speed and prediction accuracy. Recent studies have leveraged physics-informed neural networks (PINNs) for super-resolution of MRI data, but their practical applicability is limited as the prohibitively slow training process must be performed for each patient. To overcome this limitation, we propose PINGS-X, a novel framework modeling high-resolution flow velocities using axes-aligned spatiotemporal Gaussian representations. Inspired by the effectiveness of 3D Gaussian splatting (3DGS) in novel view synthesis, PINGS-X extends this concept through several non-trivial novel innovations: (i) normalized Gaussian splatting with a formal convergence guarantee, (ii) axes-aligned Gaussians that simplify training for high-dimensional data while preserving accuracy and the convergence guarantee, and (iii) a Gaussian merging procedure to prevent degenerate solutions and boost computational efficiency. Experimental results on computational fluid dynamics (CFD) and real 4D flow MRI datasets demonstrate that PINGS-X substantially reduces training time while achieving superior super-resolution accuracy. Our code and datasets are available at https://github.com/SpatialAILab/PINGS-X.

Paperid: 21, https://arxiv.org/pdf/2511.09484.pdf GitHub

Abstract:
Learning dexterous and agile policy for humanoid and dexterous hand control requires large-scale demonstrations, but collecting robot-specific data is prohibitively expensive. In contrast, abundant human motion data is readily available from motion capture, videos, and virtual reality, which could help address the data scarcity problem. However, due to the embodiment gap and missing dynamic information like force and torque, these demonstrations cannot be directly executed on robots. To bridge this gap, we propose Scalable Physics-Informed DExterous Retargeting (SPIDER), a physics-based retargeting framework to transform and augment kinematic-only human demonstrations to dynamically feasible robot trajectories at scale. Our key insight is that human demonstrations should provide global task structure and objective, while large-scale physics-based sampling with curriculum-style virtual contact guidance should refine trajectories to ensure dynamical feasibility and correct contact sequences. SPIDER scales across diverse 9 humanoid/dexterous hand embodiments and 6 datasets, improving success rates by 18% compared to standard sampling, while being 10X faster than reinforcement learning (RL) baselines, and enabling the generation of a 2.4M frames dynamic-feasible robot dataset for policy learning. As a universal physics-based retargeting method, SPIDER can work with diverse quality data and generate diverse and high-quality data to enable efficient policy learning with methods like RL.

Paperid: 22, https://arxiv.org/pdf/2511.08418.pdf GitHub

Abstract:
Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to discretisation, while canonical deep learning methods are data-hungry and struggle with chaotic dynamics and long-term predictions. Physics-Informed Neural Networks (PINNs) mitigate some of these issues by incorporating physical constraints in the learning process, yet they remain limited by mesh resolution and long-term predictive stability. In this work, we propose a Physics-Informed Neural Operator (PINO) approach to solve PDE problems in cardiac EP. Unlike PINNs, PINO models learn mappings between function spaces, allowing them to generalise to multiple mesh resolutions and initial conditions. Our results show that PINO models can accurately reproduce cardiac EP dynamics over extended time horizons and across multiple propagation scenarios, including zero-shot evaluations on scenarios unseen during training. Additionally, our PINO models maintain high predictive quality in long roll-outs (where predictions are recursively fed back as inputs), and can scale their predictive resolution by up to 10x the training resolution. These advantages come with a significant reduction in simulation time compared to numerical PDE solvers, highlighting the potential of PINO-based approaches for efficient and scalable cardiac EP simulations.

Paperid: 23, https://arxiv.org/pdf/2511.00792.pdf GitHub

Abstract:
Eigenvalue problems have a distinctive forward-inverse structure and are fundamental to characterizing a system's thermal response, stability, and natural modes. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative for solving such problems but are often orders of magnitude slower than classical numerical schemes. In this paper, we introduce a reformulated PINN approach that casts the search for eigenpairs as a biconvex optimization problem, enabling fast and provably convergent alternating convex search (ACS) over eigenvalues and eigenfunctions using analytically optimal updates. Numerical experiments show that PINN-ACS attains high accuracy with convergence speeds up to 500$\times$ faster than gradient-based PINN training. We release our codes at https://github.com/NeurIPS-ML4PS-2025/PINN_ACS_CODES.

Paperid: 24, https://arxiv.org/pdf/2510.25781.pdf GitHub

Abstract:
Kolmogorov-Arnold Networks (KANs) have recently emerged as a promising alternative to traditional Multilayer Perceptrons (MLPs), inspired by the Kolmogorov-Arnold representation theorem. Unlike MLPs, which use fixed activation functions on nodes, KANs employ learnable univariate basis functions on edges, offering enhanced expressivity and interpretability. This review provides a systematic and comprehensive overview of the rapidly expanding KAN landscape, moving beyond simple performance comparisons to offer a structured synthesis of theoretical foundations, architectural variants, and practical implementation strategies. By collecting and categorizing a vast array of open-source implementations, we map the vibrant ecosystem supporting KAN development. We begin by bridging the conceptual gap between KANs and MLPs, establishing their formal equivalence and highlighting the superior parameter efficiency of the KAN formulation. A central theme of our review is the critical role of the basis function; we survey a wide array of choices, including B-splines, Chebyshev and Jacobi polynomials, ReLU compositions, Gaussian RBFs, and Fourier series, and analyze their respective trade-offs in terms of smoothness, locality, and computational cost. We then categorize recent advancements into a clear roadmap, covering techniques for improving accuracy, efficiency, and regularization. Key topics include physics-informed loss design, adaptive sampling, domain decomposition, hybrid architectures, and specialized methods for handling discontinuities. Finally, we provide a practical "Choose-Your-KAN" guide to help practitioners select appropriate architectures, and we conclude by identifying current research gaps. The associated GitHub repository https://github.com/AmirNoori68/kan-review complements this paper and serves as a structured reference for ongoing KAN research.

Paperid: 25, https://arxiv.org/pdf/2510.23117.pdf GitHub

Abstract:
Physics Informed Neural Networks (PINNs) are gaining attention for their ability to embed physical laws into deep learning models, which is particularly useful in structural engineering tasks with limited data. This paper aims to explore the use of PINNs to predict the weight of small scale spaghetti bridges, a task relevant to understanding load limits and potential failure modes in simplified structural models. Our proposed framework incorporates physics-based constraints to the prediction model for improved performance. In addition to standard PINNs, we introduce a novel architecture named Physics Informed Kolmogorov Arnold Network (PIKAN), which blends universal function approximation theory with physical insights. The structural parameters provided as input to the model are collected either manually or through computer vision methods. Our dataset includes 15 real bridges, augmented to 100 samples, and our best model achieves an $R^2$ score of 0.9603 and a mean absolute error (MAE) of 10.50 units. From applied perspective, we also provide a web based interface for parameter entry and prediction. These results show that PINNs can offer reliable estimates of structural weight, even with limited data, and may help inform early stage failure analysis in lightweight bridge designs. The complete data and code are available at https://github.com/OmerJauhar/PINNS-For-Spaghetti-Bridges.

Paperid: 26, https://arxiv.org/pdf/2510.15750.pdf GitHub

Abstract:
Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great solution. However, selecting the architecture that emulates the FEA with great accuracy is a challenge. This paper presents a comprehensive evaluation of graph neural networks (GNNs) and 3D U-Nets as surrogates for FEA of parametric I-beams. We introduce a Physics-Informed Neural Network (PINN) framework, governed by the Navier Cauchy equations, to enforce physical laws. Crucially, we demonstrate that a curriculum learning strategy, pretraining on data followed by physics informed fine tuning, is essential for stabilizing training. Our results show that GNNs fundamentally outperform the U-Net. Even the worst performer among GNNs, the GCN framework, achieved a relative L2 error of 8.7% while the best framework among U Net, U Net with attention mechanism trained on high resolution data, achieved 13.0% score. Among the graph-based architectures, the Message Passing Neural Networks (MPNN) and Graph Transformers achieved the highest accuracy, achieving a relative L2 score of 3.5% and 2.6% respectively. The inclusion of physics fundamental laws (PINN) significantly improved the generalization, reducing error by up to 11.3% on high-signal tasks. While the Graph Transformer is the most accurate model, it is more 37.5% slower during inference when compared to second best model, MPNN PINN. The PINN enhanced MPNN (MPNN PINN) provides the most practical solution. It offers a good compromise between predictive performance, model size, and inference speed.

Paperid: 27, https://arxiv.org/pdf/2510.05351.pdf GitHub

Abstract:
We propose Physics-informed Attention-enhanced Fourier Neural Operator (PIANO) to solve the Nonlinear Force-Free Field (NLFFF) problem in solar physics. Unlike conventional approaches that rely on iterative numerical methods, our proposed PIANO directly learns the 3D magnetic field structure from 2D boundary conditions. Specifically, PIANO integrates Efficient Channel Attention (ECA) mechanisms with Dilated Convolutions (DC), which enhances the model's ability to capture multimodal input by prioritizing critical channels relevant to the magnetic field's variations. Furthermore, we apply physics-informed loss by enforcing the force-free and divergence-free conditions in the training process so that our prediction is consistent with underlying physics with high accuracy. Experimental results on the ISEE NLFFF dataset show that our PIANO not only outperforms state-of-the-art neural operators in terms of accuracy but also shows strong consistency with the physical characteristics of NLFFF data across magnetic fields reconstructed from various solar active regions. The GitHub of this project is available https://github.com/Autumnstar-cjh/PIANO

Paperid: 28, https://arxiv.org/pdf/2509.24517.pdf GitHub

Abstract:
Development of modern deep learning methods has been driven primarily by the push for improving model efficacy (accuracy metrics). This sole focus on efficacy has steered development of large-scale models that require massive resources, and results in considerable carbon footprint across the model life-cycle. In this work, we explore how physics inductive biases can offer useful trade-offs between model efficacy and model efficiency (compute, energy, and carbon). We study a variety of models for spatio-temporal forecasting, a task governed by physical laws and well-suited for exploring different levels of physics inductive bias. We show that embedding physics inductive biases into the model design can yield substantial efficiency gains while retaining or even improving efficacy for the tasks under consideration. In addition to using standard physics-informed spatio-temporal models, we demonstrate the usefulness of more recent models like flow matching as a general purpose method for spatio-temporal forecasting. Our experiments show that incorporating physics inductive biases offer a principled way to improve the efficiency and reduce the carbon footprint of machine learning models. We argue that model efficiency, along with model efficacy, should become a core consideration driving machine learning model development and deployment.

Paperid: 29, https://arxiv.org/pdf/2509.22458.pdf GitHub

Abstract:
Physics-informed graph neural networks (PIGNNs) have emerged as fast AC power-flow solvers that can replace classic Newton--Raphson (NR) solvers, especially when thousands of scenarios must be evaluated. However, current PIGNNs still need accuracy improvements at parity speed; in particular, the physics loss is inoperative at inference, which can deter operational adoption. We address this with PIGNN-Attn-LS, combining an edge-aware attention mechanism that explicitly encodes line physics via per-edge biases, capturing the grid's anisotropy, with a backtracking line-search-based globalized correction operator that restores an operative decrease criterion at inference. Training and testing use a realistic High-/Medium-Voltage scenario generator, with NR used only to construct reference states. On held-out HV cases consisting of 4--32-bus grids, PIGNN-Attn-LS achieves a test RMSE of 0.00033 p.u. in voltage and 0.08$^\circ$ in angle, outperforming the PIGNN-MLP baseline by 99.5\% and 87.1\%, respectively. With streaming micro-batches, it delivers 2--5$\times$ faster batched inference than NR on 4--1024-bus grids.

Paperid: 30, https://arxiv.org/pdf/2509.19985.pdf GitHub

Abstract:
Anomalies in multivariate time series often arise from temporal context and cross-channel coordination rather than isolated outliers. We present Pi-Transformer, a physics-informed transformer with two attention pathways: a data-driven series attention and a smoothly evolving prior attention that encodes temporal invariants such as scale-related self-similarity and phase synchrony. The prior acts as a stable reference that calibrates reconstruction error. During training, we pair a reconstruction objective with a divergence term that encourages agreement between the two attentions while keeping them meaningfully distinct; the prior is regularised to evolve smoothly and is lightly distilled towards dataset-level statistics. At inference, the model combines an alignment-weighted reconstruction signal (Energy) with a mismatch signal that highlights timing and phase disruptions, and fuses them into a single score for detection. Across five benchmarks (SMD, MSL, SMAP, SWaT, and PSM), Pi-Transformer achieves state-of-the-art or highly competitive F1, with particular strength on timing and phase-breaking anomalies. Case analyses show complementary behaviour of the two streams and interpretable detections around regime changes. Embedding physics-informed priors into attention yields a calibrated and robust approach to anomaly detection in complex multivariate systems. Code is publicly available at this GitHub repository\footnote{https://github.com/sepehr-m/Pi-Transformer}.

Paperid: 31, https://arxiv.org/pdf/2509.05117.pdf GitHub

Abstract:
We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parametrizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that compares the physics of the generated PINN to the requested PDE and uses the discrepancy to generate a "delta" PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves over 100x gain in average $L_2$ loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems. The code and model weights are publicly available at https://github.com/rbischof/hypino.

Paperid: 32, https://arxiv.org/pdf/2509.02343.pdf GitHub

Abstract:
Optical microrobots actuated by optical tweezers (OT) offer great potential for biomedical applications such as cell manipulation and microscale assembly. These tasks demand accurate three-dimensional perception to ensure precise control in complex and dynamic biological environments. However, the transparent nature of microrobots and low-contrast microscopic imaging challenge conventional deep learning methods, which also require large annotated datasets that are costly to obtain. To address these challenges, we propose a physics-informed, data-efficient framework for depth estimation of optical microrobots. Our method augments convolutional feature extraction with physics-based focus metrics, such as entropy, Laplacian of Gaussian, and gradient sharpness, calculated using an adaptive grid strategy. This approach allocates finer grids over microrobot regions and coarser grids over background areas, enhancing depth sensitivity while reducing computational complexity. We evaluate our framework on multiple microrobot types and demonstrate significant improvements over baseline models. Specifically, our approach reduces mean squared error (MSE) by over 60% and improves the coefficient of determination (R^2) across all test cases. Notably, even when trained on only 20% of the available data, our model outperforms ResNet50 trained on the full dataset, highlighting its robustness under limited data conditions. Our code is available at: https://github.com/LannWei/CBS2025.

Paperid: 33, https://arxiv.org/pdf/2508.19847.pdf GitHub

Abstract:
We present a hybrid framework that couples finite element methods (FEM) with physics-informed DeepONet to model fluid transport in porous media from sharp, localized Gaussian sources. The governing system consists of a steady-state Darcy flow equation and a time-dependent convection-diffusion equation. Our approach solves the Darcy system using FEM and transfers the resulting velocity field to a physics-informed DeepONet, which learns the mapping from source functions to solute concentration profiles. This modular strategy preserves FEM-level accuracy in the flow field while enabling fast inference for transport dynamics. To handle steep gradients induced by sharp sources, we introduce an adaptive sampling strategy for trunk collocation points. Numerical experiments demonstrate that our method is in good agreement with the reference solutions while offering orders of magnitude speedups over traditional solvers, making it suitable for practical applications in relevant scenarios. Implementation of our proposed method is available at https://github.com/erkara/fem-pi-deeponet.

Paperid: 34, https://arxiv.org/pdf/2508.19561.pdf GitHub

Abstract:
This paper presents a novel Energy-Equidistributed adaptive sampling framework for multi-dimensional conservative PDEs, introducing both location-based and velocity-based formulations of Energy-Equidistributed moving mesh PDEs (EMMPDEs). The framework utilizes the energy density function as the monitor function, ensuring that mesh adaptation dynamically tracks energy evolution during temporal integration. These theoretical developments are integrated with deep neural networks to establish the Energy-Equidistributed Moving Sampling Physics-Informed Neural Networks (EEMS-PINNs), which integrate physics-informed learning with energy-adaptive mesh optimization. Extensive numerical experiments demonstrate that EEMS-PINNs effectively maintain solution accuracy in long-time simulations while preserving conserved energy. The framework's robustness is further evidenced by its stable performance in non-conservative systems. The code for this paper can be found at https://github.com/sufe-Ran-Zhang/EMMPDE.

Paperid: 35, https://arxiv.org/pdf/2508.19249.pdf GitHub

Abstract:
We present a new efficient hybrid parameter estimation method based on the idea, that if nonlinear dynamic models are stated in terms of a system of equations that is linear in terms of the parameters, then regularized ordinary least squares can be used to estimate these parameters from time series data. We introduce the term "Physics-Informed Regression" (PIR) to describe the proposed data-driven hybrid technique as a way to bridge theory and data by use of ordinary least squares to efficiently perform parameter estimation of the model coefficients of different parameter-linear models; providing examples of models based on nonlinear ordinary equations (ODE) and partial differential equations (PDE). The focus is on parameter estimation on a selection of ODE and PDE models, each illustrating performance in different model characteristics. For two relevant epidemic models of different complexity and number of parameters, PIR is tested and compared against the related technique, physics-informed neural networks (PINN), both on synthetic data generated from known target parameters and on real public Danish time series data collected during the COVID-19 pandemic in Denmark. Both methods were able to estimate the target parameters, while PIR showed to perform noticeably better, especially on a compartment model with higher complexity. Given the difference in computational speed, it is concluded that the PIR method is superior to PINN for the models considered. It is also demonstrated how PIR can be applied to estimate the time-varying parameters of a compartment model that is fitted using real Danish data from the COVID-19 pandemic obtained during a period from 2020 to 2021. The study shows how data-driven and physics-informed techniques may support reliable and fast -- possibly real-time -- parameter estimation in parameter-linear nonlinear dynamic models.

Paperid: 36, https://arxiv.org/pdf/2508.18954.pdf GitHub

Abstract:
This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a three-stage methodology: learning Koopman embeddings through autoencoding, pre-training a transformer on next-state prediction, and fine-tuning for safety-critical control. Our results show that Koopman embeddings outperform both standard and physics-informed PCA baselines, achieving accurate and data-efficient performance. Notably, fixing the pre-trained transformer weights during fine-tuning leads to no performance degradation, indicating that the learned representations capture reusable dynamical structure rather than task-specific patterns. These findings support the use of Koopman embeddings as a foundation for multi-task learning in physics-informed machine learning. A project page is available at https://kikisprdx.github.io/.

Paperid: 37, https://arxiv.org/pdf/2508.16999.pdf GitHub

Abstract:
This paper proposes a Physics-Informed Kolmogorov-Arnold Network (PIKAN) method for analyzing elasticity problems in electronic packaging multi-material structures. The core innovation lies in replacing Multi-Layer Perceptrons (MLPs) with Kolmogorov-Arnold Networks (KANs) within the energy-based Physics-Informed Neural Networks (PINNs) framework. The method constructs admissible displacement fields that automatically satisfy essential boundary conditions and employs various numerical integration schemes to compute loss functions for network optimization. Unlike traditional PINNs that require domain decomposition and penalty terms for multi-material problems, KANs' trainable B-spline activation functions provide inherent piecewise function characteristics that naturally accommodate material property discontinuities. Consequently, this approach requires only a single KAN to achieve accurate approximation across the entire computational domain without subdomain partitioning and interface continuity constraints. Numerical validation demonstrates PIKAN's accuracy and robustness for multi-material elasticity problems. The method maintains high accuracy while significantly reducing computational complexity compared to domain decomposition approaches. Results confirm PIKAN's unique advantages in solving multi-material problems and its significant potential for electronic packaging structure analysis. Source codes are available at https://github.com/yanpeng-gong/PIKAN-MultiMaterial.

Paperid: 38, https://arxiv.org/pdf/2508.12213.pdf GitHub

Abstract:
As a critical component of Wearable AI, IMU-based Human Activity Recognition (HAR) has attracted increasing attention from both academia and industry in recent years. Although HAR performance has improved considerably in specific scenarios, its generalization capability remains a key barrier to widespread real-world adoption. For example, domain shifts caused by variations in users, sensor positions, or environments can significantly decrease the performance in practice. As a result, in this survey, we explore the rapidly evolving field of IMU-based generalizable HAR, reviewing 229 research papers alongside 25 publicly available datasets to provide a broad and insightful overview. We first present the background and overall framework of IMU-based HAR tasks, as well as the generalization-oriented training settings. Then, we categorize representative methodologies from two perspectives: (i) model-centric approaches, including pre-training method, end-to-end method, and large language model (LLM)-based learning method; and (ii) data-centric approaches, including multi-modal learning and data augmentation techniques. In addition, we summarize widely used datasets in this field, as well as relevant tools and benchmarks. Building on these methodological advances, the broad applicability of IMU-based HAR is also reviewed and discussed. Finally, we discuss persistent challenges (e.g., data scarcity, efficient training, and reliable evaluation) and also outline future directions for HAR, including the adoption of foundation and large language models, physics-informed and context-aware reasoning, generative modeling, and resource-efficient training and inference. The complete list of this survey is available at https://github.com/rh20624/Awesome-IMU-Sensing, which will be updated continuously.

Paperid: 39, https://arxiv.org/pdf/2508.09811.pdf GitHub

Abstract:
In this paper, we aim to model 3D scene geometry, appearance, and physical information just from dynamic multi-view videos in the absence of any human labels. By leveraging physics-informed losses as soft constraints or integrating simple physics models into neural nets, existing works often fail to learn complex motion physics, or doing so requires additional labels such as object types or masks. We propose a new framework named TRACE to model the motion physics of complex dynamic 3D scenes. The key novelty of our method is that, by formulating each 3D point as a rigid particle with size and orientation in space, we directly learn a translation rotation dynamics system for each particle, explicitly estimating a complete set of physical parameters to govern the particle's motion over time. Extensive experiments on three existing dynamic datasets and one newly created challenging synthetic datasets demonstrate the extraordinary performance of our method over baselines in the task of future frame extrapolation. A nice property of our framework is that multiple objects or parts can be easily segmented just by clustering the learned physical parameters.

Paperid: 40, https://arxiv.org/pdf/2508.03776.pdf GitHub

Abstract:
Estimating heat flux in the nuclear fusion device EAST is a critically important task. Traditional scientific computing methods typically model this process using the Finite Element Method (FEM). However, FEM relies on grid-based sampling for computation, which is computationally inefficient and hard to perform real-time simulations during actual experiments. Inspired by artificial intelligence-powered scientific computing, this paper proposes a novel Physics-Informed Neural Network (PINN) to address this challenge, significantly accelerating the heat conduction estimation process while maintaining high accuracy. Specifically, given inputs of different materials, we first feed spatial coordinates and time stamps into the neural network, and compute boundary loss, initial condition loss, and physical loss based on the heat conduction equation. Additionally, we sample a small number of data points in a data-driven manner to better fit the specific heat conduction scenario, further enhancing the model's predictive capability. We conduct experiments under both uniform and non-uniform heating conditions on the top surface. Experimental results show that the proposed thermal conduction physics-informed neural network achieves accuracy comparable to the finite element method, while achieving $\times$40 times acceleration in computational efficiency. The dataset and source code will be released on https://github.com/Event-AHU/OpenFusion.

Paperid: 41, https://arxiv.org/pdf/2508.00628.pdf GitHub

Abstract:
Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional physics-informed neural networks (PINNs) suffer from spectral bias, limiting their ability to capture high-frequency solution components. We introduce Separated-Variable Spectral Neural Networks (SV-SNN), a novel framework that addresses these limitations by integrating separation of variables with adaptive spectral methods. Our approach features three key innovations: (1) decomposition of multivariate functions into univariate function products, enabling independent spatial and temporal networks; (2) adaptive Fourier spectral features with learnable frequency parameters for high-frequency capture; and (3) theoretical framework based on singular value decomposition to quantify spectral bias. Comprehensive evaluation on benchmark problems including Heat equation, Helmholtz equation, Poisson equations and Navier-Stokes equations demonstrates that SV-SNN achieves 1-3 orders of magnitude improvement in accuracy while reducing parameter count by over 90\% and training time by 60\%. These results establish SV-SNN as an effective solution to the spectral bias problem in neural PDE solving. The implementation will be made publicly available upon acceptance at https://github.com/xgxgnpu/SV-SNN.

Paperid: 42, https://arxiv.org/pdf/2507.18150.pdf GitHub

Abstract:
Nuclear reactors are often modeled as inflexible baseload generators with fixed downtimes and restrictive ramping constraints. In practice, however, a reactor's operational flexibility is closely tied to its fuel cycle and associated reactivity margin. A key physical constraint for power maneuverability is xenon poisoning, caused from the transient buildup of neutron-absorbing xenon following a power reduction. This transient can delay or prevent subsequent power ramp-up due to suppressed core reactivity. Additionally, if a reactor is shutdown during periods of low reactivity, restart times can vary significantly, leading to prolonged downtimes. This work introduces a physics-informed modeling framework that embeds fuel cycle dynamics within a unit commitment (UC) formulation. The framework tracks reactivity margin, dynamically enforces xenon induced constraints, and endogenously schedules refueling outages based on core conditions. By capturing intracycle reactivity evolution, the model enables operation dependent nuclear dispatch that reflects both techno-economic requirements and irreducible nuclear physics limits. Application to a representative reactor fleet shows that flexible operation can slow reactivity degradation and extend fuel cycles. Results further demonstrate that different operational modes substantially affect VRE utilization, curtailment, and nuclear fleet capacity factors. These findings highlight the importance of fuel cycle aware flexibility modeling for accurate reactor scheduling and integration of nuclear power into energy system models.

Paperid: 43, https://arxiv.org/pdf/2507.17151.pdf GitHub

Abstract:
Neural operators offer a powerful paradigm for solving partial differential equations (PDEs) that cannot be solved analytically by learning mappings between function spaces. However, there are two main bottlenecks in training neural operators: they require a significant amount of training data to learn these mappings, and this data needs to be labeled, which can only be accessed via expensive simulations with numerical solvers. To alleviate both of these issues simultaneously, we propose PICore, an unsupervised coreset selection framework that identifies the most informative training samples without requiring access to ground-truth PDE solutions. PICore leverages a physics-informed loss to select unlabeled inputs by their potential contribution to operator learning. After selecting a compact subset of inputs, only those samples are simulated using numerical solvers to generate labels, reducing annotation costs. We then train the neural operator on the reduced labeled dataset, significantly decreasing training time as well. Across four diverse PDE benchmarks and multiple coreset selection strategies, PICore achieves up to 78% average increase in training efficiency relative to supervised coreset selection methods with minimal changes in accuracy. We provide code at https://github.com/Asatheesh6561/PICore.

Paperid: 44, https://arxiv.org/pdf/2507.12659.pdf GitHub

Abstract:
Physics-Informed Neural Networks (PINNs) are deep learning models that incorporate the governing physical laws of a system into the learning process, making them well-suited for solving complex scientific and engineering problems. Recently, PINNs have gained widespread attention as a powerful framework for combining physical principles with data-driven modeling to improve prediction accuracy. Despite their successes, however, PINNs often exhibit poor extrapolation performance outside the training domain and are highly sensitive to the choice of activation functions (AFs). In this paper, we introduce a transfer learning (TL) method to improve the extrapolation capability of PINNs. Our approach applies transfer learning (TL) within an extended training domain, using only a small number of carefully selected collocation points. Additionally, we propose an adaptive AF that takes the form of a linear combination of standard AFs, which improves both the robustness and accuracy of the model. Through a series of experiments, we demonstrate that our method achieves an average of 40% reduction in relative L2 error and an average of 50% reduction in mean absolute error in the extrapolation domain, all without a significant increase in computational cost. The code is available at https://github.com/LiuzLab/PINN-extrapolation .

Paperid: 45, https://arxiv.org/pdf/2507.09330.pdf GitHub

Abstract:
Accurate representation of wells is essential for reliable reservoir characterization and simulation of operational scenarios in subsurface flow models. Physics-informed neural networks (PINNs) have recently emerged as a promising method for reservoir modeling, offering seamless integration of monitoring data and governing physical equations. However, existing PINN-based studies face major challenges in capturing fluid pressure near wells, particularly during the early stage after injection begins. To address this, we propose WellPINN, a modeling workflow that combines the outputs of multiple sequentially trained PINN models to accurately represent wells. This workflow iteratively approximates the radius of the equivalent well to match the actual well dimensions by decomposing the domain into stepwise shrinking subdomains with a simultaneously reducing equivalent well radius. Our results demonstrate that sequential training of superimposing networks around the pumping well is the first workflow that focuses on accurate inference of fluid pressure from pumping rates throughout the entire injection period, significantly advancing the potential of PINNs for inverse modeling and operational scenario simulations. All data and code for this paper will be made openly available at https://github.com/linuswalter/WellPINN.

Paperid: 46, https://arxiv.org/pdf/2507.01340.pdf GitHub

Abstract:
Body dynamics are crucial information for the analysis of human motions in important research fields, ranging from biomechanics, sports science to computer vision and graphics. Modern approaches collect the body dynamics, external reactive force specifically, via force plates, synchronizing with human motion capture data, and learn to estimate the dynamics from a black-box deep learning model. Being specialized devices, force plates can only be installed in laboratory setups, imposing a significant limitation on the learning of human dynamics. To this end, we propose a novel method for estimating human ground reaction dynamics directly from the more reliable motion capture data with physics laws and computational simulation as constrains. We introduce a highly accurate and robust method for computing ground reaction forces from motion capture data using Euler's integration scheme and PD algorithm. The physics-based reactive forces are used to inform the learning model about the physics-informed motion dynamics thus improving the estimation accuracy. The proposed approach was tested on the GroundLink dataset, outperforming the baseline model on: 1) the ground reaction force estimation accuracy compared to the force plates measurement; and 2) our simulated root trajectory precision. The implementation code is available at https://github.com/cuongle1206/Phys-GRD

Paperid: 47, https://arxiv.org/pdf/2506.23135.pdf GitHub

Abstract:
World models have become indispensable tools for embodied intelligence, serving as powerful simulators capable of generating realistic robotic videos while addressing critical data scarcity challenges. However, current embodied world models exhibit limited physical awareness, particularly in modeling 3D geometry and motion dynamics, resulting in unrealistic video generation for contact-rich robotic scenarios. In this paper, we present RoboScape, a unified physics-informed world model that jointly learns RGB video generation and physics knowledge within an integrated framework. We introduce two key physics-informed joint training tasks: temporal depth prediction that enhances 3D geometric consistency in video rendering, and keypoint dynamics learning that implicitly encodes physical properties (e.g., object shape and material characteristics) while improving complex motion modeling. Extensive experiments demonstrate that RoboScape generates videos with superior visual fidelity and physical plausibility across diverse robotic scenarios. We further validate its practical utility through downstream applications including robotic policy training with generated data and policy evaluation. Our work provides new insights for building efficient physics-informed world models to advance embodied intelligence research. The code is available at: https://github.com/tsinghua-fib-lab/RoboScape.

Paperid: 48, https://arxiv.org/pdf/2506.20343.pdf GitHub

Abstract:
Musculoskeletal humanoids are robots that closely mimic the human musculoskeletal system, offering various advantages such as variable stiffness control, redundancy, and flexibility. However, their body structure is complex, and muscle paths often significantly deviate from geometric models. To address this, numerous studies have been conducted to learn body schema, particularly the relationships among joint angles, muscle tension, and muscle length. These studies typically rely solely on data collected from the actual robot, but this data collection process is labor-intensive, and learning becomes difficult when the amount of data is limited. Therefore, in this study, we propose a method that applies the concept of Physics-Informed Neural Networks (PINNs) to the learning of body schema in musculoskeletal humanoids, enabling high-accuracy learning even with a small amount of data. By utilizing not only data obtained from the actual robot but also the physical laws governing the relationship between torque and muscle tension under the assumption of correct joint structure, more efficient learning becomes possible. We apply the proposed method to both simulation and an actual musculoskeletal humanoid and discuss its effectiveness and characteristics.

Paperid: 49, https://arxiv.org/pdf/2506.07902.pdf GitHub

Abstract:
Recent advances in generative modeling -- particularly diffusion models and flow matching -- have achieved remarkable success in synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. Here, we introduce $\textbf{FunDiff}$, a novel framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generate continuous functions evaluable at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, showing that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results show that our method generates physically consistent samples with high fidelity to the target distribution and exhibits robustness to noisy and low-resolution data. Code and datasets are publicly available at https://github.com/sifanexisted/fundiff.

Paperid: 50, https://arxiv.org/pdf/2506.06999.pdf GitHub

Abstract:
Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal activities in international waters, such as unauthorized fishing and illicit oil transfers. The problem is challenging due to advances in AI generated in deep fakes generation (e.g., additive noise, fake trajectories) and lack of adequate amount of labeled samples for ground-truth verification. Recent literature shows promising results for anomalous trajectory detection using generative models despite data sparsity. However, they do not consider fine-scale spatiotemporal dependencies and prior physical knowledge, resulting in higher false-positive rates. To address these limitations, we propose a physics-informed diffusion model that integrates kinematic constraints to identify trajectories that do not adhere to physical laws. Experimental results on real-world datasets in the maritime and urban domains show that the proposed framework results in higher prediction accuracy and lower estimation error rate for anomaly detection and trajectory generation methods, respectively. Our implementation is available at https://github.com/arunshar/Physics-Informed-Diffusion-Probabilistic-Model.

Paperid: 51, https://arxiv.org/pdf/2506.04753.pdf GitHub

Abstract:
We present a novel dual-stream architecture that achieves state-of-the-art underwater image enhancement by explicitly integrating the Jaffe-McGlamery physical model with capsule clustering-based feature representation learning. Our method simultaneously estimates transmission maps and spatially-varying background light through a dedicated physics estimator while extracting entity-level features via capsule clustering in a parallel stream. This physics-guided approach enables parameter-free enhancement that respects underwater formation constraints while preserving semantic structures and fine-grained details. Our approach also features a novel optimization objective ensuring both physical adherence and perceptual quality across multiple spatial frequencies. To validate our approach, we conducted extensive experiments across six challenging benchmarks. Results demonstrate consistent improvements of $+0.5$dB PSNR over the best existing methods while requiring only one-third of their computational complexity (FLOPs), or alternatively, more than $+1$dB PSNR improvement when compared to methods with similar computational budgets. Code and data \textit{will} be available at https://github.com/iN1k1/.

Paperid: 52, https://arxiv.org/pdf/2505.23863.pdf GitHub

Abstract:
Long-term forecasting of chaotic systems from short-term observations remains a fundamental and underexplored challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Existing approaches often rely on long-term training data or focus on short-term sequence correlations, struggling to maintain predictive stability and dynamical coherence over extended horizons. We propose PhyxMamba, a novel framework that integrates a Mamba-based state-space model with physics-informed principles to capture the underlying dynamics of chaotic systems. By reconstructing the attractor manifold from brief observations using time-delay embeddings, PhyxMamba extracts global dynamical features essential for accurate forecasting. Our generative training scheme enables Mamba to replicate the physical process, augmented by multi-token prediction and attractor geometry regularization for physical constraints, enhancing prediction accuracy and preserving key statistical invariants. Extensive evaluations on diverse simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior long-term forecasting and faithfully captures essential dynamical invariants from short-term data. This framework opens new avenues for reliably predicting chaotic systems under observation-scarce conditions, with broad implications across climate science, neuroscience, epidemiology, and beyond. Our code is open-source at https://github.com/tsinghua-fib-lab/PhyxMamba.

Paperid: 53, https://arxiv.org/pdf/2505.13921.pdf GitHub

Abstract:
Large Language Models (LLMs) demonstrate strong reasoning and task planning capabilities but remain fundamentally limited in physical interaction modeling. Existing approaches integrate perception via Vision-Language Models (VLMs) or adaptive decision-making through Reinforcement Learning (RL), but they fail to capture dynamic object interactions or require task-specific training, limiting their real-world applicability. We introduce APEX (Anticipatory Physics-Enhanced Execution), a framework that equips LLMs with physics-driven foresight for real-time task planning. APEX constructs structured graphs to identify and model the most relevant dynamic interactions in the environment, providing LLMs with explicit physical state updates. Simultaneously, APEX provides low-latency forward simulations of physically feasible actions, allowing LLMs to select optimal strategies based on predictive outcomes rather than static observations. We evaluate APEX on three benchmarks designed to assess perception, prediction, and decision-making: (1) Physics Reasoning Benchmark, testing causal inference and object motion prediction; (2) Tetris, evaluating whether physics-informed prediction enhances decision-making performance in long-horizon planning tasks; (3) Dynamic Obstacle Avoidance, assessing the immediate integration of perception and action feasibility analysis. APEX significantly outperforms standard LLMs and VLM-based models, demonstrating the necessity of explicit physics reasoning for bridging the gap between language-based intelligence and real-world task execution. The source code and experiment setup are publicly available at https://github.com/hwj20/APEX_EXP .

Paperid: 54, https://arxiv.org/pdf/2505.11117.pdf GitHub

Abstract:
Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs) into the loss function. Despite their successes, vanilla PINNs still suffer from poor accuracy and slow convergence due to the intractable multi-objective optimization issue. In this paper, we propose a novel Dual-Balanced PINN (DB-PINN), which dynamically adjusts loss weights by integrating inter-balancing and intra-balancing to alleviate two imbalance issues in PINNs. Inter-balancing aims to mitigate the gradient imbalance between PDE residual loss and condition-fitting losses by determining an aggregated weight that offsets their gradient distribution discrepancies. Intra-balancing acts on condition-fitting losses to tackle the imbalance in fitting difficulty across diverse conditions. By evaluating the fitting difficulty based on the loss records, intra-balancing can allocate the aggregated weight proportionally to each condition loss according to its fitting difficulty level. We further introduce a robust weight update strategy to prevent abrupt spikes and arithmetic overflow in instantaneous weight values caused by large loss variances, enabling smooth weight updating and stable training. Extensive experiments demonstrate that DB-PINN achieves significantly superior performance than those popular gradient-based weighting methods in terms of convergence speed and prediction accuracy. Our code and supplementary material are available at https://github.com/chenhong-zhou/DualBalanced-PINNs.

Paperid: 55, https://arxiv.org/pdf/2505.10930.pdf GitHub

Abstract:
Auto-regressive partial differential equation (PDE) foundation models have shown great potential in handling time-dependent data. However, these models suffer from the shortcut problem deeply rooted in auto-regressive prediction, causing error accumulation. The challenge becomes particularly evident for out-of-distribution data, as the pretraining performance may approach random model initialization for downstream tasks with long-term dynamics. To deal with this problem, we propose physics-informed temporal alignment (PITA), a self-supervised learning framework inspired by inverse problem solving. Specifically, PITA aligns the physical dynamics discovered at different time steps on each given PDE trajectory by integrating physics-informed constraints into the self-supervision signal. The alignment is derived from observation data without relying on known physics priors, indicating strong generalization ability to the out-of-distribution data. Extensive experiments show that PITA significantly enhances the accuracy and robustness of existing foundation models on diverse time-dependent PDE data. The code is available at https://github.com/SCAILab-USTC/PITA.

Paperid: 56, https://arxiv.org/pdf/2505.08740.pdf GitHub

Abstract:
Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle with inverse problems, sensitivity estimation (du/dp), and concept drift. We address these limitations by introducing a sensitivity-based regularization strategy, called Sensitivity-Constrained Fourier Neural Operators (SC-FNO). SC-FNO achieves high accuracy in predicting solution paths and consistently outperforms standard FNO and FNO with physics-informed regularization. It improves performance in parameter inversion tasks, scales to high-dimensional parameter spaces (tested with up to 82 parameters), and reduces both data and training requirements. These gains are achieved with a modest increase in training time (30% to 130% per epoch) and generalize across various types of differential equations and neural operators. Code and selected experiments are available at: https://github.com/AMBehroozi/SC_Neural_Operators

Paperid: 57, https://arxiv.org/pdf/2504.17771.pdf GitHub GitHub

Abstract:
Learning-based methods, such as imitation learning (IL) and reinforcement learning (RL), can produce excel control policies over challenging agile robot tasks, such as sports robot. However, no existing work has harmonized learning-based policy with model-based methods to reduce training complexity and ensure the safety and stability for agile badminton robot control. In this paper, we introduce Hamlet, a novel hybrid control system for agile badminton robots. Specifically, we propose a model-based strategy for chassis locomotion which provides a base for arm policy. We introduce a physics-informed "IL+RL" training framework for learning-based arm policy. In this train framework, a model-based strategy with privileged information is used to guide arm policy training during both IL and RL phases. In addition, we train the critic model during IL phase to alleviate the performance drop issue when transitioning from IL to RL. We present results on our self-engineered badminton robot, achieving 94.5% success rate against the serving machine and 90.7% success rate against human players. Our system can be easily generalized to other agile mobile manipulation tasks such as agile catching and table tennis. Our project website: https://dreamstarring.github.io/HAMLET/.

Paperid: 58, https://arxiv.org/pdf/2504.16172.pdf GitHub

Abstract:
High-dimensional partial differential equations (PDEs) pose significant computational challenges across fields ranging from quantum chemistry to economics and finance. Although scientific machine learning (SciML) techniques offer approximate solutions, they often suffer from bias and neglect crucial physical insights. Inspired by inference-time scaling strategies in language models, we propose Simulation-Calibrated Scientific Machine Learning (SCaSML), a physics-informed framework that dynamically refines and debiases the SCiML predictions during inference by enforcing the physical laws. SCaSML leverages derived new physical laws that quantifies systematic errors and employs Monte Carlo solvers based on the Feynman-Kac and Elworthy-Bismut-Li formulas to dynamically correct the prediction. Both numerical and theoretical analysis confirms enhanced convergence rates via compute-optimal inference methods. Our numerical experiments demonstrate that SCaSML reduces errors by 20-50% compared to the base surrogate model, establishing it as the first algorithm to refine approximated solutions to high-dimensional PDE during inference. Code of SCaSML is available at https://github.com/Francis-Fan-create/SCaSML.

Paperid: 59, https://arxiv.org/pdf/2504.12675.pdf GitHub

Abstract:
A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data scarsity and potentially high dimensionality. Existing PINN frameworks rely on fully observed time-course data, the acquisition of which could be prohibitive for many systems. In this study, we developed a new PINN learning paradigm, namely Constrained Learning, that enables the approximation of first-order derivatives or motions using non-time course or partially observed data. Computational principles and a general mathematical formulation of Constrained Learning were developed. We further introduced MPOCtrL (Message Passing Optimization-based Constrained Learning) an optimization approach tailored for the Constrained Learning framework that strives to balance the fitting of physical models and observed data. Its code is available at github link: https://github.com/ptdang1001/MPOCtrL Experiments on synthetic and real-world data demonstrated that MPOCtrL can effectively detect the nonlinear dependency between observed data and the underlying physical properties of the system. In particular, on the task of metabolic flux analysis, MPOCtrL outperforms all existing data-driven flux estimators.

Paperid: 60, https://arxiv.org/pdf/2504.07976.pdf GitHub

Abstract:
Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, e.g., uncertainty quantification, remeshing applications, topology optimization, and so forth. This limitation has motivated the application of data-driven surrogate models, where the microscale computations are $\textit{substituted}$ with a surrogate, usually acting as a black-box mapping between macroscale quantities. These models offer significant speedups but struggle with incorporating microscale physical constraints, such as the balance of linear momentum and constitutive models. In this contribution, we propose Equilibrium Neural Operator (EquiNO) as a $\textit{complementary}$ physics-informed PDE surrogate for predicting microscale physics and compare it with variational physics-informed neural and operator networks. Our framework, applicable to the so-called multiscale FE$^{\,2}\,$ computations, introduces the FE-OL approach by integrating the finite element (FE) method with operator learning (OL). We apply the proposed FE-OL approach to quasi-static problems of solid mechanics. The results demonstrate that FE-OL can yield accurate solutions even when confronted with a restricted dataset during model development. Our results show that EquiNO achieves speedup factors exceeding 8000-fold compared to traditional methods and offers an optimal balance between data-driven and physics-based strategies.

Paperid: 61, https://arxiv.org/pdf/2504.05830.pdf GitHub

Abstract:
Human Activity Recognition (HAR) primarily relied on traditional RGB cameras to achieve high-performance activity recognition. However, the challenging factors in real-world scenarios, such as insufficient lighting and rapid movements, inevitably degrade the performance of RGB cameras. To address these challenges, biologically inspired event cameras offer a promising solution to overcome the limitations of traditional RGB cameras. In this work, we rethink human activity recognition by combining the RGB and event cameras. The first contribution is the proposed large-scale multi-modal RGB-Event human activity recognition benchmark dataset, termed HARDVS 2.0, which bridges the dataset gaps. It contains 300 categories of everyday real-world actions with a total of 107,646 paired videos covering various challenging scenarios. Inspired by the physics-informed heat conduction model, we propose a novel multi-modal heat conduction operation framework for effective activity recognition, termed MMHCO-HAR. More in detail, given the RGB frames and event streams, we first extract the feature embeddings using a stem network. Then, multi-modal Heat Conduction blocks are designed to fuse the dual features, the key module of which is the multi-modal Heat Conduction Operation layer. We integrate RGB and event embeddings through a multi-modal DCT-IDCT layer while adaptively incorporating the thermal conductivity coefficient via FVEs into this module. After that, we propose an adaptive fusion module based on a policy routing strategy for high-performance classification. Comprehensive experiments demonstrate that our method consistently performs well, validating its effectiveness and robustness. The source code and benchmark dataset will be released on https://github.com/Event-AHU/HARDVS/tree/HARDVSv2

Paperid: 62, https://arxiv.org/pdf/2503.23167.pdf GitHub

Abstract:
Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while differential equations provide a principled framework for modeling continuous dynamics across time and space. The intersection of these fields has led to innovative approaches that leverage the strengths of both, enabling applications in physics-informed learning, spatiotemporal modeling, and scientific computing. This survey aims to provide a comprehensive overview of the burgeoning research at the intersection of GNNs and DEs. We will categorize existing methods, discuss their underlying principles, and highlight their applications across domains such as molecular modeling, traffic prediction, and epidemic spreading. Furthermore, we identify open challenges and outline future research directions to advance this interdisciplinary field. A comprehensive paper list is provided at https://github.com/Emory-Melody/Awesome-Graph-NDEs. This survey serves as a resource for researchers and practitioners seeking to understand and contribute to the fusion of GNNs and DEs

Paperid: 63, https://arxiv.org/pdf/2503.17973.pdf GitHub

Abstract:
Creating a physical digital twin of a real-world object has immense potential in robotics, content creation, and XR. In this paper, we present PhysTwin, a novel framework that uses sparse videos of dynamic objects under interaction to produce a photo- and physically realistic, real-time interactive virtual replica. Our approach centers on two key components: (1) a physics-informed representation that combines spring-mass models for realistic physical simulation, generative shape models for geometry, and Gaussian splats for rendering; and (2) a novel multi-stage, optimization-based inverse modeling framework that reconstructs complete geometry, infers dense physical properties, and replicates realistic appearance from videos. Our method integrates an inverse physics framework with visual perception cues, enabling high-fidelity reconstruction even from partial, occluded, and limited viewpoints. PhysTwin supports modeling various deformable objects, including ropes, stuffed animals, cloth, and delivery packages. Experiments show that PhysTwin outperforms competing methods in reconstruction, rendering, future prediction, and simulation under novel interactions. We further demonstrate its applications in interactive real-time simulation and model-based robotic motion planning.

Paperid: 64, https://arxiv.org/pdf/2503.08929.pdf GitHub GitHub

Abstract:
Accurate and efficient 3D mapping of large-scale outdoor environments from LiDAR measurements is a fundamental challenge in robotics, particularly towards ensuring smooth and artifact-free surface reconstructions. Although the state-of-the-art methods focus on memory-efficient neural representations for high-fidelity surface generation, they often fail to produce artifact-free manifolds, with artifacts arising due to noisy and sparse inputs. To address this issue, we frame surface mapping as a physics-informed energy optimization problem, enforcing surface smoothness by optimizing an energy functional that penalizes sharp surface ridges. Specifically, we propose a deep learning based approach that learns the signed distance field (SDF) of the surface manifold from raw LiDAR point clouds using a physics-informed loss function that optimizes the $L_2$-Hessian energy of the surface. Our learning framework includes a hierarchical octree based input feature encoding and a multi-scale neural network to iteratively refine the signed distance field at different scales of resolution. Lastly, we introduce a test-time refinement strategy to correct topological inconsistencies and edge distortions that can arise in the generated mesh. We propose a \texttt{CUDA}-accelerated least-squares optimization that locally adjusts vertex positions to enforce feature-preserving smoothing. We evaluate our approach on large-scale outdoor datasets and demonstrate that our approach outperforms current state-of-the-art methods in terms of improved accuracy and smoothness. Our code is available at \href{https://github.com/HrishikeshVish/HessianForge/}{https://github.com/HrishikeshVish/HessianForge/}

Paperid: 65, https://arxiv.org/pdf/2503.08121.pdf GitHub

Abstract:
We introduce AG-VPReID, a new large-scale dataset for aerial-ground video-based person re-identification (ReID) that comprises 6,632 subjects, 32,321 tracklets and over 9.6 million frames captured by drones (altitudes ranging from 15-120m), CCTV, and wearable cameras. This dataset offers a real-world benchmark for evaluating the robustness to significant viewpoint changes, scale variations, and resolution differences in cross-platform aerial-ground settings. In addition, to address these challenges, we propose AG-VPReID-Net, an end-to-end framework composed of three complementary streams: (1) an Adapted Temporal-Spatial Stream addressing motion pattern inconsistencies and facilitating temporal feature learning, (2) a Normalized Appearance Stream leveraging physics-informed techniques to tackle resolution and appearance changes, and (3) a Multi-Scale Attention Stream handling scale variations across drone altitudes. We integrate visual-semantic cues from all streams to form a robust, viewpoint-invariant whole-body representation. Extensive experiments demonstrate that AG-VPReID-Net outperforms state-of-the-art approaches on both our new dataset and existing video-based ReID benchmarks, showcasing its effectiveness and generalizability. Nevertheless, the performance gap observed on AG-VPReID across all methods underscores the dataset's challenging nature. The dataset, code and trained models are available at https://github.com/agvpreid25/AG-VPReID-Net.

Paperid: 66, https://arxiv.org/pdf/2502.19290.pdf GitHub GitHub

Abstract:
Time-dependent partial differential equations are a significant class of equations that describe the evolution of various physical phenomena over time. One of the open problems in scientific computing is predicting the behaviour of the solution outside the given temporal region. Most traditional numerical methods are applied to a given time-space region and can only accurately approximate the solution of the given region. To address this problem, many deep learning-based methods, basically data-driven and data-free approaches, have been developed to solve these problems. However, most data-driven methods require a large amount of data, which consumes significant computational resources and fails to utilize all the necessary information embedded underlying the partial differential equations (PDEs). Moreover, data-free approaches such as Physics-Informed Neural Networks (PINNs) may not be that ideal in practice, as traditional PINNs, which primarily rely on multilayer perceptrons (MLPs) and convolutional neural networks (CNNs), tend to overlook the crucial temporal dependencies inherent in real-world physical systems. We propose a method denoted as \textbf{PhysicsSolver} that merges the strengths of two approaches: data-free methods that can learn the intrinsic properties of physical systems without using data, and data-driven methods, which are effective at making predictions. Extensive numerical experiments have demonstrated the efficiency and robustness of our proposed method. We provide the code at \href{https://github.com/PhysicsSolver/PhysicsSolver}{https://github.com/PhysicsSolver}.

Paperid: 67, https://arxiv.org/pdf/2502.17497.pdf GitHub

Abstract:
This paper develops a novel deep learning approach for solving evolutionary equations, which integrates sequential learning strategies with an enhanced hard constraint strategy featuring trainable parameters, addressing the low computational accuracy of standard Physics-Informed Neural Networks (PINNs) in large temporal domains.Sequential learning strategies divide a large temporal domain into multiple subintervals and solve them one by one in a chronological order, which naturally respects the principle of causality and improves the stability of the PINN solution. The improved hard constraint strategy strictly ensures the continuity and smoothness of the PINN solution at time interval nodes, and at the same time passes the information from the previous interval to the next interval, which avoids the incorrect/trivial solution at the position far from the initial time. Furthermore, by investigating the requirements of different types of equations on hard constraints, we design a novel influence function with trainable parameters for hard constraints, which provides theoretical and technical support for the effective implementations of hard constraint strategies, and significantly improves the universality and computational accuracy of our method. In addition, an adaptive time-domain partitioning algorithm is proposed, which plays an important role in the application of the proposed method as well as in the improvement of computational efficiency and accuracy. Numerical experiments verify the performance of the method. The data and code accompanying this paper are available at https://github.com/zhizhi4452/HCS.

Paperid: 68, https://arxiv.org/pdf/2502.09296.pdf GitHub

Abstract:
Background: MRI is crucial for brain imaging but is highly susceptible to motion artifacts due to long acquisition times. This study introduces PI-MoCoNet, a physics-informed motion correction network that integrates spatial and k-space information to remove motion artifacts without explicit motion parameter estimation, enhancing image fidelity and diagnostic reliability. Materials and Methods: PI-MoCoNet consists of a motion detection network (U-net with spatial averaging) to identify corrupted k-space lines and a motion correction network (U-net with Swin Transformer blocks) to reconstruct motion-free images. The correction is guided by three loss functions: reconstruction (L1), perceptual (LPIPS), and data consistency (Ldc). Motion artifacts were simulated via rigid phase encoding perturbations and evaluated on IXI and MR-ART datasets against Pix2Pix, CycleGAN, and U-net using PSNR, SSIM, and NMSE. Results: PI-MoCoNet significantly improved image quality. On IXI, for minor artifacts, PSNR increased from 34.15 dB to 45.95 dB, SSIM from 0.87 to 1.00, and NMSE reduced from 0.55% to 0.04%. For moderate artifacts, PSNR improved from 30.23 dB to 42.16 dB, SSIM from 0.80 to 0.99, and NMSE from 1.32% to 0.09%. For heavy artifacts, PSNR rose from 27.99 dB to 36.01 dB, SSIM from 0.75 to 0.97, and NMSE decreased from 2.21% to 0.36%. On MR-ART, PI-MoCoNet achieved PSNR gains of ~10 dB and SSIM improvements of up to 0.20, with NMSE reductions of ~6%. Ablation studies confirmed the importance of data consistency and perceptual losses, yielding a 1 dB PSNR gain and 0.17% NMSE reduction. Conclusions: PI-MoCoNet effectively mitigates motion artifacts in brain MRI, outperforming existing methods. Its ability to integrate spatial and k-space information makes it a promising tool for clinical use in motion-prone settings. Code: https://github.com/mosaf/PI-MoCoNet.git.

Paperid: 69, https://arxiv.org/pdf/2502.04018.pdf GitHub

Abstract:
This paper introduces PINT (Physics-Informed Neural Time Series Models), a framework that integrates physical constraints into neural time series models to improve their ability to capture complex dynamics. We apply PINT to the ERA5 WeatherBench dataset, focusing on long-term forecasting of 2m-temperature data. PINT incorporates the Simple Harmonic Oscillator Equation as a physics-informed prior, embedding its periodic dynamics into RNN, LSTM, and GRU architectures. This equation's analytical solutions (sine and cosine functions) facilitate rigorous evaluation of the benefits of incorporating physics-informed constraints. By benchmarking against a linear regression baseline derived from its exact solutions, we quantify the impact of embedding physical principles in data-driven models. Unlike traditional time series models that rely on future observations, PINT is designed for practical forecasting. Using only the first 90 days of observed data, it iteratively predicts the next two years, addressing challenges posed by limited real-time updates. Experiments on the WeatherBench dataset demonstrate PINT's ability to generalize, capture periodic trends, and align with physical principles. This study highlights the potential of physics-informed neural models in bridging machine learning and interpretable climate applications. Our models and datasets are publicly available on GitHub: https://github.com/KV-Park.

Paperid: 70, https://arxiv.org/pdf/2502.00318.pdf GitHub

Abstract:
Physics-Informed Neural Networks (PINNs) are a kind of deep-learning-based numerical solvers for partial differential equations (PDEs). Existing PINNs often suffer from failure modes of being unable to propagate patterns of initial conditions. We discover that these failure modes are caused by the simplicity bias of neural networks and the mismatch between PDE's continuity and PINN's discrete sampling. We reveal that the State Space Model (SSM) can be a continuous-discrete articulation allowing initial condition propagation, and that simplicity bias can be eliminated by aligning a sequence of moderate granularity. Accordingly, we propose PINNMamba, a novel framework that introduces sub-sequence modeling with SSM. Experimental results show that PINNMamba can reduce errors by up to 86.3\% compared with state-of-the-art architecture. Our code is available at https://github.com/miniHuiHui/PINNMamba.

Paperid: 71, https://arxiv.org/pdf/2501.18582.pdf GitHub

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for integrating physics-based models with data by minimizing both data and physics losses. However, this multi-objective optimization problem is notoriously challenging, with some benchmark problems leading to unfeasible solutions. To address these issues, various strategies have been proposed, including adaptive weight adjustments in the loss function. In this work, we introduce clear definitions of accuracy and robustness in the context of PINNs and propose a novel training algorithm based on the Primal-Dual (PD) optimization framework. Our approach enhances the robustness of PINNs while maintaining comparable performance to existing weight-balancing methods. Numerical experiments demonstrate that the PD method consistently achieves reliable solutions across all investigated cases, even in the low-data regime, and can be easily implemented, facilitating its practical adoption. The code is available at https://github.com/haoming-SHEN/Accuracy-and-Robustness-of-Weight-Balancing-Methods-for-Training-PINNs.git.

Paperid: 72, https://arxiv.org/pdf/2501.06081.pdf GitHub

Abstract:
Deep learning methods - usually consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays omnipresent in data-driven learning problems as well as in scientific computing tasks such as optimal control (OC) and partial differential equation (PDE) problems. In practically relevant learning tasks, often not the plain-vanilla standard SGD optimization method is employed to train the considered class of DNNs but instead more sophisticated adaptive and accelerated variants of the standard SGD method such as the popular Adam optimizer are used. Inspired by the classical Polyak-Ruppert averaging approach, in this work we apply averaged variants of the Adam optimizer to train DNNs to approximately solve exemplary scientific computing problems in the form of PDEs and OC problems. We test the averaged variants of Adam in a series of learning problems including physics-informed neural network (PINN), deep backward stochastic differential equation (deep BSDE), and deep Kolmogorov approximations for PDEs (such as heat, Black-Scholes, Burgers, and Allen-Cahn PDEs), including DNN approximations for OC problems, and including DNN approximations for image classification problems (ResNet for CIFAR-10). In each of the numerical examples the employed averaged variants of Adam outperform the standard Adam and the standard SGD optimizers, particularly, in the situation of the scientific machine learning problems. The Python source codes for the numerical experiments associated to this work can be found on GitHub at https://github.com/deeplearningmethods/averaged-adam.

Paperid: 73, https://arxiv.org/pdf/2501.04366.pdf GitHub

Abstract:
Surface wave dispersion curve inversion is crucial for estimating subsurface shear-wave velocity (vs), yet traditional methods often face challenges related to computational cost, non-uniqueness, and sensitivity to initial models. While deep learning approaches show promise, many require large labeled datasets and struggle with real-world datasets, which often exhibit varying period ranges, missing values, and low signal-to-noise ratios. To address these limitations, this study introduces DispFormer, a transformer-based neural network for $v_s$ profile inversion from Rayleigh-wave phase and group dispersion curves. DispFormer processes dispersion data independently at each period, allowing it to handle varying lengths without requiring network modifications or strict alignment between training and testing datasets. A depth-aware training strategy is also introduced, incorporating physical constraints derived from the depth sensitivity of dispersion data. DispFormer is pre-trained on a global synthetic dataset and evaluated on two regional synthetic datasets using zero-shot and few-shot strategies. Results show that even without labeled data, the zero-shot DispFormer generates inversion profiles that outperform the interpolated reference model used as the pretraining target, providing a deployable initial model generator to assist traditional workflows. When partial labeled data available, the few-shot trained DispFormer surpasses traditional global search methods. Real-world tests further confirm that DispFormer generalizes well to dispersion data with varying lengths and achieves lower data residuals than reference models. These findings underscore the potential of DispFormer as a foundation model for dispersion curve inversion and demonstrate the advantages of integrating physics-informed deep learning into geophysical applications.

Paperid: 74, https://arxiv.org/pdf/2412.09752.pdf GitHub

Abstract:
The use of neural networks for solving differential equations is practically difficult due to the exponentially increasing runtime of autodifferentiation when computing high-order derivatives. We propose $n$-TangentProp, the natural extension of the TangentProp formalism \cite{simard1991tangent} to arbitrarily many derivatives. $n$-TangentProp computes the exact derivative $d^n/dx^n f(x)$ in quasilinear, instead of exponential time, for a densely connected, feed-forward neural network $f$ with a smooth, parameter-free activation function. We validate our algorithm empirically across a range of depths, widths, and number of derivatives. We demonstrate that our method is particularly beneficial in the context of physics-informed neural networks where \ntp allows for significantly faster training times than previous methods and has favorable scaling with respect to both model size and loss-function complexity as measured by the number of required derivatives. The code for this paper can be found at https://github.com/kyrochi/n\_tangentprop.

Paperid: 75, https://arxiv.org/pdf/2412.09009.pdf GitHub

Abstract:
Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a neural network to learn a map between infinite dimensional input and output function spaces. These neural operators are trained using a combination of data (observations or simulations) and PDE-residuals (physics-loss). A major drawback of existing neural approaches is the requirement to retrain with new initial/boundary conditions, and the necessity for a large amount of simulation data for training. We develop a physics-informed transformer neural operator (named PINTO) that efficiently generalizes to unseen initial and boundary conditions, trained in a simulation-free setting using only physics loss. The main innovation lies in our new iterative kernel integral operator units, implemented using cross-attention, to transform the PDE solution's domain points into an initial/boundary condition-aware representation vector, enabling efficient learning of the solution function for new scenarios. The PINTO architecture is applied to simulate the solutions of important equations used in engineering applications: advection, Burgers, and steady and unsteady Navier-Stokes equations (three flow scenarios). For these five test cases, we show that the relative errors during testing under challenging conditions of unseen initial/boundary conditions are only one-fifth to one-third of other leading physics informed operator learning methods. Moreover, our PINTO model is able to accurately solve the advection and Burgers equations at time steps that are not included in the training collocation points. The code is available at https://github.com/quest-lab-iisc/PINTO

Paperid: 76, https://arxiv.org/pdf/2412.05994.pdf GitHub

Abstract:
The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and flexibility in implementing various PDEs, PINNs often suffer from limited accuracy due to the spectral bias of Multi-Layer Perceptrons (MLPs), which struggle to effectively learn high-frequency and nonlinear components. Recently, parametric mesh representations in combination with neural networks have been investigated as a promising approach to eliminate the inductive bias of MLPs. However, they usually require high-resolution grids and a large number of collocation points to achieve high accuracy while avoiding overfitting. In addition, the fixed positions of the mesh parameters restrict their flexibility, making accurate approximation of complex PDEs challenging. To overcome these limitations, we propose Physics-Informed Gaussians (PIGs), which combine feature embeddings using Gaussian functions with a lightweight neural network. Our approach uses trainable parameters for the mean and variance of each Gaussian, allowing for dynamic adjustment of their positions and shapes during training. This adaptability enables our model to optimally approximate PDE solutions, unlike models with fixed parameter positions. Furthermore, the proposed approach maintains the same optimization framework used in PINNs, allowing us to benefit from their excellent properties. Experimental results show the competitive performance of our model across various PDEs, demonstrating its potential as a robust tool for solving complex PDEs. Our project page is available at https://namgyukang.github.io/Physics-Informed-Gaussians/

Paperid: 77, https://arxiv.org/pdf/2412.00994.pdf GitHub

Abstract:
Time series forecasting often demands a trade-off between accuracy and efficiency. While recent Transformer models have improved forecasting capabilities, they come with high computational costs. Linear-based models have shown better accuracy than Transformers but still fall short of ideal performance. We propose PIAD-SRNN, a physics-informed adaptive decomposition state-space RNN, that separates seasonal and trend components and embeds domain equations in a recurrent framework. We evaluate PIAD-SRNN's performance on indoor air quality datasets, focusing on CO2 concentration prediction across various forecasting horizons, and results demonstrate that it consistently outperforms SoTA models in both long-term and short-term time series forecasting, including transformer-based architectures, in terms of both MSE and MAE. Besides proposing PIAD-SRNN which balances accuracy with efficiency, this paper also provides four curated datasets. Code and data: https://github.com/ahmad-shirazi/DSSRNN

Paperid: 78, https://arxiv.org/pdf/2411.19632.pdf GitHub

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual determined for a set of collocation points. Previous work has shown that the number and distribution of these collocation points have a significant influence on the accuracy of the PINN solution. Therefore, the effective placement of these collocation points is an active area of research. Specifically, available adaptive collocation point sampling methods have been reported to scale poorly in terms of computational cost when applied to high-dimensional problems. In this work, we address this issue and present the Point Adaptive Collocation Method for Artificial Neural Networks (PACMANN). PACMANN incrementally moves collocation points toward regions of higher residuals using gradient-based optimization algorithms guided by the gradient of the PINN loss function, that is, the squared PDE residual. We apply PACMANN for forward and inverse problems, and demonstrate that this method matches the performance of state-of-the-art methods in terms of the accuracy/efficiency tradeoff for the low-dimensional problems, while outperforming available approaches for high-dimensional problems. Key features of the method include its low computational cost and simplicity of integration into existing physics-informed neural network pipelines. The code is available at https://github.com/CoenVisser/PACMANN.

Paperid: 79, https://arxiv.org/pdf/2411.16663.pdf GitHub GitHub

Abstract:
Solving systems of partial differential equations (PDEs) is a fundamental task in computational science, traditionally addressed by numerical solvers. Recent advancements have introduced neural operators and physics-informed neural networks (PINNs) to tackle PDEs, achieving reduced computational costs at the expense of solution quality and accuracy. Gaussian processes (GPs) have also been applied to linear PDEs, with the advantage of always yielding precise solutions. In this work, we propose Boundary Ehrenpreis-Palamodov Gaussian Processes (B-EPGPs), a novel framework for constructing GP priors that satisfy both general systems of linear PDEs with constant coefficients and linear boundary conditions. We explicitly construct GP priors for representative PDE systems with practical boundary conditions. Formal proofs of correctness are provided and empirical results demonstrating significant accuracy improvements over state-of-the-art neural operator approaches.

Paperid: 80, https://arxiv.org/pdf/2411.08378.pdf GitHub

Abstract:
Diffusion models have recently emerged as a potent tool in generative modeling. However, their inherent iterative nature often results in sluggish image generation due to the requirement for multiple model evaluations. Recent progress has unveiled the intrinsic link between diffusion models and Probability Flow Ordinary Differential Equations (ODEs), thus enabling us to conceptualize diffusion models as ODE systems. Simultaneously, Physics Informed Neural Networks (PINNs) have substantiated their effectiveness in solving intricate differential equations through implicit modeling of their solutions. Building upon these foundational insights, we introduce Physics Informed Distillation (PID), which employs a student model to represent the solution of the ODE system corresponding to the teacher diffusion model, akin to the principles employed in PINNs. Through experiments on CIFAR 10 and ImageNet 64x64, we observe that PID achieves performance comparable to recent distillation methods. Notably, it demonstrates predictable trends concerning method-specific hyperparameters and eliminates the need for synthetic dataset generation during the distillation process. Both of which contribute to its easy-to-use nature as a distillation approach for Diffusion Models. Our code and pre-trained checkpoint are publicly available at: https://github.com/pantheon5100/pid_diffusion.git.

Paperid: 81, https://arxiv.org/pdf/2411.05867.pdf GitHub

Abstract:
Surrogate modeling of non-linear oscillator networks remains challenging due to discrepancies between simplified analytical models and real-world complexity. To bridge this gap, we investigate hybrid reservoir computing, combining reservoir computing with "expert" analytical models. Simulating the absence of an exact model, we first test the surrogate models with parameter errors in their expert model. Second, in a residual physics task, we assess their performance when their expert model lacks key non-linear coupling terms present in an extended ground-truth model. We focus on short-term forecasting across diverse dynamical regimes, evaluating the use of these surrogates for control applications. We show that hybrid reservoir computers generally outperform standard reservoir computers and exhibit greater robustness to parameter tuning. This advantage is less pronounced in the residual physics task. Notably, unlike standard reservoir computers, the performance of the hybrid does not degrade when crossing an observed spectral radius threshold. Furthermore, there is good performance for dynamical regimes not accessible to the expert model, demonstrating the contribution of the reservoir.

Paperid: 82, https://arxiv.org/pdf/2411.03671.pdf GitHub

Abstract:
Numerical methods for contact mechanics are of great importance in engineering applications, enabling the prediction and analysis of complex surface interactions under various conditions. In this work, we propose an energy-based physics-informed neural network (PINNs) framework for solving frictionless contact problems under large deformation. Inspired by microscopic Lennard-Jones potential, a surface contact energy is used to describe the contact phenomena. To ensure the robustness of the proposed PINN framework, relaxation, gradual loading and output scaling techniques are introduced. In the numerical examples, the well-known Hertz contact benchmark problem is conducted, demonstrating the effectiveness and robustness of the proposed PINNs framework. Moreover, challenging contact problems with the consideration of geometrical and material nonlinearities are tested. It has been shown that the proposed PINNs framework provides a reliable and powerful tool for nonlinear contact mechanics. More importantly, the proposed PINNs framework exhibits competitive computational efficiency to the commercial FEM software when dealing with those complex contact problems. The codes used in this manuscript are available at https://github.com/JinshuaiBai/energy_PINN_Contact.(The code will be available after acceptance)

Paperid: 83, https://arxiv.org/pdf/2410.19759.pdf GitHub

Abstract:
Arterial spin labeling (ASL) magnetic resonance imaging (MRI) enables cerebral perfusion measurement, which is crucial in detecting and managing neurological issues in infants born prematurely or after perinatal complications. However, cerebral blood flow (CBF) estimation in infants using ASL remains challenging due to the complex interplay of network physiology, involving dynamic interactions between cardiac output and cerebral perfusion, as well as issues with parameter uncertainty and data noise. We propose a new spatial uncertainty-based physics-informed neural network (PINN), SUPINN, to estimate CBF and other parameters from infant ASL data. SUPINN employs a multi-branch architecture to concurrently estimate regional and global model parameters across multiple voxels. It computes regional spatial uncertainties to weigh the signal. SUPINN can reliably estimate CBF (relative error $-0.3 \pm 71.7$), bolus arrival time (AT) ($30.5 \pm 257.8$), and blood longitudinal relaxation time ($T_{1b}$) ($-4.4 \pm 28.9$), surpassing parameter estimates performed using least squares or standard PINNs. Furthermore, SUPINN produces physiologically plausible spatially smooth CBF and AT maps. Our study demonstrates the successful modification of PINNs for accurate multi-parameter perfusion estimation from noisy and limited ASL data in infants. Frameworks like SUPINN have the potential to advance our understanding of the complex cardio-brain network physiology, aiding in the detection and management of diseases. Source code is provided at: https://github.com/cgalaz01/supinn.

Paperid: 84, https://arxiv.org/pdf/2410.18153.pdf GitHub GitHub

Abstract:
We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its unrealistic computational costs and has been a long standing problem over decades. Thus, numerical approximations of FDEs have been developed, but they often oversimplify the solutions. To tackle these two issues, we propose a hybrid approach combining physics-informed neural networks (PINNs) with the \textit{cylindrical approximation}. The cylindrical approximation expands functions and functional derivatives with an orthonormal basis and transforms FDEs into high-dimensional PDEs. To validate the reliability of the cylindrical approximation for FDE applications, we prove the convergence theorems of approximated functional derivatives and solutions. Then, the derived high-dimensional PDEs are numerically solved with PINNs. Through the capabilities of PINNs, our approach can handle a broader class of functional derivatives more efficiently than conventional discretization-based methods, improving the scalability of the cylindrical approximation. As a proof of concept, we conduct experiments on two FDEs and demonstrate that our model can successfully achieve typical $L^1$ relative error orders of PINNs $\sim 10^{-3}$. Overall, our work provides a strong backbone for physicists, mathematicians, and machine learning experts to analyze previously challenging FDEs, thereby democratizing their numerical analysis, which has received limited attention. Code is available at \url{https://github.com/TaikiMiyagawa/FunctionalPINN}.

Paperid: 85, https://arxiv.org/pdf/2410.15957.pdf GitHub

Abstract:
Recent advancements have integrated camera pose as a user-friendly and physics-informed condition in video diffusion models, enabling precise camera control. In this paper, we identify one of the key challenges as effectively modeling noisy cross-frame interactions to enhance geometry consistency and camera controllability. We innovatively associate the quality of a condition with its ability to reduce uncertainty and interpret noisy cross-frame features as a form of noisy condition. Recognizing that noisy conditions provide deterministic information while also introducing randomness and potential misguidance due to added noise, we propose applying epipolar attention to only aggregate features along corresponding epipolar lines, thereby accessing an optimal amount of noisy conditions. Additionally, we address scenarios where epipolar lines disappear, commonly caused by rapid camera movements, dynamic objects, or occlusions, ensuring robust performance in diverse environments. Furthermore, we develop a more robust and reproducible evaluation pipeline to address the inaccuracies and instabilities of existing camera control metrics. Our method achieves a 25.64% improvement in camera controllability on the RealEstate10K dataset without compromising dynamics or generation quality and demonstrates strong generalization to out-of-domain images. Training and inference require only 24GB and 12GB of memory, respectively, for 16-frame sequences at 256x256 resolution. We will release all checkpoints, along with training and evaluation code. Dynamic videos are best viewed at https://zgctroy.github.io/CamI2V.

Paperid: 86, https://arxiv.org/pdf/2410.12805.pdf GitHub

Abstract:
Motion Planning (MP) is a critical challenge in robotics, especially pertinent with the burgeoning interest in embodied artificial intelligence. Traditional MP methods often struggle with high-dimensional complexities. Recently neural motion planners, particularly physics-informed neural planners based on the Eikonal equation, have been proposed to overcome the curse of dimensionality. However, these methods perform poorly in complex scenarios with shaped robots due to multiple solutions inherent in the Eikonal equation. To address these issues, this paper presents PC-Planner, a novel physics-constrained self-supervised learning framework for robot motion planning with various shapes in complex environments. To this end, we propose several physical constraints, including monotonic and optimal constraints, to stabilize the training process of the neural network with the Eikonal equation. Additionally, we introduce a novel shape-aware distance field that considers the robot's shape for efficient collision checking and Ground Truth (GT) speed computation. This field reduces the computational intensity, and facilitates adaptive motion planning at test time. Experiments in diverse scenarios with different robots demonstrate the superiority of the proposed method in efficiency and robustness for robot motion planning, particularly in complex environments.

Paperid: 87, https://arxiv.org/pdf/2410.09883.pdf GitHub

Abstract:
Mapping and motion planning are two essential elements of robot intelligence that are interdependent in generating environment maps and navigating around obstacles. The existing mapping methods create maps that require computationally expensive motion planning tools to find a path solution. In this paper, we propose a new mapping feature called arrival time fields, which is a solution to the Eikonal equation. The arrival time fields can directly guide the robot in navigating the given environments. Therefore, this paper introduces a new approach called Active Neural Time Fields (Active NTFields), which is a physics-informed neural framework that actively explores the unknown environment and maps its arrival time field on the fly for robot motion planning. Our method does not require any expert data for learning and uses neural networks to directly solve the Eikonal equation for arrival time field mapping and motion planning. We benchmark our approach against state-of-the-art mapping and motion planning methods and demonstrate its superior performance in both simulated and real-world environments with a differential drive robot and a 6 degrees-of-freedom (DOF) robot manipulator. The supplementary videos can be found at https://youtu.be/qTPL5a6pRKk, and the implementation code repository is available at https://github.com/Rtlyc/antfields-demo.

Paperid: 88, https://arxiv.org/pdf/2410.06820.pdf GitHub

Abstract:
Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable training. These challenges arise particularly from the ill-conditioning of the optimization problem caused by the differential terms in the loss function. To address these issues, we propose learning a solver, i.e., solving PDEs using a physics-informed iterative algorithm trained on data. Our method learns to condition a gradient descent algorithm that automatically adapts to each PDE instance, significantly accelerating and stabilizing the optimization process and enabling faster convergence of physics-aware models. Furthermore, while traditional physics-informed methods solve for a single PDE instance, our approach extends to parametric PDEs. Specifically, we integrate the physical loss gradient with PDE parameters, allowing our method to solve over a distribution of PDE parameters, including coefficients, initial conditions, and boundary conditions. We demonstrate the effectiveness of our approach through empirical experiments on multiple datasets, comparing both training and test-time optimization performance. The code is available at https://github.com/2ailesB/neural-parametric-solver.

Paperid: 89, https://arxiv.org/pdf/2410.02242.pdf GitHub

Abstract:
As a neural network's depth increases, it can improve generalization performance. However, training deep networks is challenging due to gradient and signal propagation issues. To address these challenges, extensive theoretical research and various methods have been introduced. Despite these advances, effective weight initialization methods for tanh neural networks remain insufficiently investigated. This paper presents a novel weight initialization method for neural networks with tanh activation function. Based on an analysis of the fixed points of the function $\tanh(ax)$, the proposed method aims to determine values of $a$ that mitigate activation saturation. A series of experiments on various classification datasets and physics-informed neural networks demonstrates that the proposed method outperforms Xavier initialization methods~(with or without normalization) in terms of robustness across different network sizes, data efficiency, and convergence speed. Code is available at https://github.com/1HyunwooLee/Tanh-Init

Paperid: 90, https://arxiv.org/pdf/2409.14248.pdf GitHub

Abstract:
Finding solutions to partial differential equations (PDEs) is an important and essential component in many scientific and engineering discoveries. One of the common approaches empowered by deep learning is Physics-informed Neural Networks (PINNs). Recently, a new type of fundamental neural network model, Kolmogorov-Arnold Networks (KANs), has been proposed as a substitute of Multilayer Perceptions (MLPs), and possesses trainable activation functions. To enhance KANs in fitting accuracy, a modification of KANs, so called ReLU-KANs, using "square of ReLU" as the basis of its activation functions, has been suggested. In this work, we propose another basis of activation functions, namely, Higherorder-ReLU (HR), which is simpler than the basis of activation functions used in KANs, namely, Bsplines; allows efficient KAN matrix operations; and possesses smooth and non-zero higher-order derivatives, essential to physicsinformed neural networks. We name such KANs with Higher-order-ReLU (HR) as their activations, HRKANs. Our detailed experiments on two famous and representative PDEs, namely, the linear Poisson equation and nonlinear Burgers' equation with viscosity, reveal that our proposed Higher-order-ReLU-KANs (HRKANs) achieve the highest fitting accuracy and training robustness and lowest training time significantly among KANs, ReLU-KANs and HRKANs. The codes to replicate our experiments are available at https://github.com/kelvinhkcs/HRKAN.

Paperid: 91, https://arxiv.org/pdf/2409.13532.pdf GitHub

Abstract:
Recent advances in generative models for medical imaging have shown promise in representing multiple modalities. However, the variability in modality availability across datasets limits the general applicability of the synthetic data they produce. To address this, we present a novel physics-informed generative model capable of synthesizing a variable number of brain MRI modalities, including those not present in the original dataset. Our approach utilizes latent diffusion models and a two-step generative process: first, unobserved physical tissue property maps are synthesized using a latent diffusion model, and then these maps are combined with a physical signal model to generate the final MRI scan. Our experiments demonstrate the efficacy of this approach in generating unseen MR contrasts and preserving physical plausibility. Furthermore, we validate the distributions of generated tissue properties by comparing them to those measured in real brain tissue.

Paperid: 92, https://arxiv.org/pdf/2409.08958.pdf GitHub

Abstract:
Recently, physics-informed neural networks (PINNs) have emerged as a flexible and promising application of deep learning to partial differential equations in the physical sciences. While offering strong performance and competitive inference speeds on forward and inverse problems, their black-box nature limits interpretability, particularly regarding alignment with expected physical behavior. In the present work, we explore the application of influence functions (IFs) to validate and debug PINNs post-hoc. Specifically, we apply variations of IF-based indicators to gauge the influence of different types of collocation points on the prediction of PINNs applied to a 2D Navier-Stokes fluid flow problem. Our results demonstrate how IFs can be adapted to PINNs to reveal the potential for further studies. The code is publicly available at https://github.com/aleks-krasowski/PINNfluence.

Paperid: 93, https://arxiv.org/pdf/2409.03231.pdf GitHub

Abstract:
Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions. However, existing models, including recurrent neural networks (RNNs), transformers, and neural operators, face challenges such as long-time integration, long-range dependencies, chaotic dynamics, and extrapolation, to name a few. To this end, this paper introduces state-space models implemented in Mamba for accurate and efficient dynamical system operator learning. Mamba addresses the limitations of existing architectures by dynamically capturing long-range dependencies and enhancing computational efficiency through reparameterization techniques. To extensively test Mamba and compare against another 11 baselines, we introduce several strict extrapolation testbeds that go beyond the standard interpolation benchmarks. We demonstrate Mamba's superior performance in both interpolation and challenging extrapolation tasks. Mamba consistently ranks among the top models while maintaining the lowest computational cost and exceptional extrapolation capabilities. Moreover, we demonstrate the good performance of Mamba for a real-world application in quantitative systems pharmacology for assessing the efficacy of drugs in tumor growth under limited data scenarios. Taken together, our findings highlight Mamba's potential as a powerful tool for advancing scientific machine learning in dynamical systems modeling. (The code will be available at https://github.com/zheyuanhu01/State_Space_Model_Neural_Operator upon acceptance.)

Paperid: 94, https://arxiv.org/pdf/2409.01899.pdf GitHub

Abstract:
This paper introduces an efficient tensor-vector product technique for the rapid and accurate approximation of integral operators within physics-informed deep learning frameworks. Our approach leverages neural network architectures to evaluate problem dynamics at specific points, while employing Gaussian quadrature formulas to approximate the integral components, even in the presence of infinite domains or singularities. We demonstrate the applicability of this method to both Fredholm and Volterra integral operators, as well as to optimal control problems involving continuous time. Additionally, we outline how this approach can be extended to approximate fractional derivatives and integrals and propose a fast matrix-vector product algorithm for efficiently computing the fractional Caputo derivative. In the numerical section, we conduct comprehensive experiments on forward and inverse problems. For forward problems, we evaluate the performance of our method on over 50 diverse mathematical problems, including multi-dimensional integral equations, systems of integral equations, partial and fractional integro-differential equations, and various optimal control problems in delay, fractional, multi-dimensional, and nonlinear configurations. For inverse problems, we test our approach on several integral equations and fractional integro-differential problems. Finally, we introduce the pinnies Python package to facilitate the implementation and usability of the proposed method.

Paperid: 95, https://arxiv.org/pdf/2506.13777.pdf

Abstract:
Urban systems are typical examples of complex systems, where the integration of physics-based modeling with artificial intelligence (AI) presents a promising paradigm for enhancing predictive accuracy, interpretability, and decision-making. In this context, AI excels at capturing complex, nonlinear relationships, while physics-based models ensure consistency with real-world laws and provide interpretable insights. We provide a comprehensive review of physics-informed AI methods in urban applications. The proposed taxonomy categorizes existing approaches into three paradigms - Physics-Integrated AI, Physics-AI Hybrid Ensemble, and AI-Integrated Physics - and further details seven representative methods. This classification clarifies the varying degrees and directions of physics-AI integration, guiding the selection and development of appropriate methods based on application needs and data availability. We systematically examine their applications across eight key urban domains: energy, environment, economy, transportation, information, public services, emergency management, and the urban system as a whole. Our analysis highlights how these methodologies leverage physical laws and data-driven models to address urban challenges, enhancing system reliability, efficiency, and adaptability. By synthesizing existing methodologies and their urban applications, we identify critical gaps and outline future research directions, paving the way toward next-generation intelligent urban system modeling.

Paperid: 96, https://arxiv.org/pdf/2505.13919.pdf

Abstract:
Data-driven methods offer an effective equation-free solution for predicting physical dynamics. However, the same physical system can exhibit significantly different dynamic behaviors in various environments. This causes prediction functions trained for specific environments to fail when transferred to unseen environments. Therefore, cross-environment prediction requires modeling the dynamic functions of different environments. In this work, we propose a model weight generation method, \texttt{EnvAd-Diff}. \texttt{EnvAd-Diff} operates in the weight space of the dynamic function, generating suitable weights from scratch based on environmental condition for zero-shot prediction. Specifically, we first train expert prediction functions on dynamic trajectories from a limited set of visible environments to create a model zoo, thereby constructing sample pairs of prediction function weights and their corresponding environments. Subsequently, we train a latent space diffusion model conditioned on the environment to model the joint distribution of weights and environments. Considering the lack of environmental prior knowledge in real-world scenarios, we propose a physics-informed surrogate label to distinguish different environments. Generalization experiments across multiple systems demonstrate that a 1M parameter prediction function generated by \texttt{EnvAd-Diff} outperforms a pre-trained 500M parameter foundation model.

Paperid: 97, https://arxiv.org/pdf/2505.03140.pdf

Abstract:
Quantum machine learning for spin and molecular systems faces critical challenges of scarce labeled data and computationally expensive simulations. To address these limitations, we introduce Hamiltonian-Masked Autoencoding (HMAE), a novel self-supervised framework that pre-trains transformers on unlabeled quantum Hamiltonians, enabling efficient few-shot transfer learning. Unlike random masking approaches, HMAE employs a physics-informed strategy based on quantum information theory to selectively mask Hamiltonian terms based on their physical significance. Experiments on 12,500 quantum Hamiltonians (60% real-world, 40% synthetic) demonstrate that HMAE achieves 85.3% $\pm$ 1.5% accuracy in phase classification and 0.15 $\pm$ 0.02 eV MAE in ground state energy prediction with merely 10 labeled examples - a statistically significant improvement (p < 0.01) over classical graph neural networks (78.1% $\pm$ 2.1%) and quantum neural networks (76.8% $\pm$ 2.3%). Our method's primary advantage is exceptional sample efficiency - reducing required labeled examples by 3-5x compared to baseline methods - though we emphasize that ground truth values for fine-tuning and evaluation still require exact diagonalization or tensor networks. We explicitly acknowledge that our current approach is limited to small quantum systems (specifically limited to 12 qubits during training, with limited extension to 16-20 qubits in testing) and that, while promising within this regime, this size restriction prevents immediate application to larger systems of practical interest in materials science and quantum chemistry.

Paperid: 98, https://arxiv.org/pdf/2411.19125.pdf

Abstract:
Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To overcome this limitation, we propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations, including varying initial conditions, PDE coefficients, and training time horizons. PIDO exploits the shared underlying structure of dynamical systems with different properties by projecting PDE solutions into a latent space using auto-decoding. It then learns the dynamics of these latent representations, conditioned on the PDE coefficients. Despite its promise, integrating latent dynamics models within a physics-informed framework poses challenges due to the optimization difficulties associated with physics-informed losses. To address these challenges, we introduce a novel approach that diagnoses and mitigates these issues within the latent space. This strategy employs straightforward yet effective regularization techniques, enhancing both the temporal extrapolation performance and the training stability of PIDO. We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations. Additionally, we demonstrate the transferability of its learned representations to downstream applications such as long-term integration and inverse problems.

Paperid: 99, https://arxiv.org/pdf/2510.25731.pdf

Abstract:
We introduce a method for efficiently solving initial-boundary value problems (IBVPs) that uses Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations, the model inherently incorporates the physical laws and learns solutions from initial and boundary data. As a result, the loss directly measures the model's accuracy, leading to improved convergence. Moreover, for well-posed IBVPs, our method enables rigorous error estimation. The approach yields compact models, facilitating an efficient optimization. We implement LieSolver and demonstrate its application to linear homogeneous PDEs with a range of initial conditions, showing that it is faster and more accurate than physics-informed neural networks (PINNs). Overall, our method improves both computational efficiency and the reliability of predictions for PDE-constrained problems.

Paperid: 100, https://arxiv.org/pdf/2506.16443.pdf

Abstract:
Physics-informed neural networks (PINNs) offer a powerful approach to solving partial differential equations (PDEs), which are ubiquitous in the quantitative sciences. Applied to both forward and inverse problems across various scientific domains, PINNs have recently emerged as a valuable tool in the field of scientific machine learning. A key aspect of their training is that the data -- spatio-temporal points sampled from the PDE's input domain -- are readily available. Influence functions, a tool from the field of explainable AI (XAI), approximate the effect of individual training points on the model, enhancing interpretability. In the present work, we explore the application of influence function-based sampling approaches for the training data. Our results indicate that such targeted resampling based on data attribution methods has the potential to enhance prediction accuracy in physics-informed neural networks, demonstrating a practical application of an XAI method in PINN training.

Paperid: 101, https://arxiv.org/pdf/2505.23444.pdf

Abstract:
Cryo-electron microscopy (cryo-EM) offers near-atomic resolution imaging of macromolecules, but developing robust models for downstream analysis is hindered by the scarcity of high-quality annotated data. While synthetic data generation has emerged as a potential solution, existing methods often fail to capture both the structural diversity of biological specimens and the complex, spatially varying noise inherent in cryo-EM imaging. To overcome these limitations, we propose CryoCCD, a synthesis framework that integrates biophysical modeling with generative techniques. Specifically, CryoCCD produces multi-scale cryo-EM micrographs that reflect realistic biophysical variability through compositional heterogeneity, cellular context, and physics-informed imaging. To generate realistic noise, we employ a conditional diffusion model, enhanced by cycle consistency to preserve structural fidelity and mask-aware contrastive learning to capture spatially adaptive noise patterns. Extensive experiments show that CryoCCD generates structurally accurate micrographs and enhances performance in downstream tasks, outperforming state-of-the-art baselines in both particle picking and reconstruction.

Paperid: 102, https://arxiv.org/pdf/2512.17152.pdf

Abstract:
Fine-grained fire prediction plays a crucial role in emergency response. Infrared images and fire masks provide complementary thermal and boundary information, yet current methods are predominantly limited to binary mask modeling with inherent signal sparsity, failing to capture the complex dynamics of fire. While world models show promise in video generation, their physical inconsistencies pose significant challenges for fire forecasting. This paper introduces PhysFire-WM, a Physics-informed World Model for emulating Fire spread dynamics. Our approach internalizes combustion dynamics by encoding structured priors from a Physical Simulator to rectify physical discrepancies, coupled with a Cross-task Collaborative Training strategy (CC-Train) that alleviates the issue of limited information in mask-based modeling. Through parameter sharing and gradient coordination, CC-Train effectively integrates thermal radiation dynamics and spatial boundary delineation, enhancing both physical realism and geometric accuracy. Extensive experiments on a fine-grained multimodal fire dataset demonstrate the superior accuracy of PhysFire-WM in fire spread prediction. Validation underscores the importance of physical priors and cross-task collaboration, providing new insights for applying physics-informed world models to disaster prediction.

Paperid: 103, https://arxiv.org/pdf/2512.04385.pdf

Abstract:
Fine-grained air pollution forecasting is crucial for urban management and the development of healthy buildings. Deploying portable sensors on mobile platforms such as cars and buses offers a low-cost, easy-to-maintain, and wide-coverage data collection solution. However, due to the random and uncontrollable movement patterns of these non-dedicated mobile platforms, the resulting sensor data are often incomplete and temporally inconsistent. By exploring potential training patterns in the reverse process of diffusion models, we propose Spatio-Temporal Physics-Informed Diffusion Models (STeP-Diff). STeP-Diff leverages DeepONet to model the spatial sequence of measurements along with a PDE-informed diffusion model to forecast the spatio-temporal field from incomplete and time-varying data. Through a PDE-constrained regularization framework, the denoising process asymptotically converges to the convection-diffusion dynamics, ensuring that predictions are both grounded in real-world measurements and aligned with the fundamental physics governing pollution dispersion. To assess the performance of the system, we deployed 59 self-designed portable sensing devices in two cities, operating for 14 days to collect air pollution data. Compared to the second-best performing algorithm, our model achieved improvements of up to 89.12% in MAE, 82.30% in RMSE, and 25.00% in MAPE, with extensive evaluations demonstrating that STeP-Diff effectively captures the spatio-temporal dependencies in air pollution fields.

Paperid: 104, https://arxiv.org/pdf/2511.01928.pdf

Abstract:
Human mobility generation in disaster scenarios plays a vital role in resource allocation, emergency response, and rescue coordination. During disasters such as wildfires and hurricanes, human mobility patterns often deviate from their normal states, which makes the task more challenging. However, existing works usually rely on limited data from a single city or specific disaster, significantly restricting the model's generalization capability in new scenarios. In fact, disasters are highly sudden and unpredictable, and any city may encounter new types of disasters without prior experience. Therefore, we aim to develop a one-for-all model for mobility generation that can generalize to new disaster scenarios. However, building a universal framework faces two key challenges: 1) the diversity of disaster types and 2) the heterogeneity among different cities. In this work, we propose a unified model for human mobility generation in natural disasters (named UniDisMob). To enable cross-disaster generalization, we design physics-informed prompt and physics-guided alignment that leverage the underlying common patterns in mobility changes after different disasters to guide the generation process. To achieve cross-city generalization, we introduce a meta-learning framework that extracts universal patterns across multiple cities through shared parameters and captures city-specific features via private parameters. Extensive experiments across multiple cities and disaster scenarios demonstrate that our method significantly outperforms state-of-the-art baselines, achieving an average performance improvement exceeding 13%.

Paperid: 105, https://arxiv.org/pdf/2506.22843.pdf

Abstract:
Person re-identification (ReID) across aerial and ground vantage points has become crucial for large-scale surveillance and public safety applications. Although significant progress has been made in ground-only scenarios, bridging the aerial-ground domain gap remains a formidable challenge due to extreme viewpoint differences, scale variations, and occlusions. Building upon the achievements of the AG-ReID 2023 Challenge, this paper introduces the AG-VPReID 2025 Challenge - the first large-scale video-based competition focused on high-altitude (80-120m) aerial-ground ReID. Constructed on the new AG-VPReID dataset with 3,027 identities, over 13,500 tracklets, and approximately 3.7 million frames captured from UAVs, CCTV, and wearable cameras, the challenge featured four international teams. These teams developed solutions ranging from multi-stream architectures to transformer-based temporal reasoning and physics-informed modeling. The leading approach, X-TFCLIP from UAM, attained 72.28% Rank-1 accuracy in the aerial-to-ground ReID setting and 70.77% in the ground-to-aerial ReID setting, surpassing existing baselines while highlighting the dataset's complexity. For additional details, please refer to the official website at https://agvpreid25.github.io.

Paperid: 106, https://arxiv.org/pdf/2502.16828.pdf

Abstract:
Energy landscapes play a crucial role in shaping dynamics of many real-world complex systems. System evolution is often modeled as particles moving on a landscape under the combined effect of energy-driven drift and noise-induced diffusion, where the energy governs the long-term motion of the particles. Estimating the energy landscape of a system has been a longstanding interdisciplinary challenge, hindered by the high operational costs or the difficulty of obtaining supervisory signals. Therefore, the question of how to infer the energy landscape in the absence of true energy values is critical. In this paper, we propose a physics-informed self-supervised learning method to learn the energy landscape from the evolution trajectories of the system. It first maps the system state from the observation space to a discrete landscape space by an adaptive codebook, and then explicitly integrates energy into the graph neural Fokker-Planck equation, enabling the joint learning of energy estimation and evolution prediction. Experimental results across interdisciplinary systems demonstrate that our estimated energy has a correlation coefficient above 0.9 with the ground truth, and evolution prediction accuracy exceeds the baseline by an average of 17.65\%. The code is available at github.com/tsinghua-fib-lab/PESLA.

Paperid: 107, https://arxiv.org/pdf/2505.17434.pdf

Abstract:
Goal-conditioned dynamic manipulation is inherently challenging due to complex system dynamics and stringent task constraints, particularly in deformable object scenarios characterized by high degrees of freedom and underactuation. Prior methods often simplify the problem to low-speed or 2D settings, limiting their applicability to real-world 3D tasks. In this work, we explore 3D goal-conditioned rope manipulation as a representative challenge. To mitigate data scarcity, we introduce a novel simulation framework and benchmark grounded in reduced-order dynamics, which enables compact state representation and facilitates efficient policy learning. Building on this, we propose Dynamics Informed Diffusion Policy (DIDP), a framework that integrates imitation pretraining with physics-informed test-time adaptation. First, we design a diffusion policy that learns inverse dynamics within the reduced-order space, enabling imitation learning to move beyond naÃ¯ve data fitting and capture the underlying physical structure. Second, we propose a physics-informed test-time adaptation scheme that imposes kinematic boundary conditions and structured dynamics priors on the diffusion process, ensuring consistency and reliability in manipulation execution. Extensive experiments validate the proposed approach, demonstrating strong performance in terms of accuracy and robustness in the learned policy.

Paperid: 108, https://arxiv.org/pdf/2601.15113.pdf

Abstract:
Wireless imaging is emerging as a key capability in next-generation integrated sensing and communication (ISAC) systems, supporting diverse context-aware applications. However, conventional imaging approaches, whether based on physical models or data-driven learning, face challenges such as accurate multipath separation and representative dataset acquisition. To address these issues, this study explores the use of implicit neural representation (INR), a paradigm that has achieved notable advancements in computer vision, for wireless imaging in reconfigurable intelligent surface-aided ISAC systems. The neural network of INR is specifically designed with positional encoding and sine activation functions. Leveraging physics-informed loss functions, INR is optimized through deep learning to represent continuous target shapes and scattering profiles, enabling resolution-agnostic imaging with strong generalization capability. Extensive simulations demonstrate that the proposed INR-based method achieves significant improvements over state-of-the-art techniques and further reveals the focal length characteristics of the imaging system.

Paperid: 109, https://arxiv.org/pdf/2512.00255.pdf

Abstract:
We present Relightable Holoported Characters (RHC), a novel person-specific method for free-view rendering and relighting of full-body and highly dynamic humans solely observed from sparse-view RGB videos at inference. In contrast to classical one-light-at-a-time (OLAT)-based human relighting, our transformer-based RelightNet predicts relit appearance within a single network pass, avoiding costly OLAT-basis capture and generation. For training such a model, we introduce a new capture strategy and dataset recorded in a multi-view lightstage, where we alternate frames lit by random environment maps with uniformly lit tracking frames, simultaneously enabling accurate motion tracking and diverse illumination as well as dynamics coverage. Inspired by the rendering equation, we derive physics-informed features that encode geometry, albedo, shading, and the virtual camera view from a coarse human mesh proxy and the input views. Our RelightNet then takes these features as input and cross-attends them with a novel lighting condition, and regresses the relit appearance in the form of texel-aligned 3D Gaussian splats attached to the coarse mesh proxy. Consequently, our RelightNet implicitly learns to efficiently compute the rendering equation for novel lighting conditions within a single feed-forward pass. Experiments demonstrate our method's superior visual fidelity and lighting reproduction compared to state-of-the-art approaches. Project page: https://vcai.mpi-inf.mpg.de/projects/RHC/

Paperid: 110, https://arxiv.org/pdf/2503.17978.pdf

Abstract:
Human activity recognition (HAR) with deep learning models relies on large amounts of labeled data, often challenging to obtain due to associated cost, time, and labor. Self-supervised learning (SSL) has emerged as an effective approach to leverage unlabeled data through pretext tasks, such as masked reconstruction and multitask learning with signal processing-based data augmentations, to pre-train encoder models. However, such methods are often derived from computer vision approaches that disregard physical mechanisms and constraints that govern wearable sensor data and the phenomena they reflect. In this paper, we propose a physics-informed multi-task pre-training (PIM) framework for IMU-based HAR. PIM generates pre-text tasks based on the understanding of basic physical aspects of human motion: including movement speed, angles of movement, and symmetry between sensor placements. Given a sensor signal, we calculate corresponding features using physics-based equations and use them as pretext tasks for SSL. This enables the model to capture fundamental physical characteristics of human activities, which is especially relevant for multi-sensor systems. Experimental evaluations on four HAR benchmark datasets demonstrate that the proposed method outperforms existing state-of-the-art methods, including data augmentation and masked reconstruction, in terms of accuracy and F1 score. We have observed gains of almost 10\% in macro f1 score and accuracy with only 2 to 8 labeled examples per class and up to 3% when there is no reduction in the amount of training data.

Paperid: 111, https://arxiv.org/pdf/2512.10965.pdf

Abstract:
Radio maps (RMs) provide a spatially continuous description of wireless propagation, enabling cross-layer optimization and unifying communication and sensing for integrated sensing and communications (ISAC). However, constructing high-fidelity RMs at operational scales is difficult, since physics-based solvers are time-consuming and require precise scene models, while learning methods degrade under incomplete priors and sparse measurements, often smoothing away critical discontinuities. We present RMSup, a physics-informed super-resolution framework that functions with uniform sparse sampling and imperfect environment priors. RMSup extracts Helmholtz equation-informed boundary and singularity prompts from the measurements, fuses them with base-station side information and coarse scene descriptors as conditional inputs, and employs a boundary-aware dual-head network to reconstruct a high-fidelity RM and recover environmental contours jointly. Experimental results show the proposed RMsup achieves state-of-the-art performance both in RM construction and ISAC-related environment sensing.

Paperid: 112, https://arxiv.org/pdf/2504.15623.pdf

Abstract:
In this paper, we propose a novel physics-informed generative learning approach, termed RadioDiff-$\bm{k^2}$, for accurate and efficient multipath-aware radio map (RM) construction. As wireless communication evolves towards environment-aware paradigms, driven by the increasing demand for intelligent and proactive optimization in sixth-generation (6G) networks, accurate construction of RMs becomes crucial yet highly challenging. Conventional electromagnetic (EM)-based methods, such as full-wave solvers and ray-tracing approaches, exhibit substantial computational overhead and limited adaptability to dynamic scenarios. Although, existing neural network (NN) approaches have efficient inferencing speed, they lack sufficient consideration of the underlying physics of EM wave propagation, limiting their effectiveness in accurately modeling critical EM singularities induced by complex multipath environments. To address these fundamental limitations, we propose a novel physics-inspired RM construction method guided explicitly by the Helmholtz equation, which inherently governs EM wave propagation. Specifically, we theoretically establish a direct correspondence between EM singularities, which correspond to the critical spatial features influencing wireless propagation, and regions defined by negative wave numbers in the Helmholtz equation. Based on this insight, we design an innovative dual generative diffusion model (DM) framework comprising one DM dedicated to accurately inferring EM singularities and another DM responsible for reconstructing the complete RM using these singularities along with environmental contextual information. Our physics-informed approach uniquely combines the efficiency advantages of data-driven methods with rigorous physics-based EM modeling, significantly enhancing RM accuracy, particularly in complex propagation environments dominated by multipath effects.

Paperid: 113, https://arxiv.org/pdf/2504.12169.pdf

Abstract:
Low-light conditions pose significant challenges for both human and machine annotation. This in turn has led to a lack of research into machine understanding for low-light images and (in particular) videos. A common approach is to apply annotations obtained from high quality datasets to synthetically created low light versions. In addition, these approaches are often limited through the use of unrealistic noise models. In this paper, we propose a new Degradation Estimation Network (DEN), which synthetically generates realistic standard RGB (sRGB) noise without the requirement for camera metadata. This is achieved by estimating the parameters of physics-informed noise distributions, trained in a self-supervised manner. This zero-shot approach allows our method to generate synthetic noisy content with a diverse range of realistic noise characteristics, unlike other methods which focus on recreating the noise characteristics of the training data. We evaluate our proposed synthetic pipeline using various methods trained on its synthetic data for typical low-light tasks including synthetic noise replication, video enhancement, and object detection, showing improvements of up to 24\% KLD, 21\% LPIPS, and 62\% AP$_{50-95}$, respectively.

Paperid: 114, https://arxiv.org/pdf/2502.03236.pdf

Abstract:
Dynamic interacting system modeling is important for understanding and simulating real world systems. The system is typically described as a graph, where multiple objects dynamically interact with each other and evolve over time. In recent years, graph Ordinary Differential Equations (ODE) receive increasing research attentions. While achieving encouraging results, existing solutions prioritize the traditional Euclidean space, and neglect the intrinsic geometry of the system and physics laws, e.g., the principle of entropy increasing. The limitations above motivate us to rethink the system dynamics from a fresh perspective of Riemannian geometry, and pose a more realistic problem of physics-informed dynamic system modeling, considering the underlying geometry and physics law for the first time. In this paper, we present a novel physics-informed Riemannian graph ODE for a wide range of entropy-increasing dynamic systems (termed as Pioneer). In particular, we formulate a differential system on the Riemannian manifold, where a manifold-valued graph ODE is governed by the proposed constrained Ricci flow, and a manifold preserving Gyro-transform aware of system geometry. Theoretically, we report the provable entropy non-decreasing of our formulation, obeying the physics laws. Empirical results show the superiority of Pioneer on real datasets.

Paperid: 115, https://arxiv.org/pdf/2412.13811.pdf

Abstract:
Glioblastoma, the most aggressive primary brain tumor, poses a severe clinical challenge due to its diffuse microscopic infiltration, which remains largely undetected on standard MRI. As a result, current radiotherapy planning employs a uniform 15 mm margin around the resection cavity, failing to capture patient-specific tumor spread. Tumor growth modeling offers a promising approach to reveal this hidden infiltration. However, methods based on partial differential equations or physics-informed neural networks tend to be computationally intensive or overly constrained, limiting their clinical adaptability to individual patients. In this work, we propose a lightweight, rapid, and robust optimization framework that estimates the 3D tumor concentration by fitting it to MRI tumor segmentations while enforcing a smooth concentration landscape. This approach achieves superior tumor recurrence prediction on 192 brain tumor patients across two public datasets, outperforming state-of-the-art baselines while reducing runtime from 30 minutes to less than one minute. Furthermore, we demonstrate the framework's versatility and adaptability by showing its ability to seamlessly integrate additional imaging modalities or physical constraints.

Paperid: 116, https://arxiv.org/pdf/2511.22963.pdf

Abstract:
Enabling humanoid robots to follow free-form language commands is critical for seamless human-robot interaction, collaborative task execution, and general-purpose embodied intelligence. While recent advances have improved low-level humanoid locomotion and robot manipulation, language-conditioned whole-body control remains a significant challenge. Existing methods are often limited to simple instructions and sacrifice either motion diversity or physical plausibility. To address this, we introduce Humanoid-LLA, a Large Language Action Model that maps expressive language commands to physically executable whole-body actions for humanoid robots. Our approach integrates three core components: a unified motion vocabulary that aligns human and humanoid motion primitives into a shared discrete space; a vocabulary-directed controller distilled from a privileged policy to ensure physical feasibility; and a physics-informed fine-tuning stage using reinforcement learning with dynamics-aware rewards to enhance robustness and stability. Extensive evaluations in simulation and on a real-world Unitree G1 humanoid show that Humanoid-LLA delivers strong language generalization while maintaining high physical fidelity, outperforming existing language-conditioned controllers in motion naturalness, stability, and execution success rate.

Paperid: 117, https://arxiv.org/pdf/2410.06366.pdf

Abstract:
Learning complex physical dynamics purely from data is challenging due to the intrinsic properties of systems to be satisfied. Incorporating physics-informed priors, such as in Hamiltonian Neural Networks (HNNs), achieves high-precision modeling for energy-conservative systems. However, real-world systems often deviate from strict energy conservation and follow different physical priors. To address this, we present a framework that achieves high-precision modeling for a wide range of dynamical systems from the numerical aspect, by enforcing Time-Reversal Symmetry (TRS) via a novel regularization term. It helps preserve energies for conservative systems while serving as a strong inductive bias for non-conservative, reversible systems. While TRS is a domain-specific physical prior, we present the first theoretical proof that TRS loss can universally improve modeling accuracy by minimizing higher-order Taylor terms in ODE integration, which is numerically beneficial to various systems regardless of their properties, even for irreversible systems. By integrating the TRS loss within neural ordinary differential equation models, the proposed model TREAT demonstrates superior performance on diverse physical systems. It achieves a significant 11.5% MSE improvement in a challenging chaotic triple-pendulum scenario, underscoring TREAT's broad applicability and effectiveness.

Paperid: 118, https://arxiv.org/pdf/2409.01626.pdf

Abstract:
The growing computational demands of artificial intelligence (AI) in addressing climate change raise significant concerns about inefficiencies and environmental impact, as highlighted by the Jevons paradox. We propose an attention-enhanced quantum physics-informed neural networks model (AQ-PINNs) to tackle these challenges. This approach integrates quantum computing techniques into physics-informed neural networks (PINNs) for climate modeling, aiming to enhance predictive accuracy in fluid dynamics governed by the Navier-Stokes equations while reducing the computational burden and carbon footprint. By harnessing variational quantum multi-head self-attention mechanisms, our AQ-PINNs achieve a 51.51% reduction in model parameters compared to classical multi-head self-attention methods while maintaining comparable convergence and loss. It also employs quantum tensor networks to enhance representational capacity, which can lead to more efficient gradient computations and reduced susceptibility to barren plateaus. Our AQ-PINNs represent a crucial step towards more sustainable and effective climate modeling solutions.

Paperid: 119, https://arxiv.org/pdf/2507.19205.pdf

Abstract:
Real-time particle transverse momentum ($p_T$) estimation in high-energy physics demands algorithms that are both efficient and accurate under strict hardware constraints. Static machine learning models degrade under high pileup and lack physics-aware optimization, while generic graph neural networks (GNNs) often neglect domain structure critical for robust $p_T$ regression. We propose a physics-informed GNN framework that systematically encodes detector geometry and physical observables through four distinct graph construction strategies that systematically encode detector geometry and physical observables: station-as-node, feature-as-node, bending angle-centric, and pseudorapidity ($Î·$)-centric representations. This framework integrates these tailored graph structures with a novel Message Passing Layer (MPL), featuring intra-message attention and gated updates, and domain-specific loss functions incorporating $p_{T}$-distribution priors. Our co-design methodology yields superior accuracy-efficiency trade-offs compared to existing baselines. Extensive experiments on the CMS Trigger Dataset validate the approach: a station-informed EdgeConv model achieves a state-of-the-art MAE of 0.8525 with $\ge55\%$ fewer parameters than deep learning baselines, especially TabNet, while an $Î·$-centric MPL configuration also demonstrates improved accuracy with comparable efficiency. These results establish the promise of physics-guided GNNs for deployment in resource-constrained trigger systems.

Paperid: 120, https://arxiv.org/pdf/2509.24615.pdf

Abstract:
The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN's major difficulties in coupling with external forward solvers arise from the inability to access the discretized form (Finite difference, finite volume, finite element, etc.) of the governing equation directly through the network and to include them in its computational graph. This poses a significant challenge to conventional automatic-differentiation-based derivative computation of physics-based loss terms concerning the neural network hyperparameters if gradient-based optimization techniques are adopted. Therefore, we propose modifying the physics-based loss term to account for the residual arising from the external solver and to compute the derivative required for the optimization machinery. The proposed methodologies are demonstrated on benchmark full-order and reduced-order systems.

Paperid: 121, https://arxiv.org/pdf/2506.21765.pdf

Abstract:
Trackerless freehand ultrasound reconstruction aims to reconstruct 3D volumes from sequences of 2D ultrasound images without relying on external tracking systems, offering a low-cost, portable, and widely deployable alternative for volumetric imaging. However, it presents significant challenges, including accurate inter-frame motion estimation, minimisation of drift accumulation over long sequences, and generalisability across scanning protocols. The TUS-REC2024 Challenge was established to benchmark and accelerate progress in trackerless 3D ultrasound reconstruction by providing a publicly available dataset for the first time, along with a baseline model and evaluation framework. The Challenge attracted over 43 registered teams, of which 6 teams submitted 21 valid dockerized solutions. Submitted methods spanned a wide range of algorithmic approaches, including recurrent models, registration-driven volume refinement, attention, and physics-informed models. This paper presents an overview of the Challenge design, summarises the key characteristics of the dataset, provides a concise literature review, introduces the technical details of the underlying methodology working with tracked freehand ultrasound data, and offers a comparative analysis of submitted methods across multiple evaluation metrics. The results highlight both the progress and current limitations of state-of-the-art approaches in this domain, and inform directions for future research. The data, evaluation code, and baseline are publicly available to facilitate ongoing development and reproducibility. As a live and evolving benchmark, this Challenge is designed to be continuously developed and improved. The Challenge was held at MICCAI 2024 and will be organised again at MICCAI 2025, reflecting its growing impact and the sustained commitment to advancing this field.

Paperid: 122, https://arxiv.org/pdf/2502.00803.pdf

Abstract:
Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function. By analyzing the loss distribution, previous research observed the propagation failure phenomenon of PINNs, intuitively described as the correct supervision for model outputs cannot ''propagate'' from initial states or boundaries to the interior domain. Going beyond intuitive understanding, this paper provides a formal and in-depth study of propagation failure and its root cause. Based on a detailed comparison with classical finite element methods, we ascribe the failure to the conventional single-point-processing architecture of PINNs and further prove that propagation failure is essentially caused by the lower gradient correlation of PINN models on nearby collocation points. Compared to superficial loss maps, this new perspective provides a more precise quantitative criterion to identify where and why PINN fails. The theoretical finding also inspires us to present a new PINN architecture, named ProPINN, which can effectively unite the gradients of region points for better propagation. ProPINN can reliably resolve PINN failure modes and significantly surpass advanced Transformer-based models with 46% relative promotion.

Paperid: 123, https://arxiv.org/pdf/2501.19160.pdf

Abstract:
Radio map reconstruction is essential for enabling advanced applications, yet challenges such as complex signal propagation and sparse observational data hinder accurate reconstruction in practical scenarios. Existing methods often fail to align physical constraints with data-driven features, particularly under sparse measurement conditions. To address these issues, we propose **Phy**sics-Aligned **R**adio **M**ap **D**iffusion **M**odel (**PhyRMDM**), a novel framework that establishes cross-domain representation alignment between physical principles and neural network features through dual learning pathways. The proposed model integrates **Physics-Informed Neural Networks (PINNs)** with a **representation alignment mechanism** that explicitly enforces consistency between Helmholtz equation constraints and environmental propagation patterns. Experimental results demonstrate significant improvements over state-of-the-art methods, achieving **NMSE of 0.0031** under *Static Radio Map (SRM)* conditions, and **NMSE of 0.0047** with **Dynamic Radio Map (DRM)** scenarios. The proposed representation alignment paradigm provides **37.2%** accuracy enhancement in ultra-sparse cases (**1%** sampling rate), confirming its effectiveness in bridging physics-based modeling and deep learning for radio map reconstruction.

Paperid: 124, https://arxiv.org/pdf/2512.08248.pdf

Abstract:
This paper presents a Spatiotemporal Tube (STT)-based control framework for general control-affine MIMO nonlinear pure-feedback systems with unknown dynamics to satisfy prescribed time reach-avoid-stay tasks under external disturbances. The STT is defined as a time-varying ball, whose center and radius are jointly approximated by a Physics-Informed Neural Network (PINN). The constraints governing the STT are first formulated as loss functions of the PINN, and a training algorithm is proposed to minimize the overall violation. The PINN being trained on certain collocation points, we propose a Lipschitz-based validity condition to formally verify that the learned PINN satisfies the conditions over the continuous time horizon. Building on the learned STT representation, an approximation-free closed-form controller is defined to guarantee satisfaction of the T-RAS specification. Finally, the effectiveness and scalability of the framework are validated through two case studies involving a mobile robot and an aerial vehicle navigating through cluttered environments.

Paperid: 125, https://arxiv.org/pdf/2601.01321.pdf

Abstract:
Digital twins, as precise digital representations of physical systems, have evolved from passive simulation tools into intelligent and autonomous entities through the integration of artificial intelligence technologies. This paper presents a unified four-stage framework that systematically characterizes AI integration across the digital twin lifecycle, spanning modeling, mirroring, intervention, and autonomous management. By synthesizing existing technologies and practices, we distill a unified four-stage framework that systematically characterizes how AI methodologies are embedded across the digital twin lifecycle: (1) modeling the physical twin through physics-based and physics-informed AI approaches, (2) mirroring the physical system into a digital twin with real-time synchronization, (3) intervening in the physical twin through predictive modeling, anomaly detection, and optimization strategies, and (4) achieving autonomous management through large language models, foundation models, and intelligent agents. We analyze the synergy between physics-based modeling and data-driven learning, highlighting the shift from traditional numerical solvers to physics-informed and foundation models for physical systems. Furthermore, we examine how generative AI technologies, including large language models and generative world models, transform digital twins into proactive and self-improving cognitive systems capable of reasoning, communication, and creative scenario generation. Through a cross-domain review spanning eleven application domains, including healthcare, aerospace, smart manufacturing, robotics, and smart cities, we identify common challenges related to scalability, explainability, and trustworthiness, and outline directions for responsible AI-driven digital twin systems.

Paperid: 126, https://arxiv.org/pdf/2510.09543.pdf

Abstract:
Animals achieve energy-efficient locomotion by their implicit passive dynamics, a marvel that has captivated roboticists for decades.Recently, methods incorporated Adversarial Motion Prior (AMP) and Reinforcement learning (RL) shows promising progress to replicate Animals' naturalistic motion. However, such imitation learning approaches predominantly capture explicit kinematic patterns, so-called gaits, while overlooking the implicit passive dynamics. This work bridges this gap by incorporating a reward term guided by Impact Mitigation Factor (IMF), a physics-informed metric that quantifies a robot's ability to passively mitigate impacts. By integrating IMF with AMP, our approach enables RL policies to learn both explicit motion trajectories from animal reference motion and the implicit passive dynamic. We demonstrate energy efficiency improvements of up to 32%, as measured by the Cost of Transport (CoT), across both AMP and handcrafted reward structure.

Paperid: 127, https://arxiv.org/pdf/2511.14218.pdf

Abstract:
Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere, necessitating probabilistic approaches to quantify uncertainty. While traditional ensemble prediction (EPS) addresses this through computationally intensive simulations, recent advances in Bayesian Deep Learning (BDL) offer a promising but often disconnected alternative. We bridge these paradigms through a unified hybrid Bayesian Deep Learning framework for ensemble weather forecasting that explicitly decomposes predictive uncertainty into epistemic and aleatoric components, learned via variational inference and a physics-informed stochastic perturbation scheme modeling flow-dependent atmospheric dynamics, respectively. We further establish a unified theoretical framework that rigorously connects BDL and EPS, providing formal theorems that decompose total predictive uncertainty into epistemic and aleatoric components under the hybrid BDL framework. We validate our framework on the large-scale 40-year ERA5 reanalysis dataset (1979-2019) with 0.25° spatial resolution. Experimental results show that our method not only improves forecast accuracy and yields better-calibrated uncertainty quantification but also achieves superior computational efficiency compared to state-of-the-art probabilistic diffusion models. We commit to making our code open-source upon acceptance of this paper.

Paperid: 128, https://arxiv.org/pdf/2510.03360.pdf

Abstract:
Assessing turbulence control effects for wall friction numerically is a significant challenge since it requires expensive simulations of turbulent fluid dynamics. We instead propose an efficient deep reinforcement learning (RL) framework for modeling and control of turbulent flows. It is model-based RL for predictive control (PC), where both the policy and the observer models for turbulence control are learned jointly using Physics Informed Neural Operators (PINO), which are discretization invariant and can capture fine scales in turbulent flows accurately. Our PINO-PC outperforms prior model-free reinforcement learning methods in various challenging scenarios where the flows are of high Reynolds numbers and unseen, i.e., not provided during model training. We find that PINO-PC achieves a drag reduction of 39.0\% under a bulk-velocity Reynolds number of 15,000, outperforming previous fluid control methods by more than 32\%.

Paperid: 129, https://arxiv.org/pdf/2509.09936.pdf

Abstract:
Recent work in scientific machine learning aims to tackle scientific tasks directly by predicting target values with neural networks (e.g., physics-informed neural networks, neural ODEs, neural operators, etc.), but attaining high accuracy and robustness has been challenging. We explore an alternative view: use LLMs to write code that leverages decades of numerical algorithms. This shifts the burden from learning a solution function to making domain-aware numerical choices. We ask whether LLMs can act as SciML agents that, given a natural-language ODE description, generate runnable code that is scientifically appropriate, selecting suitable solvers (stiff vs. non-stiff), and enforcing stability checks. There is currently no benchmark to measure this kind of capability for scientific computing tasks. As such, we first introduce two new datasets: a diagnostic dataset of adversarial "misleading" problems; and a large-scale benchmark of 1,000 diverse ODE tasks. The diagnostic set contains problems whose superficial appearance suggests stiffness, and that require algebraic simplification to demonstrate non-stiffness; and the large-scale benchmark spans stiff and non-stiff ODE regimes. We evaluate open- and closed-source LLM models along two axes: (i) unguided versus guided prompting with domain-specific knowledge; and (ii) off-the-shelf versus fine-tuned variants. Our evaluation measures both executability and numerical validity against reference solutions. We find that with sufficient context and guided prompts, newer instruction-following models achieve high accuracy on both criteria. In many cases, recent open-source systems perform strongly without fine-tuning, while older or smaller models still benefit from fine-tuning. Overall, our preliminary results indicate that careful prompting and fine-tuning can yield a specialized LLM agent capable of reliably solving simple ODE problems.

Paperid: 130, https://arxiv.org/pdf/2504.08277.pdf

Abstract:
Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these derivatives remains challenging, with spectral and finite difference methods introducing approximation errors due to finite resolution. Here, we propose the mollified graph neural operator (mGNO), the first method to leverage automatic differentiation and compute \emph{exact} gradients on arbitrary geometries. This enhancement enables efficient training on irregular grids and varying geometries while allowing seamless evaluation of physics losses at randomly sampled points for improved generalization. For a PDE example on regular grids, mGNO paired with autograd reduced the L2 relative data error by 20x compared to finite differences, although training was slower. It can also solve PDEs on unstructured point clouds seamlessly, using physics losses only, at resolutions vastly lower than those needed for finite differences to be accurate enough. On these unstructured point clouds, mGNO leads to errors that are consistently 2 orders of magnitude lower than machine learning baselines (Meta-PDE) for comparable runtimes, and also delivers speedups from 1 to 3 orders of magnitude compared to the numerical solver for similar accuracy. mGNOs can also be used to solve inverse design and shape optimization problems on complex geometries.

Paperid: 131, https://arxiv.org/pdf/2502.09346.pdf

Abstract:
Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper provides a comprehensive review of advanced ML methodologies designed to handle unstructured grid data in high-dimensional dynamical systems. Key approaches discussed include graph neural networks, transformer models with spatial attention mechanisms, interpolation-integrated ML methods, and meshless techniques such as physics-informed neural networks. These methodologies have proven effective across diverse fields, including fluid dynamics and environmental simulations. This review is intended as a guidebook for computational scientists seeking to apply ML approaches to unstructured grid data in their domains, as well as for ML researchers looking to address challenges in computational physics. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques and, conversely, how insights from computational physics can inform ML development. To support benchmarking, this review also provides a summary of open-access datasets of unstructured grid data in computational physics. Finally, emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed to inspire future advancements in this evolving field.

Paperid: 132, https://arxiv.org/pdf/2409.18438.pdf

Abstract:
Early diagnosis of Autism Spectrum Disorder (ASD) is an effective and favorable step towards enhancing the health and well-being of children with ASD. Manual ASD diagnosis testing is labor-intensive, complex, and prone to human error due to several factors contaminating the results. This paper proposes a novel framework that exploits the laws of physics for ASD severity recognition. The proposed physics-informed neural network architecture encodes the behaviour of the subject extracted by observing a part of the skeleton-based motion trajectory in a higher dimensional latent space. Two decoders, namely physics-based and non-physics-based decoder, use this latent embedding and predict the future motion patterns. The physics branch leverages the laws of physics that apply to a skeleton sequence in the prediction process while the non-physics-based branch is optimised to minimise the difference between the predicted and actual motion of the subject. A classifier also leverages the same latent space embeddings to recognise the ASD severity. This dual generative objective explicitly forces the network to compare the actual behaviour of the subject with the general normal behaviour of children that are governed by the laws of physics, aiding the ASD recognition task. The proposed method attains state-of-the-art performance on multiple ASD diagnosis benchmarks. To illustrate the utility of the proposed framework beyond the task ASD diagnosis, we conduct a third experiment using a publicly available benchmark for the task of fall prediction and demonstrate the superiority of our model.

Paperid: 133, https://arxiv.org/pdf/2509.18105.pdf

Abstract:
We study learning of continuous-time inventory dynamics under stochastic demand and quantify when structure helps or hurts forecasting of the bullwhip effect. BULL-ODE compares a fully learned Neural ODE (NODE) that models the entire right-hand side against a physics-informed Universal Differential Equation (UDE) that preserves conservation and order-up-to structure while learning a small residual policy term. Classical supply chain models explain the bullwhip through control/forecasting choices and information sharing, while recent physics-informed and neural differential equation methods blend domain constraints with learned components. It is unclear whether structural bias helps or hinders forecasting under different demand regimes. We address this by using a single-echelon testbed with three demand regimes - AR(1) (autocorrelated), i.i.d. Gaussian, and heavy-tailed lognormal. Training is done on varying fractions of each trajectory, followed by evaluation of multi-step forecasts for inventory I, order rate O, and demand D. Across the structured regimes, UDE consistently generalizes better: with 90% of the training horizon, inventory RMSE drops from 4.92 (NODE) to 0.26 (UDE) under AR(1) and from 5.96 to 0.95 under Gaussian demand. Under heavy-tailed lognormal shocks, the flexibility of NODE is better. These trends persist as train18 ing data shrinks, with NODE exhibiting phase drift in extrapolation while UDE remains stable but underreacts to rare spikes. Our results provide concrete guidance: enforce structure when noise is light-tailed or temporally correlated; relax structure when extreme events dominate. Beyond inventory control, the results offer guidance for hybrid modeling in scientific and engineering systems: enforce known structure when conservation laws and modest noise dominate, and relax structure to capture extremes in settings where rare events drive dynamics.

Paperid: 134, https://arxiv.org/pdf/2509.12437.pdf

Abstract:
A major challenge in deploying world models is the trade-off between size and performance. Large world models can capture rich physical dynamics but require massive computing resources, making them impractical for edge devices. Small world models are easier to deploy but often struggle to learn accurate physics, leading to poor predictions. We propose the Physics-Informed BEV World Model (PIWM), a compact model designed to efficiently capture physical interactions in bird's-eye-view (BEV) representations. PIWM uses Soft Mask during training to improve dynamic object modeling and future prediction. We also introduce a simple yet effective technique, Warm Start, for inference to enhance prediction quality with a zero-shot model. Experiments show that at the same parameter scale (400M), PIWM surpasses the baseline by 60.6% in weighted overall score. Moreover, even when compared with the largest baseline model (400M), the smallest PIWM (130M Soft Mask) achieves a 7.4% higher weighted overall score with a 28% faster inference speed.

Paperid: 135, https://arxiv.org/pdf/2507.08834.pdf

Abstract:
Traditional numerical methods often struggle with the complexity and scale of modeling pollutant transport across vast and dynamic oceanic domains. This paper introduces a Physics-Informed Neural Network (PINN) framework to simulate the dispersion of pollutants governed by the 2D advection-diffusion equation. The model achieves physically consistent predictions by embedding physical laws and fitting to noisy synthetic data, generated via a finite difference method (FDM), directly into the neural network training process. This approach addresses challenges such as non-linear dynamics and the enforcement of boundary and initial conditions. Synthetic data sets, augmented with varying noise levels, are used to capture real-world variability. The training incorporates a hybrid loss function including PDE residuals, boundary/initial condition conformity, and a weighted data fit term. The approach takes advantage of the Julia language scientific computing ecosystem for high-performance simulations, offering a scalable and flexible alternative to traditional solvers

Paperid: 136, https://arxiv.org/pdf/2507.07143.pdf

Abstract:
Accurately modeling malware propagation is essential for designing effective cybersecurity defenses, particularly against adaptive threats that evolve in real time. While traditional epidemiological models and recent neural approaches offer useful foundations, they often fail to fully capture the nonlinear feedback mechanisms present in real-world networks. In this work, we apply scientific machine learning to malware modeling by evaluating three approaches: classical Ordinary Differential Equations (ODEs), Universal Differential Equations (UDEs), and Neural ODEs. Using data from the Code Red worm outbreak, we show that the UDE approach substantially reduces prediction error compared to both traditional and neural baselines by 44%, while preserving interpretability. We introduce a symbolic recovery method that transforms the learned neural feedback into explicit mathematical expressions, revealing suppression mechanisms such as network saturation, security response, and malware variant evolution. Our results demonstrate that hybrid physics-informed models can outperform both purely analytical and purely neural approaches, offering improved predictive accuracy and deeper insight into the dynamics of malware spread. These findings support the development of early warning systems, efficient outbreak response strategies, and targeted cyber defense interventions.

Paperid: 137, https://arxiv.org/pdf/2412.16724.pdf

Abstract:
Estimating the evolution of the battery's State of Charge (SoC) in response to its usage is critical for implementing effective power management policies and for ultimately improving the system's lifetime. Most existing estimation methods are either physics-based digital twins of the battery or data-driven models such as Neural Networks (NNs). In this work, we propose two new contributions in this domain. First, we introduce a novel NN architecture formed by two cascaded branches: one to predict the current SoC based on sensor readings, and one to estimate the SoC at a future time as a function of the load behavior. Second, we integrate battery dynamics equations into the training of our NN, merging the physics-based and data-driven approaches, to improve the models' generalization over variable prediction horizons. We validate our approach on two publicly accessible datasets, showing that our Physics-Informed Neural Networks (PINNs) outperform purely data-driven ones while also obtaining superior prediction accuracy with a smaller architecture with respect to the state-of-the-art.

Paperid: 138, https://arxiv.org/pdf/2410.06452.pdf

Abstract:
In climate science, models for global warming and weather prediction face significant challenges due to the limited availability of high-quality data and the difficulty in obtaining it, making data efficiency crucial. In the past few years, Scientific Machine Learning (SciML) models have gained tremendous traction as they can be trained in a data-efficient manner, making them highly suitable for real-world climate applications. Despite this, very little attention has been paid to chaotic climate system modeling utilizing SciML methods. In this paper, we have integrated SciML methods into foundational weather models, where we have enhanced large-scale climate predictions with a physics-informed approach that achieves high accuracy with reduced data. We successfully demonstrate that by combining the interpretability of physical climate models with the computational power of neural networks, SciML models can prove to be a reliable tool for modeling climate. This indicates a shift from the traditional black box-based machine learning modeling of climate systems to physics-informed decision-making, leading to effective climate policy implementation.

Paperid: 139, https://arxiv.org/pdf/2508.07841.pdf

Abstract:
Attitude control is a fundamental aspect of spacecraft operations. Model Predictive Control (MPC) has emerged as a powerful strategy for these tasks, relying on accurate models of the system dynamics to optimize control actions over a prediction horizon. In scenarios where physics models are incomplete, difficult to derive, or computationally expensive, machine learning offers a flexible alternative by learning the system behavior directly from data. However, purely data-driven models often struggle with generalization and stability, especially when applied to inputs outside their training domain. To address these limitations, we investigate the benefits of incorporating Physics-Informed Neural Networks (PINNs) into the learning of spacecraft attitude dynamics, comparing their performance with that of purely data-driven approaches. Using a Real-valued Non-Volume Preserving (Real NVP) neural network architecture with a self-attention mechanism, we trained several models on simulated data generated with the Basilisk simulator. Two training strategies were considered: a purely data-driven baseline and a physics-informed variant to improve robustness and stability. Our results demonstrate that the inclusion of physics-based information significantly enhances the performance in terms of the mean relative error of the best architectures found by 27.08%. These advantages are particularly evident when the learned models are integrated into an MPC framework, where PINN-based models consistently outperform their purely data-driven counterparts in terms of control accuracy and robustness, yielding improvements of up to 42.86% in performance stability error and increased robustness-to-noise.

Paperid: 140, https://arxiv.org/pdf/2504.02015.pdf

Abstract:
Satellites are used for a multitude of applications, including communications, Earth observation, and space science. Neural networks and deep learning-based approaches now represent the state-of-the-art to enhance the performance and efficiency of these tasks. Given that satellites are susceptible to various faults, one critical application of Artificial Intelligence (AI) is fault detection. However, despite the advantages of neural networks, these systems are vulnerable to radiation errors, which can significantly impact their reliability. Ensuring the dependability of these solutions requires extensive testing and validation, particularly using fault injection methods. This study analyses a physics-informed (PI) real-valued non-volume preserving (Real NVP) normalizing flow model for fault detection in space systems, with a focus on resilience to Single-Event Upsets (SEUs). We present a customized fault injection framework in TensorFlow to assess neural network resilience. Fault injections are applied through two primary methods: Layer State injection, targeting internal network components such as weights and biases, and Layer Output injection, which modifies layer outputs across various activations. Fault types include zeros, random values, and bit-flip operations, applied at varying levels and across different network layers. Our findings reveal several critical insights, such as the significance of bit-flip errors in critical bits, that can lead to substantial performance degradation or even system failure. With this work, we aim to exhaustively study the resilience of Real NVP models against errors due to radiation, providing a means to guide the implementation of fault tolerance measures.

Paperid: 141, https://arxiv.org/pdf/2601.14517.pdf

Abstract:
Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the emergence of various physics-aware data-driven approaches, the field still lacks a unified perspective to uncover their relationships, limitations, and appropriate roles in scientific workflows. To this end, we propose a unifying perspective to place two dominant paradigms: Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), within a shared design space. We organize existing methods from three fundamental dimensions: what is learned, how physical structures are integrated into the learning process, and how the computational load is amortized across problem instances. In this way, many challenges can be best understood as consequences of these structural properties of learning PDEs. By analyzing advances through this unifying view, our survey aims to facilitate the development of reliable learning-based PDE solvers and catalyze a synthesis of physics and data.

Paperid: 142, https://arxiv.org/pdf/2507.06826.pdf

Abstract:
This paper presents a physics-informed neural network (PINN) for modeling first-order Ambisonic (FOA) room impulse responses (RIRs). PINNs have demonstrated promising performance in sound field interpolation by combining the powerful modeling capability of neural networks and the physical principles of sound propagation. In room acoustics, PINNs have typically been trained to represent the sound pressure measured by omnidirectional microphones where the wave equation or its frequency-domain counterpart, i.e., the Helmholtz equation, is leveraged. Meanwhile, FOA RIRs additionally provide spatial characteristics and are useful for immersive audio generation with a wide range of applications. In this paper, we extend the PINN framework to model FOA RIRs. We derive two physics-informed priors for FOA RIRs based on the correspondence between the particle velocity and the (X, Y, Z)-channels of FOA. These priors associate the predicted W-channel and other channels through their partial derivatives and impose the physically feasible relationship on the four channels. Our experiments confirm the effectiveness of the proposed method compared with a neural network without the physics-informed prior.

Paperid: 143, https://arxiv.org/pdf/2504.06242.pdf

Abstract:
In robotics, control barrier function (CBF)-based safety filters are commonly used to enforce state constraints. A critical challenge arises when the relative degree of the CBF varies across the state space. This variability can create regions within the safe set where the control input becomes unconstrained. When implemented as a safety filter, this may result in chattering near the safety boundary and ultimately compromise system safety. To address this issue, we propose a novel approach for CBF synthesis by formulating it as solving a set of boundary value problems. The solutions to the boundary value problems are determined using physics-informed neural networks (PINNs). Our approach ensures that the synthesized CBFs maintain a constant relative degree across the set of admissible states, thereby preventing unconstrained control scenarios. We illustrate the approach in simulation and further verify it through real-world quadrotor experiments, demonstrating its effectiveness in preserving desired system safety properties.

Paperid: 144, https://arxiv.org/pdf/2409.20409.pdf

Abstract:
Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient's anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models. In this work, we introduce a novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks (PINNs). However, our approach parametrizes the solution directly on a dynamic discrete mesh, allowing for the effective modeling of complex biomechanical behaviors. Specifically, we propose a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations. This quantification acts as a regularization term, offering greater flexibility and improved integration of patient data compared to existing models. We demonstrate enhanced coverage of tumor recurrence areas using real-world data from a patient cohort, highlighting the potential of our method to improve model-driven treatment planning for glioblastoma in clinical practice.

Paperid: 145, https://arxiv.org/pdf/2509.25704.pdf

Abstract:
Accurate and physically feasible human motion prediction is crucial for safe and seamless human-robot collaboration. While recent advancements in human motion capture enable real-time pose estimation, the practical value of many existing approaches is limited by the lack of future predictions and consideration of physical constraints. Conventional motion prediction schemes rely heavily on past poses, which are not always available in real-world scenarios. To address these limitations, we present a physics-informed learning framework that integrates domain knowledge into both training and inference to predict human motion using inertial measurements from only 5 IMUs. We propose a network that accounts for the spatial characteristics of human movements. During training, we incorporate forward and differential kinematics functions as additional loss components to regularize the learned joint predictions. At the inference stage, we refine the prediction from the previous iteration to update a joint state buffer, which is used as extra inputs to the network. Experimental results demonstrate that our approach achieves high accuracy, smooth transitions between motions, and generalizes well to unseen subjects

Paperid: 146, https://arxiv.org/pdf/2506.00478.pdf

Abstract:
Alternating Current Optimal Power Flow (AC-OPF) aims to optimize generator power outputs by utilizing the non-linear relationships between voltage magnitudes and phase angles in a power system. However, current AC-OPF solvers struggle to effectively represent the complex relationship between variable distributions in the constraint space and their corresponding optimal solutions. This limitation in constraint modeling restricts the system's ability to develop diverse knowledge representations. Additionally, modeling the power grid solely based on spatial topology further limits the integration of additional prior knowledge, such as temporal information. To overcome these challenges, we propose DDA-PIGCN (Dynamic Domain Adaptation-Driven Physics-Informed Graph Convolutional Network), a new method designed to address constraint-related issues and build a graph-based learning framework that incorporates spatiotemporal features. DDA-PIGCN improves consistency optimization for features with varying long-range dependencies by applying multi-layer, hard physics-informed constraints. It also uses a dynamic domain adaptation learning mechanism that iteratively updates and refines key state variables under predefined constraints, enabling precise constraint verification. Moreover, it captures spatiotemporal dependencies between generators and loads by leveraging the physical structure of the power grid, allowing for deep integration of topological information across time and space. Extensive comparative and ablation studies show that DDA-PIGCN delivers strong performance across several IEEE standard test cases (such as case9, case30, and case300), achieving mean absolute errors (MAE) from 0.0011 to 0.0624 and constraint satisfaction rates between 99.6% and 100%, establishing it as a reliable and efficient AC-OPF solver.

Paperid: 147, https://arxiv.org/pdf/2504.06070.pdf

Abstract:
Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings between past and future states, overlooking the fluid dynamics, or only modeling the velocity field, neglecting the coupling of multiple physical quantities. In this paper, we propose a new physics-informed learning approach that incorporates coupled physical quantities into the prediction process to assist with forecasting. Central to our method lies in the discretization of physical equations, which are directly integrated into the model architecture and loss function. This integration enables the model to provide robust, long-term future predictions. By incorporating physical equations, our model demonstrates temporal extrapolation and spatial generalization capabilities. Experimental results show that our approach achieves the state-of-the-art performance in spatiotemporal prediction across both numerical simulations and real-world extreme-precipitation nowcasting benchmarks.

Paperid: 148, https://arxiv.org/pdf/2511.10108.pdf

Abstract:
The discovery of advanced metallic alloys is hindered by vast composition spaces, competing property objectives, and real-world constraints on manufacturability. Here we introduce MATAI, a generalist machine learning framework for property prediction and inverse design of as-cast alloys. MATAI integrates a curated alloy database, deep neural network-based property predictors, a constraint-aware optimization engine, and an iterative AI-experiment feedback loop. The framework estimates key mechanical propertie, sincluding density, yield strength, ultimate tensile strength, and elongation, directly from composition, using multi-task learning and physics-informed inductive biases. Alloy design is framed as a constrained optimization problem and solved using a bi-level approach that combines local search with symbolic constraint programming. We demonstrate MATAI's capabilities on the Ti-based alloy system, a canonical class of lightweight structural materials, where it rapidly identifies candidates that simultaneously achieve lower density (<4.45 g/cm3), higher strength (>1000 MPa) and appreciable ductility (>5%) through only seven iterations. Experimental validation confirms that MATAI-designed alloys outperform commercial references such as TC4, highlighting the framework's potential to accelerate the discovery of lightweight, high-performance materials under real-world design constraints.

Paperid: 149, https://arxiv.org/pdf/2509.24697.pdf

Abstract:
Recent trends in humanoid robot control have successfully employed imitation learning to enable the learned generation of smooth, human-like trajectories from human data. While these approaches make more realistic motions possible, they are limited by the amount of available motion data, and do not incorporate prior knowledge about the physical laws governing the system and its interactions with the environment. Thus they may violate such laws, leading to divergent trajectories and sliding contacts which limit real-world stability. We address such limitations via a two-pronged learning strategy which leverages the known physics of the system and fundamental control principles. First, we encode physics priors during supervised imitation learning to promote trajectory feasibility. Second, we minimize drift at inference time by applying a proportional-integral controller directly to the generated output state. We validate our method on various locomotion behaviors for the ergoCub humanoid robot, where a physics-informed loss encourages zero contact foot velocity. Our experiments demonstrate that the proposed approach is compatible with multiple controllers on a real robot and significantly improves the accuracy and physical constraint conformity of generated trajectories.

Paperid: 150, https://arxiv.org/pdf/2509.20570.pdf

Abstract:
Diffusion models have demonstrated strong generative capabilities across scientific domains, but often produce outputs that violate physical laws. We propose a new perspective by framing physics-informed generation as a sparse reward optimization problem, where adherence to physical constraints is treated as a reward signal. This formulation unifies prior approaches under a reward-based paradigm and reveals a shared bottleneck: reliance on diffusion posterior sampling (DPS)-style value function approximations, which introduce non-negligible errors and lead to training instability and inference inefficiency. To overcome this, we introduce Physics-Informed Reward Fine-tuning (PIRF), a method that bypasses value approximation by computing trajectory-level rewards and backpropagating their gradients directly. However, a naive implementation suffers from low sample efficiency and compromised data fidelity. PIRF mitigates these issues through two key strategies: (1) a layer-wise truncated backpropagation method that leverages the spatiotemporally localized nature of physics-based rewards, and (2) a weight-based regularization scheme that improves efficiency over traditional distillation-based methods. Across five PDE benchmarks, PIRF consistently achieves superior physical enforcement under efficient sampling regimes, highlighting the potential of reward fine-tuning for advancing scientific generative modeling.

Paperid: 151, https://arxiv.org/pdf/2506.19243.pdf

Abstract:
We investigate the high-precision training of Physics-Informed Neural Networks (PINNs) in unbounded domains, with a special focus on applications to singularity formulation in PDEs. We propose a modularized approach and study the choices of neural network ansatz, sampling strategy, and optimization algorithm. When combined with rigorous computer-assisted proofs and PDE analysis, the numerical solutions identified by PINNs, provided they are of high precision, can serve as a powerful tool for studying singularities in PDEs. For 1D Burgers equation, our framework can lead to a solution with very high precision, and for the 2D Boussinesq equation, which is directly related to the singularity formulation in 3D Euler and Navier-Stokes equations, we obtain a solution whose loss is $4$ digits smaller than that obtained in \cite{wang2023asymptotic} with fewer training steps. We also discuss potential directions for pushing towards machine precision for higher-dimensional problems.

Paperid: 152, https://arxiv.org/pdf/2508.08254.pdf

Abstract:
Humans possess an exceptional ability to imagine 4D scenes, encompassing both motion and 3D geometry, from a single still image. This ability is rooted in our accumulated observations of similar scenes and an intuitive understanding of physics. In this paper, we aim to replicate this capacity in neural networks, specifically focusing on natural fluid imagery. Existing methods for this task typically employ simplistic 2D motion estimators to animate the image, leading to motion predictions that often defy physical principles, resulting in unrealistic animations. Our approach introduces a novel method for generating 4D scenes with physics-consistent animation from a single image. We propose the use of a physics-informed neural network that predicts motion for each surface point, guided by a loss term derived from fundamental physical principles, including the Navier-Stokes equations. To capture appearance, we predict feature-based 3D Gaussians from the input image and its estimated depth, which are then animated using the predicted motions and rendered from any desired camera perspective. Experimental results highlight the effectiveness of our method in producing physically plausible animations, showcasing significant performance improvements over existing methods. Our project page is https://physfluid.github.io/ .

Paperid: 153, https://arxiv.org/pdf/2512.16214.pdf

Abstract:
Solving Partial Differential Equations (PDEs) is a cornerstone of engineering and scientific research. Traditional methods for PDE solving are cumbersome, relying on manual setup and domain expertise. While Physics-Informed Neural Network (PINNs) introduced end-to-end neural network-based solutions, and frameworks like DeepXDE further enhanced automation, these approaches still depend on expert knowledge and lack full autonomy. In this work, we frame PDE solving as tool invocation via LLM-driven agents and introduce PDE-Agent, the first toolchain-augmented multi-agent collaboration framework, inheriting the reasoning capacity of LLMs and the controllability of external tools and enabling automated PDE solving from natural language descriptions. PDE-Agent leverages the strengths of multi-agent and multi-tool collaboration through two key innovations: (1) A Prog-Act framework with graph memory for multi-agent collaboration, which enables effective dynamic planning and error correction via dual-loop mechanisms (localized fixes and global revisions). (2) A Resource-Pool integrated with a tool-parameter separation mechanism for multi-tool collaboration. This centralizes the management of runtime artifacts and resolves inter-tool dependency gaps in existing frameworks. To validate and evaluate this new paradigm for PDE solving , we develop PDE-Bench, a multi-type PDE Benchmark for agent-based tool collaborative solving, and propose multi-level metrics for assessing tool coordination. Evaluations verify that PDE-Agent exhibits superior applicability and performance in complex multi-step, cross-step dependent tasks. This new paradigm of toolchain-augmented multi-agent PDE solving will further advance future developments in automated scientific computing. Our source code and dataset will be made publicly available.

Paperid: 154, https://arxiv.org/pdf/2504.09069.pdf

Abstract:
Video imaging is often affected by complex degradations such as blur, noise, and compression artifacts. Traditional restoration methods follow a "single-task single-model" paradigm, resulting in poor generalization and high computational cost, limiting their applicability in real-world scenarios with diverse degradation types. We propose UniFlowRestore, a general video restoration framework that models restoration as a time-continuous evolution under a prompt-guided and physics-informed vector field. A physics-aware backbone PhysicsUNet encodes degradation priors as potential energy, while PromptGenerator produces task-relevant prompts as momentum. These components define a Hamiltonian system whose vector field integrates inertial dynamics, decaying physical gradients, and prompt-based guidance. The system is optimized via a fixed-step ODE solver to achieve efficient and unified restoration across tasks. Experiments show that UniFlowRestore delivers stateof-the-art performance with strong generalization and efficiency. Quantitative results demonstrate that UniFlowRestore achieves state-of-the-art performance, attaining the highest PSNR (33.89 dB) and SSIM (0.97) on the video denoising task, while maintaining top or second-best scores across all evaluated tasks.

Paperid: 155, https://arxiv.org/pdf/2410.22371.pdf

Abstract:
Stochastic differential equations are commonly used to describe the evolution of stochastic processes. The state uncertainty of such processes is best represented by the probability density function (PDF), whose evolution is governed by the Fokker-Planck partial differential equation (FP-PDE). However, it is generally infeasible to solve the FP-PDE in closed form. In this work, we show that physics-informed neural networks (PINNs) can be trained to approximate the solution PDF. Our main contribution is the analysis of PINN approximation error: we develop a theoretical framework to construct tight error bounds using PINNs. In addition, we derive a practical error bound that can be efficiently constructed with standard training methods. We discuss that this error-bound framework generalizes to approximate solutions of other linear PDEs. Empirical results on nonlinear, high-dimensional, and chaotic systems validate the correctness of our error bounds while demonstrating the scalability of PINNs and their significant computational speedup in obtaining accurate PDF solutions compared to the Monte Carlo approach.

Paperid: 156, https://arxiv.org/pdf/2512.13727.pdf

Abstract:
Ride-hailing platforms face the challenge of balancing passenger waiting times with overall system efficiency under highly uncertain supply-demand conditions. Adaptive delayed matching creates a trade-off between matching and pickup delays by deciding whether to assign drivers immediately or batch requests. Since outcomes accumulate over long horizons with stochastic dynamics, reinforcement learning (RL) is a suitable framework. However, existing approaches often oversimplify traffic dynamics or use shallow encoders that miss complex spatiotemporal patterns. We introduce the Regime-Aware Spatio-Temporal Mixture-of-Experts (RAST-MoE), which formalizes adaptive delayed matching as a regime-aware MDP equipped with a self-attention MoE encoder. Unlike monolithic networks, our experts specialize automatically, improving representation capacity while maintaining computational efficiency. A physics-informed congestion surrogate preserves realistic density-speed feedback, enabling millions of efficient rollouts, while an adaptive reward scheme guards against pathological strategies. With only 12M parameters, our framework outperforms strong baselines. On real-world Uber trajectory data (San Francisco), it improves total reward by over 13%, reducing average matching and pickup delays by 10% and 15% respectively. It demonstrates robustness across unseen demand regimes and stable training. These findings highlight the potential of MoE-enhanced RL for large-scale decision-making with complex spatiotemporal dynamics.

Paperid: 157, https://arxiv.org/pdf/2509.17293.pdf

Abstract:
Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with adversarial or contrastive objectives to enforce partial differential equation constraints. While effective, these enhancements introduce significant training and implementation complexity, limiting scalability and practical deployment. We investigate physics-informed neural operator learning models as efficient supervisory signals for training simplified architectures through knowledge distillation. Our approach pre-trains a physics-informed DeepONet (PI-DeepONet) on high-fidelity cuffless blood pressure recordings to learn operator mappings from raw wearable waveforms to beat-to-beat pressure signals under embedded physics constraints. This pre-trained operator serves as a frozen supervisor in a lightweight knowledge-distillation pipeline, guiding streamlined base models that eliminate complex adversarial and contrastive learning components while maintaining performance. We characterize the role of physics-informed regularization in operator learning and demonstrate its effectiveness for supervisory guidance. Through extensive experiments, our operator-supervised approach achieves performance parity with complex baselines (correlation: 0.766 vs. 0.770, RMSE: 4.452 vs. 4.501), while dramatically reducing architectural complexity from eight critical hyperparameters to a single regularization coefficient and decreasing training overhead by 4%. Our results demonstrate that operator-based supervision effectively replaces intricate multi-component training strategies, offering a more scalable and interpretable approach to physiological modeling with reduced implementation burden.

Paperid: 158, https://arxiv.org/pdf/2509.04060.pdf

Abstract:
As the number of satellites in orbit has increased exponentially in recent years, ensuring their correct functionality has started to require automated methods to decrease human workload. In this work, we present an algorithm that analyzes the on-board data related to friction from the Reaction Wheel Assemblies (RWA) of a satellite and determines their operating status, distinguishing between nominal status and several possible anomalies that require preventive measures to be taken. The algorithm first uses a model based on hybrid systems theory to extract the information relevant to the problem. The extraction process combines techniques in changepoint detection, dynamic programming, and maximum likelihood in a structured way. A classifier then uses the extracted information to determine the status of the RWA. This last classifier has been previously trained with a labelled dataset produced by a high-fidelity simulator, comprised for the most part of nominal data. The final algorithm combines model-based and data-based approaches to obtain satisfactory results with an accuracy around 95%.

Paperid: 159, https://arxiv.org/pdf/2509.00936.pdf

Abstract:
Cities today generate enormous streams of data from sensors, cameras, and connected infrastructure. While this information offers unprecedented opportunities to improve urban life, most existing systems struggle with scale, latency, and fragmented insights. This work introduces a framework that blends physics-informed machine learning, multimodal data fusion, and knowledge graph representation with adaptive, rule-based intelligence powered by large language models (LLMs). Physics-informed methods ground learning in real-world constraints, ensuring predictions remain meaningful and consistent with physical dynamics. Knowledge graphs act as the semantic backbone, integrating heterogeneous sensor data into a connected, queryable structure. At the edge, LLMs generate context-aware rules that adapt filtering and decision-making in real time, enabling efficient operation even under constrained resources. Together, these elements form a foundation for digital twin systems that go beyond passive monitoring to provide actionable insights. By uniting physics-based reasoning, semantic data fusion, and adaptive rule generation, this approach opens new possibilities for creating responsive, trustworthy, and sustainable smart infrastructures.

Paperid: 160, https://arxiv.org/pdf/2508.20414.pdf

Abstract:
Artificial intelligence (AI) has demonstrated considerable potential in the realm of medical imaging. However, the development of high-performance AI models typically necessitates training on large-scale, centralized datasets. This approach is confronted with significant challenges due to strict patient privacy regulations and legal restrictions on data sharing and utilization. These limitations hinder the development of large-scale models in medical domains and impede continuous updates and training with new data. Federated Learning (FL), a privacy-preserving distributed training framework, offers a new solution by enabling collaborative model development across fragmented medical datasets. In this survey, we review FL's contributions at two stages of the full-stack medical analysis pipeline. First, in upstream tasks such as CT or MRI reconstruction, FL enables joint training of robust reconstruction networks on diverse, multi-institutional datasets, alleviating data scarcity while preserving confidentiality. Second, in downstream clinical tasks like tumor diagnosis and segmentation, FL supports continuous model updating by allowing local fine-tuning on new data without centralizing sensitive images. We comprehensively analyze FL implementations across the medical imaging pipeline, from physics-informed reconstruction networks to diagnostic AI systems, highlighting innovations that improve communication efficiency, align heterogeneous data, and ensure secure parameter aggregation. Meanwhile, this paper provides an outlook on future research directions, aiming to serve as a valuable reference for the field's development.

Paperid: 161, https://arxiv.org/pdf/2506.21349.pdf

Abstract:
Solving Electromagnetic Inverse Scattering Problems (EISP) is fundamental in applications such as medical imaging, where the goal is to reconstruct the relative permittivity from scattered electromagnetic field. This inverse process is inherently ill-posed and highly nonlinear, making it particularly challenging. A recent machine learning-based approach, Img-Interiors, shows promising results by leveraging continuous implicit functions. However, it requires case-specific optimization, lacks generalization to unseen data, and fails under sparse transmitter setups (e.g., with only one transmitter). To address these limitations, we revisit EISP from a physics-informed perspective, reformulating it as a two stage inverse transmission-scattering process. This formulation reveals the induced current as a generalizable intermediate representation, effectively decoupling the nonlinear scattering process from the ill-posed inverse problem. Built on this insight, we propose the first generalizable physics-driven framework for EISP, comprising a current estimator and a permittivity solver, working in an end-to-end manner. The current estimator explicitly learns the induced current as a physical bridge between the incident and scattered field, while the permittivity solver computes the relative permittivity directly from the estimated induced current. This design enables data-driven training and generalizable feed-forward prediction of relative permittivity on unseen data while maintaining strong robustness to transmitter sparsity. Extensive experiments show that our method outperforms state-of-the-art approaches in reconstruction accuracy, generalization, and robustness. This work offers a fundamentally new perspective on electromagnetic inverse scattering and represents a major step toward cost-effective practical solutions for electromagnetic imaging.

Paperid: 162, https://arxiv.org/pdf/2503.00908.pdf

Abstract:
Reducing radiation doses benefits patients, however, the resultant low-dose computed tomography (LDCT) images often suffer from clinically unacceptable noise and artifacts. While deep learning (DL) shows promise in LDCT reconstruction, it requires large-scale data collection from multiple clients, raising privacy concerns. Federated learning (FL) has been introduced to address these privacy concerns; however, current methods are typically tailored to specific scanning protocols, which limits their generalizability and makes them less effective for unseen protocols. To address these issues, we propose SCAN-PhysFed, a novel SCanning- and ANatomy-level personalized Physics-Driven Federated learning paradigm for LDCT reconstruction. Since the noise distribution in LDCT data is closely tied to scanning protocols and anatomical structures being scanned, we design a dual-level physics-informed way to address these challenges. Specifically, we incorporate physical and anatomical prompts into our physics-informed hypernetworks to capture scanning- and anatomy-specific information, enabling dual-level physics-driven personalization of imaging features. These prompts are derived from the scanning protocol and the radiology report generated by a medical large language model (MLLM), respectively. Subsequently, client-specific decoders project these dual-level personalized imaging features back into the image domain. Besides, to tackle the challenge of unseen data, we introduce a novel protocol vector-quantization strategy (PVQS), which ensures consistent performance across new clients by quantifying the unseen scanning code as one of the codes in the scanning codebook. Extensive experimental results demonstrate the superior performance of SCAN-PhysFed on public datasets.

Paperid: 163, https://arxiv.org/pdf/2501.06572.pdf

Abstract:
Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically expressible laws of nature into their training loss function. By complying with physical laws, PINNs provide advantages over purely data-driven models in limited-data regimes and present as a promising route towards Physical AI. This feature has propelled them to the forefront of scientific machine learning, a domain characterized by scarce and costly data. However, the vision of accurate physics-informed learning comes with significant challenges. This work examines PINNs for the first time in terms of model optimization and generalization, shedding light on the need for new algorithmic advances to overcome issues pertaining to the training speed, precision, and generalizability of today's PINN models. Of particular interest are gradient-free evolutionary algorithms (EAs) for optimizing the uniquely complex loss landscapes arising in PINN training. Methods synergizing gradient descent and EAs for discovering bespoke neural architectures and balancing multiple terms in physics-informed learning objectives are positioned as important avenues for future research. Another exciting track is to cast evolutionary as a meta-learner of generalizable PINN models. To substantiate these proposed avenues, we further highlight results from recent literature to showcase the early success of such approaches in addressing the aforementioned challenges in PINN optimization and generalization.

Paperid: 164, https://arxiv.org/pdf/2410.16132.pdf

Abstract:
Traditional rule-based physical models are limited by their reliance on singular physical formulas and parameters, making it difficult to effectively tackle the intricate tasks associated with crowd simulation. Recent research has introduced deep learning methods to tackle these issues, but most current approaches focus primarily on generating pedestrian trajectories, often lacking interpretability and failing to provide real-time dynamic simulations.To address the aforementioned issues, we propose a novel data-driven crowd simulation framework that integrates Physics-informed Machine Learning (PIML) with navigation potential fields. Our approach leverages the strengths of both physical models and PIML. Specifically, we design an innovative Physics-informed Spatio-temporal Graph Convolutional Network (PI-STGCN) as a data-driven module to predict pedestrian movement trends based on crowd spatio-temporal data. Additionally, we construct a physical model of navigation potential fields based on flow field theory to guide pedestrian movements, thereby reinforcing physical constraints during the simulation. In our framework, navigation potential fields are dynamically computed and updated based on the movement trends predicted by the PI-STGCN, while the updated crowd dynamics, guided by these fields, subsequently feed back into the PI-STGCN. Comparative experiments on two publicly available large-scale real-world datasets across five scenes demonstrate that our proposed framework outperforms existing rule-based methods in accuracy and fidelity. The similarity between simulated and actual pedestrian trajectories increases by 10.8%, while the average error is reduced by 4%. Moreover, our framework exhibits greater adaptability and better interpretability compared to methods that rely solely on deep learning for trajectory generation.

Paperid: 165, https://arxiv.org/pdf/2601.18399.pdf

Abstract:
Separating liquid-liquid dispersions in gravity settlers is critical in chemical, pharmaceutical, and recycling processes. The dense-packed zone height is an important performance and safety indicator but it is often expensive and impractical to measure due to optical limitations. We propose to estimate phase heights using only inexpensive volume flow measurements. To this end, a physics-informed neural network (PINN) is first pretrained on synthetic data and physics equations derived from a low-fidelity (approximate) mechanistic model to reduce the need for extensive experimental data. While the mechanistic model is used to generate synthetic training data, only volume balance equations are used in the PINN, since the integration of submodels describing droplet coalescence and sedimentation into the PINN would be computationally prohibitive. The pretrained PINN is then fine-tuned with scarce experimental data to capture the actual dynamics of the separator. We then employ the differentiable PINN as a predictive model in an Extended Kalman Filter inspired state estimation framework, enabling the phase heights to be tracked and updated from flow-rate measurements. We first test the two-stage trained PINN by forward simulation from a known initial state against the mechanistic model and a non-pretrained PINN. We then evaluate phase height estimation performance with the filter, comparing the two-stage trained PINN with a two-stage trained purely data-driven neural network. All model types are trained and evaluated using ensembles to account for model parameter uncertainty. In all evaluations, the two-stage trained PINN yields the most accurate phase-height estimates.

Paperid: 166, https://arxiv.org/pdf/2511.11734.pdf

Abstract:
Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of magnitude more iterations, and even then may converge to suboptimal solutions that fail to preserve oscillatory frequency or amplitude. We introduce PhysicsInformed Neural ODEs with with Scale-Aware Residuals (PI-NODE-SR), a framework that combines a low-order explicit solver (Heun method) residual normalisation to balance contributions between state variables evolving on disparate timescales. This combination stabilises training under realistic iteration budgets and avoids reliance on computationally expensive implicit solvers. On the Hodgkin-Huxley equations, PI-NODE-SR learns from a single oscillation simulated with a stiff solver (Rodas5P) and extrapolates beyond 100 ms, capturing both oscillation frequency and near-correct amplitudes. Remarkably, end-to-end learning of the vector field enables PI-NODE-SR to recover morphological features such as sharp subthreshold curvature in gating variables that are typically reserved for higher-order solvers, suggesting that neural correction can offset numerical diffusion. While performance remains sensitive to initialisation, PI-NODE-SR consistently reduces long-horizon errors relative to baseline Neural-ODEs and PINNs, offering a principled route to stable and efficient learning of stiff biological dynamics.

Paperid: 167, https://arxiv.org/pdf/2508.20527.pdf

Abstract:
We present a perspective on molecular machine learning (ML) in the field of chemical process engineering. Recently, molecular ML has demonstrated great potential in (i) providing highly accurate predictions for properties of pure components and their mixtures, and (ii) exploring the chemical space for new molecular structures. We review current state-of-the-art molecular ML models and discuss research directions that promise further advancements. This includes ML methods, such as graph neural networks and transformers, which can be further advanced through the incorporation of physicochemical knowledge in a hybrid or physics-informed fashion. Then, we consider leveraging molecular ML at the chemical process scale, which is highly desirable yet rather unexplored. We discuss how molecular ML can be integrated into process design and optimization formulations, promising to accelerate the identification of novel molecules and processes. To this end, it will be essential to create molecule and process design benchmarks and practically validate proposed candidates, possibly in collaboration with the chemical industry.

Paperid: 168, https://arxiv.org/pdf/2508.20288.pdf

Abstract:
Accurately quantifying long-term risk probabilities in diverse stochastic systems is essential for safety-critical control. However, existing sampling-based and partial differential equation (PDE)-based methods often struggle to handle complex varying dynamics. Physics-informed neural networks learn surrogate mappings for risk probabilities from varying system parameters of fixed and finite dimensions, yet can not account for functional variations in system dynamics. To address these challenges, we introduce physics-informed neural operator (PINO) methods to risk quantification problems, to learn mappings from varying \textit{functional} system dynamics to corresponding risk probabilities. Specifically, we propose Neural Spline Operators (NeSO), a PINO framework that leverages B-spline representations to improve training efficiency and achieve better initial and boundary condition enforcements, which are crucial for accurate risk quantification. We provide theoretical analysis demonstrating the universal approximation capability of NeSO. We also present two case studies, one with varying functional dynamics and another with high-dimensional multi-agent dynamics, to demonstrate the efficacy of NeSO and its significant online speed-up over existing methods. The proposed framework and the accompanying universal approximation theorem are expected to be beneficial for other control or PDE-related problems beyond risk quantification.

Paperid: 169, https://arxiv.org/pdf/2504.04052.pdf

Abstract:
Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh regions. This challenge, known as the 'over-squashing' problem, hinders information propagation. While existing graph rewiring methods address this issue to some extent, they only consider graph topology, overlooking the underlying physical phenomena. We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology. PIORF uses Ollivier-Ricci curvature (ORC) to identify bottleneck regions and connects these areas with nodes in high-velocity gradient nodes, enabling long-range interactions and mitigating over-squashing. Our approach is computationally efficient in rewiring edges and can scale to larger simulations. Experimental results on 3 fluid dynamics benchmark datasets show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.

Paperid: 170, https://arxiv.org/pdf/2503.18787.pdf

Abstract:
Reinforcement learning (RL) can be used to tune data-driven (economic) nonlinear model predictive controllers ((e)NMPCs) for optimal performance in a specific control task by optimizing the dynamic model or parameters in the policy's objective function or constraints, such as state bounds. However, the sample efficiency of RL is crucial, and to improve it, we combine a model-based RL algorithm with our published method that turns Koopman (e)NMPCs into automatically differentiable policies. We apply our approach to an eNMPC case study of a continuous stirred-tank reactor (CSTR) model from the literature. The approach outperforms benchmark methods, i.e., data-driven eNMPCs using models based on system identification without further RL tuning of the resulting policy, and neural network controllers trained with model-based RL, by achieving superior control performance and higher sample efficiency. Furthermore, utilizing partial prior knowledge about the system dynamics via physics-informed learning further increases sample efficiency.

Paperid: 171, https://arxiv.org/pdf/2503.16777.pdf

Abstract:
Physics-informed machine learning provides an approach to combining data and governing physics laws for solving complex partial differential equations (PDEs). However, efficiently solving PDEs with varying parameters and changing initial conditions and boundary conditions (ICBCs) with theoretical guarantees remains an open challenge. We propose a hybrid framework that uses a neural network to learn B-spline control points to approximate solutions to PDEs with varying system and ICBC parameters. The proposed network can be trained efficiently as one can directly specify ICBCs without imposing losses, calculate physics-informed loss functions through analytical formulas, and requires only learning the weights of B-spline functions as opposed to both weights and basis as in traditional neural operator learning methods. We provide theoretical guarantees that the proposed B-spline networks serve as universal approximators for the set of solutions of PDEs with varying ICBCs under mild conditions and establish bounds on the generalization errors in physics-informed learning. We also demonstrate in experiments that the proposed B-spline network can solve problems with discontinuous ICBCs and outperforms existing methods, and is able to learn solutions of 3D dynamics with diverse initial conditions.

Paperid: 172, https://arxiv.org/pdf/2508.16235.pdf

Abstract:
Solving time-dependent partial differential equations (PDEs) is fundamental to modeling critical phenomena across science and engineering. Physics-Informed Neural Networks (PINNs) solve PDEs using deep learning. However, PINNs perform pointwise predictions that neglect the autoregressive property of dynamical systems, leading to instabilities and inaccurate predictions. We introduce Physics-Informed Autoregressive Networks (PIANO) -- a framework that redesigns PINNs to model dynamical systems. PIANO operates autoregressively, explicitly conditioning future predictions on the past. It is trained through a self-supervised rollout mechanism while enforcing physical constraints. We present a rigorous theoretical analysis demonstrating that PINNs suffer from temporal instability, while PIANO achieves stability through autoregressive modeling. Extensive experiments on challenging time-dependent PDEs demonstrate that PIANO achieves state-of-the-art performance, significantly improving accuracy and stability over existing methods. We further show that PIANO outperforms existing methods in weather forecasting.

Paperid: 173, https://arxiv.org/pdf/2411.06278.pdf

Abstract:
We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves lower-order differential operators. The Primal-Dual Hybrid Gradient (PDHG) algorithm is then leveraged for this saddle point problem. By introducing suitable precondition operators to the proximal steps in the PDHG algorithm, we obtain an alternative natural gradient ascent-descent optimization scheme for updating the neural network parameters. We apply the Krylov subspace method (MINRES) to evaluate the natural gradients efficiently. Such treatment readily handles the inversion of precondition matrices via matrix-vector multiplication. A posterior convergence analysis is established for the time-continuous version of the proposed method. The algorithm is tested on various types of PDEs with dimensions ranging from $1$ to $50$, including linear and nonlinear elliptic equations, reaction-diffusion equations, and Monge-AmpÃ¨re equations stemming from the $L^2$ optimal transport problems. We compare the performance of the proposed method with several commonly used deep learning algorithms such as physics-informed neural networks (PINNs), the DeepRitz method, weak adversarial networks (WANs), etc, for solving PDEs using the Adam and L-BFGS optimizers. The numerical results suggest that the proposed method performs efficiently and robustly and converges more stably.

Paperid: 174, https://arxiv.org/pdf/2409.20206.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal solutions. We introduce SetPINNs, a framework that effectively captures local dependencies. With a finite element-inspired sampling scheme, we partition the domain into sets to model local dependencies while simultaneously enforcing physical laws. We provide a rigorous theoretical analysis showing that SetPINNs yield unbiased, lower-variance estimates of residual energy and its gradients, ensuring improved domain coverage and reduced residual error. Extensive experiments on synthetic and real-world tasks show improved accuracy, efficiency, and robustness.

Paperid: 175, https://arxiv.org/pdf/2509.21207.pdf

Abstract:
Prognostics and Health Management ensures the reliability, safety, and efficiency of complex engineered systems by enabling fault detection, anticipating equipment failures, and optimizing maintenance activities throughout an asset lifecycle. However, real-world PHM presents persistent challenges: sensor data is often noisy or incomplete, available labels are limited, and degradation behaviors and system interdependencies can be highly complex and nonlinear. Physics-informed machine learning has emerged as a promising approach to address these limitations by embedding physical knowledge into data-driven models. This review examines how incorporating learning and observational biases through physics-informed modeling and data strategies can guide models toward physically consistent and reliable predictions. Learning biases embed physical constraints into model training through physics-informed loss functions and governing equations, or by incorporating properties like monotonicity. Observational biases influence data selection and synthesis to ensure models capture realistic system behavior through virtual sensing for estimating unmeasured states, physics-based simulation for data augmentation, and multi-sensor fusion strategies. The review then examines how these approaches enable the transition from passive prediction to active decision-making through reinforcement learning, which allows agents to learn maintenance policies that respect physical constraints while optimizing operational objectives. This closes the loop between model-based predictions, simulation, and actual system operation, empowering adaptive decision-making. Finally, the review addresses the critical challenge of scaling PHM solutions from individual assets to fleet-wide deployment. Fast adaptation methods including meta-learning and few-shot learning are reviewed alongside domain generalization techniques ...

Paperid: 176, https://arxiv.org/pdf/2507.10105.pdf

Abstract:
This paper presents a novel framework for whole-body torque control of humanoid robots without joint torque sensors, designed for systems with electric motors and high-ratio harmonic drives. The approach integrates Physics-Informed Neural Networks (PINNs) for friction modeling and Unscented Kalman Filtering (UKF) for joint torque estimation, within a real-time torque control architecture. PINNs estimate nonlinear static and dynamic friction from joint and motor velocity readings, capturing effects like motor actuation without joint movement. The UKF utilizes PINN-based friction estimates as direct measurement inputs, improving torque estimation robustness. Experimental validation on the ergoCub humanoid robot demonstrates improved torque tracking accuracy, enhanced energy efficiency, and superior disturbance rejection compared to the state-of-the-art Recursive Newton-Euler Algorithm (RNEA), using a dynamic balancing experiment. The framework's scalability is shown by consistent performance across robots with similar hardware but different friction characteristics, without re-identification. Furthermore, a comparative analysis with position control highlights the advantages of the proposed torque control approach. The results establish the method as a scalable and practical solution for sensorless torque control in humanoid robots, ensuring torque tracking, adaptability, and stability in dynamic environments.

Paperid: 177, https://arxiv.org/pdf/2506.08049.pdf

Abstract:
Subseasonal-to-seasonal (S2S) forecasting, which predicts climate conditions from several weeks to months in advance, represents a critical frontier for agricultural planning, energy management, and disaster preparedness. However, it remains one of the most challenging problems in atmospheric science, due to the chaotic dynamics of atmospheric systems and complex interactions across multiple scales. Current approaches often fail to explicitly model underlying physical processes and teleconnections that are crucial at S2S timescales. We introduce \textbf{TelePiT}, a novel deep learning architecture that enhances global S2S forecasting through integrated multi-scale physics and teleconnection awareness. Our approach consists of three key components: (1) Spherical Harmonic Embedding, which accurately encodes global atmospheric variables onto spherical geometry; (2) Multi-Scale Physics-Informed Neural ODE, which explicitly captures atmospheric physical processes across multiple learnable frequency bands; (3) Teleconnection-Aware Transformer, which models critical global climate interactions through explicitly modeling teleconnection patterns into the self-attention. Extensive experiments demonstrate that \textbf{TelePiT} significantly outperforms state-of-the-art data-driven baselines and operational numerical weather prediction systems across all forecast horizons, marking a significant advance toward reliable S2S forecasting.

Paperid: 178, https://arxiv.org/pdf/2505.22861.pdf

Abstract:
Tasks that involve complex interactions between objects with unknown dynamics make planning before execution difficult. These tasks require agents to iteratively improve their actions after actively exploring causes and effects in the environment. For these type of tasks, we propose Causal-PIK, a method that leverages Bayesian optimization to reason about causal interactions via a Physics-Informed Kernel to help guide efficient search for the best next action. Experimental results on Virtual Tools and PHYRE physical reasoning benchmarks show that Causal-PIK outperforms state-of-the-art results, requiring fewer actions to reach the goal. We also compare Causal-PIK to human studies, including results from a new user study we conducted on the PHYRE benchmark. We find that Causal-PIK remains competitive on tasks that are very challenging, even for human problem-solvers.

Paperid: 179, https://arxiv.org/pdf/2504.03955.pdf

Abstract:
Thermal analysis is crucial in three-dimensional integrated circuit (3D-IC) design due to increased power density and complex heat dissipation paths. Although operator learning frameworks such as DeepOHeat have demonstrated promising preliminary results in accelerating thermal simulation, they face critical limitations in prediction capability for multi-scale thermal patterns, training efficiency, and trustworthiness of results during design optimization. This paper presents DeepOHeat-v1, an enhanced physics-informed operator learning framework that addresses these challenges through three key innovations. First, we integrate Kolmogorov-Arnold Networks with learnable activation functions as trunk networks, enabling an adaptive representation of multi-scale thermal patterns. This approach achieves a $1.25\times$ and $6.29\times$ reduction in error in two representative test cases. Second, we introduce a separable training method that decomposes the basis function along the coordinate axes, achieving $62\times$ training speedup and $31\times$ GPU memory reduction in our baseline case, and enabling thermal analysis at resolutions previously infeasible due to GPU memory constraints. Third, we propose a confidence score to evaluate the trustworthiness of the predicted results, and further develop a hybrid optimization workflow that combines operator learning with finite difference (FD) using Generalized Minimal Residual (GMRES) method for incremental solution refinement, enabling efficient and trustworthy thermal optimization. Experimental results demonstrate that DeepOHeat-v1 achieves accuracy comparable to optimization using high-fidelity finite difference solvers, while speeding up the entire optimization process by $70.6\times$ in our test cases, effectively minimizing the peak temperature through optimal placement of heat-generating components.

Paperid: 180, https://arxiv.org/pdf/2504.03166.pdf

Abstract:
The rapid advancement of foundation models has revolutionized visual representation learning in a self-supervised manner. However, their application in remote sensing (RS) remains constrained by a fundamental gap: existing models predominantly handle single or limited modalities, overlooking the inherently multi-modal nature of RS observations. Optical, synthetic aperture radar (SAR), and multi-spectral data offer complementary insights that significantly reduce the inherent ambiguity and uncertainty in single-source analysis. To bridge this gap, we introduce RingMoE, a unified multi-modal RS foundation model with 14.7 billion parameters, pre-trained on 400 million multi-modal RS images from nine satellites. RingMoE incorporates three key innovations: (1) A hierarchical Mixture-of-Experts (MoE) architecture comprising modal-specialized, collaborative, and shared experts, effectively modeling intra-modal knowledge while capturing cross-modal dependencies to mitigate conflicts between modal representations; (2) Physics-informed self-supervised learning, explicitly embedding sensor-specific radiometric characteristics into the pre-training objectives; (3) Dynamic expert pruning, enabling adaptive model compression from 14.7B to 1B parameters while maintaining performance, facilitating efficient deployment in Earth observation applications. Evaluated across 23 benchmarks spanning six key RS tasks (i.e., classification, detection, segmentation, tracking, change detection, and depth estimation), RingMoE outperforms existing foundation models and sets new SOTAs, demonstrating remarkable adaptability from single-modal to multi-modal scenarios. Beyond theoretical progress, it has been deployed and trialed in multiple sectors, including emergency response, land management, marine sciences, and urban planning.

Paperid: 181, https://arxiv.org/pdf/2502.12384.pdf

Abstract:
Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs), with growing interest in their energy-efficient, real-time training on edge devices. Photonic computing offers a potential solution to achieve this goal because of its ultra-high operation speed. However, the lack of photonic memory and the large device sizes prevent training real-size PINNs on photonic chips. This paper proposes a completely back-propagation-free (BP-free) and highly salable framework for training real-size PINNs on silicon photonic platforms. Our approach involves three key innovations: (1) a sparse-grid Stein derivative estimator to avoid the BP in the loss evaluation of a PINN, (2) a dimension-reduced zeroth-order optimization via tensor-train decomposition to achieve better scalability and convergence in BP-free training, and (3) a scalable on-chip photonic PINN training accelerator design using photonic tensor cores. We validate our numerical methods on both low- and high-dimensional PDE benchmarks. Through circuit simulation based on real device parameters, we further demonstrate the significant performance benefit (e.g., real-time training, huge chip area reduction) of our photonic accelerator.

Paperid: 182, https://arxiv.org/pdf/2501.00742.pdf

Abstract:
This paper presents a scalable method for friction identification in robots equipped with electric motors and high-ratio harmonic drives, utilizing Physics-Informed Neural Networks (PINN). This approach eliminates the need for dedicated setups and joint torque sensors by leveraging the roboÅ¥s intrinsic model and state data. We present a comprehensive pipeline that includes data acquisition, preprocessing, ground truth generation, and model identification. The effectiveness of the PINN-based friction identification is validated through extensive testing on two different joints of the humanoid robot ergoCub, comparing its performance against traditional static friction models like the Coulomb-viscous and Stribeck-Coulomb-viscous models. Integrating the identified PINN-based friction models into a two-layer torque control architecture enhances real-time friction compensation. The results demonstrate significant improvements in control performance and reductions in energy losses, highlighting the scalability and robustness of the proposed method, also for application across a large number of joints as in the case of humanoid robots.

Paperid: 184, https://arxiv.org/pdf/2511.15870.pdf

Abstract:
Underground pipeline leaks and infiltrations pose significant threats to water security and environmental safety. Traditional manual inspection methods provide limited coverage and delayed response, often missing critical anomalies. This paper proposes AquaSentinel, a novel physics-informed AI system for real-time anomaly detection in urban underground water pipeline networks. We introduce four key innovations: (1) strategic sparse sensor deployment at high-centrality nodes combined with physics-based state augmentation to achieve network-wide observability from minimal infrastructure; (2) the RTCA (Real-Time Cumulative Anomaly) detection algorithm, which employs dual-threshold monitoring with adaptive statistics to distinguish transient fluctuations from genuine anomalies; (3) a Mixture of Experts (MoE) ensemble of spatiotemporal graph neural networks that provides robust predictions by dynamically weighting model contributions; (4) causal flow-based leak localization that traces anomalies upstream to identify source nodes and affected pipe segments. Our system strategically deploys sensors at critical network junctions and leverages physics-based modeling to propagate measurements to unmonitored nodes, creating virtual sensors that enhance data availability across the entire network. Experimental evaluation using 110 leak scenarios demonstrates that AquaSentinel achieves 100% detection accuracy. This work advances pipeline monitoring by demonstrating that physics-informed sparse sensing can match the performance of dense deployments at a fraction of the cost, providing a practical solution for aging urban infrastructure.

Paperid: 185, https://arxiv.org/pdf/2509.24850.pdf

Abstract:
Remote photoplethysmography (rPPG) measurement enables non-contact physiological monitoring but suffers from accuracy degradation under head motion and illumination changes. Existing deep learning methods are mostly heuristic and lack theoretical grounding, which limits robustness and interpretability. In this work, we propose a physics-informed rPPG paradigm derived from the Navier-Stokes equations of hemodynamics, showing that the pulse signal follows a second-order dynamical system whose discrete solution naturally leads to a causal convolution. This provides a theoretical justification for using a Temporal Convolutional Network (TCN). Based on this principle, we design PHASE-Net, a lightweight model with three key components: (1) Zero-FLOPs Axial Swapper module, which swaps or transposes a few spatial channels to mix distant facial regions and enhance cross-region feature interaction without breaking temporal order; (2) Adaptive Spatial Filter, which learns a soft spatial mask per frame to highlight signal-rich areas and suppress noise; and (3) Gated TCN, a causal dilated TCN with gating that models long-range temporal dynamics for accurate pulse recovery. Extensive experiments demonstrate that PHASE-Net achieves state-of-the-art performance with strong efficiency, offering a theoretically grounded and deployment-ready rPPG solution.

Paperid: 186, https://arxiv.org/pdf/2509.20447.pdf

Abstract:
Accretion disks are ubiquitous in astrophysics, appearing in diverse environments from planet-forming systems to X-ray binaries and active galactic nuclei. Traditionally, modeling their dynamics requires computationally intensive (magneto)hydrodynamic simulations. Recently, Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative. This approach trains neural networks directly on physical laws without requiring data. We for the first time demonstrate PINNs for solving the two-dimensional, time-dependent hydrodynamics of non-self-gravitating accretion disks. Our models provide solutions at arbitrary times and locations within the training domain, and successfully reproduce key physical phenomena, including the excitation and propagation of spiral density waves and gap formation from disk-companion interactions. Notably, the boundary-free approach enabled by PINNs naturally eliminates the spurious wave reflections at disk edges, which are challenging to suppress in numerical simulations. These results highlight how advanced machine learning techniques can enable physics-driven, data-free modeling of complex astrophysical systems, potentially offering an alternative to traditional numerical simulations in the future.

Paperid: 187, https://arxiv.org/pdf/2509.15778.pdf

Abstract:
This paper presents a unified framework that integrates modeling, optimization, and sensorless control of an all-electric heavy-duty robotic manipulator (HDRM) driven by electromechanical linear actuators (EMLAs). An EMLA model is formulated to capture motor electromechanics and direction-dependent transmission efficiencies, while a mathematical model of the HDRM, incorporating both kinematics and dynamics, is established to generate joint-space motion profiles for prescribed TCP trajectories. A safety-ensured trajectory generator, tailored to this model, maps Cartesian goals to joint space while enforcing joint-limit and velocity margins. Based on the resulting force and velocity demands, a multi-objective Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to select the optimal EMLA configuration. To accelerate this optimization, a deep neural network, trained with EMLA parameters, is embedded in the optimization process to predict steady-state actuator efficiency from trajectory profiles. For the chosen EMLA design, a physics-informed Kriging surrogate, anchored to the analytic model and refined with experimental data, learns residuals of EMLA outputs to support force and velocity sensorless control. The actuator model is further embedded in a hierarchical virtual decomposition control (VDC) framework that outputs voltage commands. Experimental validation on a one-degree-of-freedom EMLA testbed confirms accurate trajectory tracking and effective sensorless control under varying loads.

Paperid: 188, https://arxiv.org/pdf/2507.08972.pdf

Abstract:
Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically different approach that trains neural networks directly from physical equations rather than data, offering the potential for continuous, mesh-free solutions. Here we show that appropriately designed PINNs can successfully simulate fully turbulent flows in both two and three dimensions, directly learning solutions to the fundamental fluid equations without traditional computational grids or training data. Our approach combines several algorithmic innovations including adaptive network architectures, causal training, and advanced optimization methods to overcome the inherent challenges of learning chaotic dynamics. Through rigorous validation on challenging turbulence problems, we demonstrate that PINNs accurately reproduce key flow statistics including energy spectra, kinetic energy, enstrophy, and Reynolds stresses. Our results demonstrate that neural equation solvers can handle complex chaotic systems, opening new possibilities for continuous turbulence modeling that transcends traditional computational limitations.

Paperid: 189, https://arxiv.org/pdf/2506.09100.pdf

Abstract:
Quantitative magnetic resonance imaging (qMRI) provides tissue-specific parameters vital for clinical diagnosis. Although simultaneous multi-parametric qMRI (MP-qMRI) technologies enhance imaging efficiency, robustly reconstructing qMRI from highly undersampled, high-dimensional measurements remains a significant challenge. This difficulty arises primarily because current reconstruction methods that rely solely on a single prior or physics-informed model to solve the highly ill-posed inverse problem, which often leads to suboptimal results. To overcome this limitation, we propose LoREIN, a novel unsupervised and dual-prior-integrated framework for accelerated 3D MP-qMRI reconstruction. Technically, LoREIN incorporates both low-rank prior and continuity prior via low-rank representation (LRR) and implicit neural representation (INR), respectively, to enhance reconstruction fidelity. The powerful continuous representation of INR enables the estimation of optimal spatial bases within the low-rank subspace, facilitating high-fidelity reconstruction of weighted images. Simultaneously, the predicted multi-contrast weighted images provide essential structural and quantitative guidance, further enhancing the reconstruction accuracy of quantitative parameter maps. Furthermore, our work introduces a zero-shot learning paradigm with broad potential in complex spatiotemporal and high-dimensional image reconstruction tasks, further advancing the field of medical imaging.

Paperid: 190, https://arxiv.org/pdf/2505.08123.pdf

Abstract:
Multi-material decomposition (MMD) enables quantitative reconstruction of tissue compositions in the human body, supporting a wide range of clinical applications. However, traditional MMD typically requires spectral CT scanners and pre-measured X-ray energy spectra, significantly limiting clinical applicability. To this end, various methods have been developed to perform MMD using conventional (i.e., single-energy, SE) CT systems, commonly referred to as SEMMD. Despite promising progress, most SEMMD methods follow a two-step image decomposition pipeline, which first reconstructs monochromatic CT images using algorithms such as FBP, and then performs decomposition on these images. The initial reconstruction step, however, neglects the energy-dependent attenuation of human tissues, introducing severe nonlinear beam hardening artifacts and noise into the subsequent decomposition. This paper proposes JSover, a fundamentally reformulated one-step SEMMD framework that jointly reconstructs multi-material compositions and estimates the energy spectrum directly from SECT projections. By explicitly incorporating physics-informed spectral priors into the SEMMD process, JSover accurately simulates a virtual spectral CT system from SE acquisitions, thereby improving the reliability and accuracy of decomposition. Furthermore, we introduce implicit neural representation (INR) as an unsupervised deep learning solver for representing the underlying material maps. The inductive bias of INR toward continuous image patterns constrains the solution space and further enhances estimation quality. Extensive experiments on both simulated and real CT datasets show that JSover outperforms state-of-the-art SEMMD methods in accuracy and computational efficiency.

Paperid: 191, https://arxiv.org/pdf/2504.16693.pdf

Abstract:
While non-prehensile manipulation (e.g., controlled pushing/poking) constitutes a foundational robotic skill, its learning remains challenging due to the high sensitivity to complex physical interactions involving friction and restitution. To achieve robust policy learning and generalization, we opt to learn a world model of the 3D rigid body dynamics involved in non-prehensile manipulations and use it for model-based reinforcement learning. We propose PIN-WM, a Physics-INformed World Model that enables efficient end-to-end identification of a 3D rigid body dynamical system from visual observations. Adopting differentiable physics simulation, PIN-WM can be learned with only few-shot and task-agnostic physical interaction trajectories. Further, PIN-WM is learned with observational loss induced by Gaussian Splatting without needing state estimation. To bridge Sim2Real gaps, we turn the learned PIN-WM into a group of Digital Cousins via physics-aware randomizations which perturb physics and rendering parameters to generate diverse and meaningful variations of the PIN-WM. Extensive evaluations on both simulation and real-world tests demonstrate that PIN-WM, enhanced with physics-aware digital cousins, facilitates learning robust non-prehensile manipulation skills with Sim2Real transfer, surpassing the Real2Sim2Real state-of-the-arts.

Paperid: 192, https://arxiv.org/pdf/2503.11029.pdf

Abstract:
Spectral bias is a significant phenomenon in neural network training and can be explained by neural tangent kernel (NTK) theory. In this work, we develop the NTK theory for deep neural networks with physics-informed loss, providing insights into the convergence of NTK during initialization and training, and revealing its explicit structure. We find that, in most cases, the differential operators in the loss function do not induce a faster eigenvalue decay rate and stronger spectral bias. Some experimental results are also presented to verify the theory.

Paperid: 193, https://arxiv.org/pdf/2502.00604.pdf

Abstract:
Multi-task learning through composite loss functions is fundamental to modern deep learning, yet optimizing competing objectives remains challenging. We present new theoretical and practical approaches for addressing directional conflicts between loss terms, demonstrating their effectiveness in physics-informed neural networks (PINNs) where such conflicts are particularly challenging to resolve. Through theoretical analysis, we demonstrate how these conflicts limit first-order methods and show that second-order optimization naturally resolves them through implicit gradient alignment. We prove that SOAP, a recently proposed quasi-Newton method, efficiently approximates the Hessian preconditioner, enabling breakthrough performance in PINNs: state-of-the-art results on 10 challenging PDE benchmarks, including the first successful application to turbulent flows with Reynolds numbers up to 10,000, with 2-10x accuracy improvements over existing methods. We also introduce a novel gradient alignment score that generalizes cosine similarity to multiple gradients, providing a practical tool for analyzing optimization dynamics. Our findings establish frameworks for understanding and resolving gradient conflicts, with broad implications for optimization beyond scientific computing.

Paperid: 194, https://arxiv.org/pdf/2410.04818.pdf

Abstract:
The energy transition is driving the integration of large shares of intermittent power sources in the electric power grid. Therefore, addressing the AC optimal power flow (AC-OPF) effectively becomes increasingly essential. The AC-OPF, which is a fundamental optimization problem in power systems, must be solved more frequently to ensure the safe and cost-effective operation of power systems. Due to its non-linear nature, AC-OPF is often solved in its linearized form, despite inherent inaccuracies. Non-linear solvers, such as the interior point method, are typically employed to solve the full OPF problem. However, these iterative methods may not converge for large systems and do not guarantee global optimality. This work explores a physics-informed graph neural network, PINCO, to solve the AC-OPF. We demonstrate that this method provides accurate solutions in a fraction of the computational time when compared to the established non-linear programming solvers. Remarkably, PINCO generalizes effectively across a diverse set of loading conditions in the power system. We show that our method can solve the AC-OPF without violating inequality constraints. Furthermore, it can function both as a solver and as a hybrid universal function approximator. Moreover, the approach can be easily adapted to different power systems with minimal adjustments to the hyperparameters, including systems with multiple generators at each bus. Overall, this work demonstrates an advancement in the field of power system optimization to tackle the challenges of the energy transition. The code and data utilized in this paper are available at https://anonymous.4open.science/r/opf_pinn_iclr-B83E/.

Paperid: 195, https://arxiv.org/pdf/2510.26022.pdf

Abstract:
Multiparametric mapping MRI has become a viable tool for myocardial tissue characterization. However, misalignment between multiparametric maps makes pixel-wise analysis challenging. To address this challenge, we developed a generalizable physics-informed deep-learning model using test-time adaptation to enable group image registration across contrast weighted images acquired from multiple physical models (e.g., a T1 mapping model and T2 mapping model). The physics-informed adaptation utilized the synthetic images from specific physics model as registration reference, allows for transductive learning for various tissue contrast. We validated the model in healthy volunteers with various MRI sequences, demonstrating its improvement for multi-modal registration with a wide range of image contrast variability.

Paperid: 196, https://arxiv.org/pdf/2509.23960.pdf

Abstract:
Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge. Existing approaches based on multi-agent reinforcement learning (MARL), safety filtering, or Model Predictive Control (MPC) either lack strict safety guarantees, suffer from conservatism, or fail to scale effectively. We propose MAD-PINN, a decentralized physics-informed machine learning framework for solving the multi-agent state-constrained optimal control problem (MASC-OCP). Our method leverages an epigraph-based reformulation of SC-OCP to simultaneously capture performance and safety, and approximates its solution via a physics-informed neural network. Scalability is achieved by training the SC-OCP value function on reduced-agent systems and deploying them in a decentralized fashion, where each agent relies only on local observations of its neighbours for decision-making. To further enhance safety and efficiency, we introduce an Hamilton-Jacobi (HJ) reachability-based neighbour selection strategy to prioritize safety-critical interactions, and a receding-horizon policy execution scheme that adapts to dynamic interactions while reducing computational burden. Experiments on multi-agent navigation tasks demonstrate that MAD-PINN achieves superior safety-performance trade-offs, maintains scalability as the number of agents grows, and consistently outperforms state-of-the-art baselines.

Paperid: 197, https://arxiv.org/pdf/2507.00613.pdf

Abstract:
Spin-lattice relaxation time ($T_1$) is an important biomarker in cardiac parametric mapping for characterizing myocardial tissue and diagnosing cardiomyopathies. Conventional Modified Look-Locker Inversion Recovery (MOLLI) acquires 11 breath-hold baseline images with interleaved rest periods to ensure mapping accuracy. However, prolonged scanning can be challenging for patients with poor breathholds, often leading to motion artifacts that degrade image quality. In addition, $T_1$ mapping requires voxel-wise nonlinear fitting to a signal recovery model involving an iterative estimation process. Recent studies have proposed deep-learning approaches for rapid $T_1$ mapping using shortened sequences to reduce acquisition time for patient comfort. Nevertheless, existing methods overlook important physics constraints, limiting interpretability and generalization. In this work, we present an accelerated, end-to-end $T_1$ mapping framework leveraging Physics-Informed Neural Ordinary Differential Equations (ODEs) to model temporal dynamics and address these challenges. Our method achieves high-accuracy $T_1$ estimation from a sparse subset of baseline images and ensures efficient null index estimation at test time. Specifically, we develop a continuous-time LSTM-ODE model to enable selective Look-Locker (LL) data acquisition with arbitrary time lags. Experimental results show superior performance in $T_1$ estimation for both native and post-contrast sequences and demonstrate the strong benefit of our physics-based formulation over direct data-driven $T_1$ priors.

Paperid: 198, https://arxiv.org/pdf/2505.10949.pdf

Abstract:
Physics Informed Neural Networks (PINNs) often exhibit failure modes in which the PDE residual loss converges while the solution error stays large, a phenomenon traditionally blamed on local optima separated from the true solution by steep loss barriers. We challenge this understanding by demonstrate that the real culprit is insufficient arithmetic precision: with standard FP32, the LBFGS optimizer prematurely satisfies its convergence test, freezing the network in a spurious failure phase. Simply upgrading to FP64 rescues optimization, enabling vanilla PINNs to solve PDEs without any failure modes. These results reframe PINN failure modes as precision induced stalls rather than inescapable local minima and expose a three stage training dynamic unconverged, failure, success whose boundaries shift with numerical precision. Our findings emphasize that rigorous arithmetic precision is the key to dependable PDE solving with neural networks.

Paperid: 199, https://arxiv.org/pdf/2504.11045.pdf

Abstract:
As autonomous systems become increasingly prevalent in daily life, ensuring their safety is paramount. Control Barrier Functions (CBFs) have emerged as an effective tool for guaranteeing safety; however, manually designing them for specific applications remains a significant challenge. With the advent of deep learning techniques, recent research has explored synthesizing CBFs using neural networks-commonly referred to as neural CBFs. This paper introduces a novel class of neural CBFs that leverages a physics-inspired neural network framework by incorporating Zubov's Partial Differential Equation (PDE) within the context of safety. This approach provides a scalable methodology for synthesizing neural CBFs applicable to high-dimensional systems. Furthermore, by utilizing reciprocal CBFs instead of zeroing CBFs, the proposed framework allows for the specification of flexible, user-defined safe regions. To validate the effectiveness of the approach, we present case studies on three different systems: an inverted pendulum, autonomous ground navigation, and aerial navigation in obstacle-laden environments.

Paperid: 200, https://arxiv.org/pdf/2503.07070.pdf

Abstract:
In many science and engineering settings, system dynamics are characterized by governing PDEs, and a major challenge is to solve inverse problems (IPs) where unknown PDE parameters are inferred based on observational data gathered under limited budget. Due to the high costs of setting up and running experiments, experimental design (ED) is often done with the help of PDE simulations to optimize for the most informative design parameters to solve such IPs, prior to actual data collection. This process of optimizing design parameters is especially critical when the budget and other practical constraints make it infeasible to adjust the design parameters between trials during the experiments. However, existing experimental design (ED) methods tend to require sequential and frequent design parameter adjustments between trials. Furthermore, they also have significant computational bottlenecks due to the need for complex numerical simulations for PDEs, and do not exploit the advantages provided by physics informed neural networks (PINNs), such as its meshless solutions, differentiability, and amortized training. This work presents PIED, the first ED framework that makes use of PINNs in a fully differentiable architecture to perform continuous optimization of design parameters for IPs for one-shot deployments. PIED overcomes existing methods' computational bottlenecks through parallelized computation and meta-learning of PINN parameter initialization, and proposes novel methods to effectively take into account PINN training dynamics in optimizing the ED parameters. Through experiments based on noisy simulated data and even real world experimental data, we empirically show that given limited observation budget, PIED significantly outperforms existing ED methods in solving IPs, including challenging settings where the inverse parameters are unknown functions rather than just finite-dimensional.

Paperid: 201, https://arxiv.org/pdf/2502.11057.pdf

Abstract:
As autonomous systems become more ubiquitous in daily life, ensuring high performance with guaranteed safety is crucial. However, safety and performance could be competing objectives, which makes their co-optimization difficult. Learning-based methods, such as Constrained Reinforcement Learning (CRL), achieve strong performance but lack formal safety guarantees due to safety being enforced as soft constraints, limiting their use in safety-critical settings. Conversely, formal methods such as Hamilton-Jacobi (HJ) Reachability Analysis and Control Barrier Functions (CBFs) provide rigorous safety assurances but often neglect performance, resulting in overly conservative controllers. To bridge this gap, we formulate the co-optimization of safety and performance as a state-constrained optimal control problem, where performance objectives are encoded via a cost function and safety requirements are imposed as state constraints. We demonstrate that the resultant value function satisfies a Hamilton-Jacobi-Bellman (HJB) equation, which we approximate efficiently using a novel physics-informed machine learning framework. In addition, we introduce a conformal prediction-based verification strategy to quantify the learning errors, recovering a high-confidence safety value function, along with a probabilistic error bound on performance degradation. Through several case studies, we demonstrate the efficacy of the proposed framework in enabling scalable learning of safe and performant controllers for complex, high-dimensional autonomous systems.

Paperid: 202, https://arxiv.org/pdf/2601.09467.pdf

Abstract:
Accurate global medium-range weather forecasting is fundamental to Earth system science. Most existing Transformer-based forecasting models adopt vision-centric architectures that neglect the Earth's spherical geometry and zonal periodicity. In addition, conventional autoregressive training is computationally expensive and limits forecast horizons due to error accumulation. To address these challenges, we propose the Shifted Earth Transformer (Searth Transformer), a physics-informed architecture that incorporates zonal periodicity and meridional boundaries into window-based self-attention for physically consistent global information exchange. We further introduce a Relay Autoregressive (RAR) fine-tuning strategy that enables learning long-range atmospheric evolution under constrained memory and computational budgets. Based on these methods, we develop YanTian, a global medium-range weather forecasting model. YanTian achieves higher accuracy than the high-resolution forecast of the European Centre for Medium-Range Weather Forecasts and performs competitively with state-of-the-art AI models at one-degree resolution, while requiring roughly 200 times lower computational cost than standard autoregressive fine-tuning. Furthermore, YanTian attains a longer skillful forecast lead time for Z500 (10.3 days) than HRES (9 days). Beyond weather forecasting, this work establishes a robust algorithmic foundation for predictive modeling of complex global-scale geophysical circulation systems, offering new pathways for Earth system science.

Paperid: 203, https://arxiv.org/pdf/2512.23056.pdf

Abstract:
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator learning approaches are data-hungry and neglect physics during training. Here, we propose a physics-informed multimodal foundation model (PI-MFM) framework that directly enforces governing equations during pretraining and adaptation. PI-MFM takes symbolic representations of PDEs as the input, and automatically assembles PDE residual losses from the input expression via a vectorized derivative computation. These designs enable any PDE-encoding multimodal foundation model to be trained or adapted with unified physics-informed objectives across equation families. On a benchmark of 13 parametric one-dimensional time-dependent PDE families, PI-MFM consistently outperforms purely data-driven counterparts, especially with sparse labeled spatiotemporal points, partially observed time domains, or few labeled function pairs. Physics losses further improve robustness against noise, and simple strategies such as resampling collocation points substantially improve accuracy. We also analyze the accuracy, precision, and computational cost of automatic differentiation and finite differences for derivative computation within PI-MFM. Finally, we demonstrate zero-shot physics-informed fine-tuning to unseen PDE families: starting from a physics-informed pretrained model, adapting using only PDE residuals and initial/boundary conditions, without any labeled solution data, rapidly reduces test errors to around 1% and clearly outperforms physics-only training from scratch. These results show that PI-MFM provides a practical and scalable path toward data-efficient, transferable PDE solvers.

Paperid: 204, https://arxiv.org/pdf/2511.03113.pdf

Abstract:
Computational antibody design holds immense promise for therapeutic discovery, yet existing generative models are fundamentally limited by two core challenges: (i) a lack of dynamical consistency, which yields physically implausible structures, and (ii) poor generalization due to data scarcity and structural bias. We introduce FP-AbDiff, the first antibody generator to enforce Fokker-Planck Equation (FPE) physics along the entire generative trajectory. Our method minimizes a novel FPE residual loss over the mixed manifold of CDR geometries (R^3 x SO(3)), compelling locally-learned denoising scores to assemble into a globally coherent probability flow. This physics-informed regularizer is synergistically integrated with deep biological priors within a state-of-the-art SE(3)-equivariant diffusion framework. Rigorous evaluation on the RAbD benchmark confirms that FP-AbDiff establishes a new state-of-the-art. In de novo CDR-H3 design, it achieves a mean Root Mean Square Deviation of 0.99 Å when superposing on the variable region, a 25% improvement over the previous state-of-the-art model, AbX, and the highest reported Contact Amino Acid Recovery of 39.91%. This superiority is underscored in the more challenging six-CDR co-design task, where our model delivers consistently superior geometric precision, cutting the average full-chain Root Mean Square Deviation by ~15%, and crucially, achieves the highest full-chain Amino Acid Recovery on the functionally dominant CDR-H3 loop (45.67%). By aligning generative dynamics with physical laws, FP-AbDiff enhances robustness and generalizability, establishing a principled approach for physically faithful and functionally viable antibody design.

Paperid: 205, https://arxiv.org/pdf/2509.01234.pdf

Abstract:
Physics-informed neural networks (PINNs) and neural operators, two leading scientific machine learning (SciML) paradigms, have emerged as powerful tools for solving partial differential equations (PDEs). Although increasing the training sample size generally enhances network performance, it also increases computational costs for physics-informed or data-driven training. To address this trade-off, different sampling strategies have been developed to sample more points in regions with high PDE residuals. However, existing sampling methods are computationally demanding for high-dimensional problems, such as high-dimensional PDEs or operator learning tasks. Here, we propose a residual-based adversarial-gradient moving sample (RAMS) method, which moves samples according to the adversarial gradient direction to maximize the PDE residual via gradient-based optimization. RAMS can be easily integrated into existing sampling methods. Extensive experiments, ranging from PINN applied to high-dimensional PDEs to physics-informed and data-driven operator learning problems, have been conducted to demonstrate the effectiveness of RAMS. Notably, RAMS represents the first efficient adaptive sampling approach for operator learning, marking a significant advancement in the SciML field.

Paperid: 206, https://arxiv.org/pdf/2508.10680.pdf

Abstract:
T2 mapping in fetal brain MRI has the potential to improve characterization of the developing brain, especially at mid-field (0.55T), where T2 decay is slower. However, this is challenging as fetal MRI acquisition relies on multiple motion-corrupted stacks of thick slices, requiring slice-to-volume reconstruction (SVR) to estimate a high-resolution (HR) 3D volume. Currently, T2 mapping involves repeated acquisitions of these stacks at each echo time (TE), leading to long scan times and high sensitivity to motion. We tackle this challenge with a method that jointly reconstructs data across TEs, addressing severe motion. Our approach combines implicit neural representations with a physics-informed regularization that models T2 decay, enabling information sharing across TEs while preserving anatomical and quantitative T2 fidelity. We demonstrate state-of-the-art performance on simulated fetal brain and in vivo adult datasets with fetal-like motion. We also present the first in vivo fetal T2 mapping results at 0.55T. Our study shows potential for reducing the number of stacks per TE in T2 mapping by leveraging anatomical redundancy.

Paperid: 207, https://arxiv.org/pdf/2505.18365.pdf

Abstract:
Magnetic resonance (MR) tagging is an imaging technique for noninvasively tracking tissue motion in vivo by creating a visible pattern of magnetization saturation (tags) that deforms with the tissue. Due to longitudinal relaxation and progression to steady-state, the tags and tissue brightnesses change over time, which makes tracking with optical flow methods error-prone. Although Fourier methods can alleviate these problems, they are also sensitive to brightness changes as well as spectral spreading due to motion. To address these problems, we introduce the brightness-invariant tracking estimation (BRITE) technique for tagged MRI. BRITE disentangles the anatomy from the tag pattern in the observed tagged image sequence and simultaneously estimates the Lagrangian motion. The inherent ill-posedness of this problem is addressed by leveraging the expressive power of denoising diffusion probabilistic models to represent the probabilistic distribution of the underlying anatomy and the flexibility of physics-informed neural networks to estimate biologically-plausible motion. A set of tagged MR images of a gel phantom was acquired with various tag periods and imaging flip angles to demonstrate the impact of brightness variations and to validate our method. The results show that BRITE achieves more accurate motion and strain estimates as compared to other state of the art methods, while also being resistant to tag fading.

Paperid: 208, https://arxiv.org/pdf/2505.09260.pdf

Abstract:
We present a hybrid quantum-classical electrostatic Particle-in-Cell (PIC) method, where the electrostatic field Poisson solver is implemented on a quantum computer simulator using a hybrid classical-quantum Neural Network (HNN) using data-driven and physics-informed learning approaches. The HNN is trained on classical PIC simulation results and executed via a PennyLane quantum simulator. The remaining computational steps, including particle motion and field interpolation, are performed on a classical system. To evaluate the accuracy and computational cost of this hybrid approach, we test the hybrid quantum-classical electrostatic PIC against the two-stream instability, a standard benchmark in plasma physics. Our results show that the quantum Poisson solver achieves comparable accuracy to classical methods. It also provides insights into the feasibility of using quantum computing and HNNs for plasma simulations. We also discuss the computational overhead associated with current quantum computer simulators, showing the challenges and potential advantages of hybrid quantum-classical numerical methods.

Paperid: 209, https://arxiv.org/pdf/2503.06994.pdf

Abstract:
General-sum differential games can approximate values solved by Hamilton-Jacobi-Isaacs (HJI) equations for efficient inference when information is incomplete. However, solving such games through conventional methods encounters the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a scalable approach to alleviate the CoD and approximate values, but there exist convergence issues for value approximations through vanilla PINNs when state constraints lead to values with large Lipschitz constants, particularly in safety-critical applications. In addition to addressing CoD, it is necessary to learn a generalizable value across a parametric space of games, rather than training multiple ones for each specific player-type configuration. To overcome these challenges, we propose a Hybrid Neural Operator (HNO), which is an operator that can map parameter functions for games to value functions. HNO leverages informative supervised data and samples PDE-driven data across entire spatial-temporal space for model refinement. We evaluate HNO on 9D and 13D scenarios with nonlinear dynamics and state constraints, comparing it against a Supervised Neural Operator (a variant of DeepONet). Under the same computational budget and training data, HNO outperforms SNO for safety performance. This work provides a step toward scalable and generalizable value function approximation, enabling real-time inference for complex human-robot or multi-agent interactions.

Paperid: 210, https://arxiv.org/pdf/2502.00162.pdf

Abstract:
Koopman operator theory provides a powerful data-driven technique for modeling nonlinear dynamical systems in a linear framework, in comparison to computationally expensive and highly nonlinear physics-based simulations. However, Koopman operator-based models for soft robots are very high dimensional and require considerable amounts of data to properly resolve. Inspired by physics-informed techniques from machine learning, we present a novel physics-informed Koopman operator identification method that improves simulation accuracy for small dataset sizes. Through Strang splitting, the method takes advantage of both continuous and discrete Koopman operator approximation to obtain information both from trajectory and phase space data. The method is validated on a tendon-driven soft robotic arm, showing orders of magnitude improvement over standard methods in terms of the shape error. We envision this method can significantly reduce the data requirement of Koopman operators for systems with partially known physical models, and thus reduce the cost of obtaining data.

Paperid: 211, https://arxiv.org/pdf/2501.03432.pdf

Abstract:
The Large Hadron Collider at CERN produces immense volumes of complex data from high-energy particle collisions, demanding sophisticated analytical techniques for effective interpretation. Neural Networks, including Graph Neural Networks, have shown promise in tasks such as event classification and object identification by representing collisions as graphs. However, while Graph Neural Networks excel in predictive accuracy, their "black box" nature often limits their interpretability, making it difficult to trust their decision-making processes. In this paper, we propose a novel approach that combines a Graph Transformer model with Mixture-of-Expert layers to achieve high predictive performance while embedding interpretability into the architecture. By leveraging attention maps and expert specialization, the model offers insights into its internal decision-making, linking predictions to physics-informed features. We evaluate the model on simulated events from the ATLAS experiment, focusing on distinguishing rare Supersymmetric signal events from Standard Model background. Our results highlight that the model achieves competitive classification accuracy while providing interpretable outputs that align with known physics, demonstrating its potential as a robust and transparent tool for high-energy physics data analysis. This approach underscores the importance of explainability in machine learning methods applied to high energy physics, offering a path toward greater trust in AI-driven discoveries.

Paperid: 212, https://arxiv.org/pdf/2411.06842.pdf

Abstract:
Fetal brain tissue segmentation in magnetic resonance imaging (MRI) is a crucial tool that supports understanding of neurodevelopment, yet it faces challenges due to the heterogeneity of data coming from different scanners and settings, as well as data scarcity. Recent approaches based on domain randomization, like SynthSeg, have shown great potential for single-source domain generalization by simulating images with randomized contrast and image resolution from the label maps. In this work, we investigate how to maximize the out-of-domain (OOD) generalization potential of SynthSegbased methods in fetal brain MRI. Specifically, we demonstrate that the simple Gaussian mixture models employed in FetalSynthSeg outperform physics-informed generation methods in terms of OOD generalization. We further show that incorporating intensity clustering significantly enhances generalization in settings with limited label classes by producing more realistic synthetic data. By combining synthetic pretraining with fine-tuning on real images and applying weight-space interpolation between the two models, we propose DRIFTS as an effective and practical solution for single-source domain generalization. DRIFTS consistently outperforms current state-of-the-art models across multiple benchmarks and is, to our knowledge, the first method to achieve accurate brain tissue segmentation on fetal T1-weighted images. We validate our approach on 308 subjects from four datasets acquired at three different sites, covering a range of scanner field strengths (0.55T to 3T) and both T1w and T2w modalities. We conclude with five practical recommendations to guide the development of SynthSeg-based methods for other organs and imaging modalities.

Paperid: 213, https://arxiv.org/pdf/2511.12055.pdf

Abstract:
In this work, we propose the frequency-guided physics-informed neural networks (FG-PINNs), specifically designed for solving partial differential equations (PDEs) with high-frequency components. The proposed algorithm relies on prior knowledge about high-frequency components obtained from PDEs. It aims to use this prior knowledge to guide the neural network in rapidly approximating the solution's high-frequency components. The FG-PINNs consist of two subnetworks, including a high-frequency subnetwork for capturing high-frequency components and a low-frequency subnetwork for capturing low-frequency components. The key innovation in the high-frequency subnetworks is to embed prior knowledge for high-frequency components into the network structure. For nonhomogeneous PDEs ($f(x)\neq c, c\in R$), we embed the source term as an additional feature into the neural network. The source term typically contains partial or complete frequency information of the target solution, particularly its high-frequency components. This provides prior knowledge about the high-frequency components of the target solution. For homogeneous PDEs, we embed the initial/boundary conditions with high-frequency components into the neural network. Based on spectral bias, we use a fully connected neural network as the low-frequency subnetwork to capture low-frequency components of the target solution. A series of numerical examples demonstrate the effectiveness of the FG-PINNs, including the one-dimensional heat equation (relative $L^{2}$ error: $O(10^{-4})$), the nonlinear wave equations (relative $L^{2}$ error: $O(10^{-4})$) and the two-dimensional heat equation (relative $L^{2}$ error: $O(10^{-3})$).

Paperid: 214, https://arxiv.org/pdf/2511.00886.pdf

Abstract:
We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a single-hidden layer neural network with randomized heat-kernels arising from the fundamental solution (Green's functions) of the heat operator, that we call HEATNET, that provides an unbiased universal approximator to the solution of parabolic PDEs in arbitrary (high) dimensions, with the rate of convergence being analogous to the ${O}(N^{-1/2})$, where $N$ is the size of HEATNET. Thus, HEATNETs are explainable schemes, based on the analytical framework of parabolic PDEs, exploiting insights from physics-informed neural networks aided by numerical and functional analysis, and the structure of the corresponding solution operators. Importantly, we show how HEATNETs can be scaled up for the efficient numerical solution of arbitrary high-dimensional parabolic PDEs using suitable transformations and importance Monte Carlo sampling of the integral representation of the solution, in order to deal with the singularities of the heat kernel around the collocation points. We evaluate the performance of HEATNETs through benchmark linear parabolic problems up to 2,000 dimensions. We show that HEATNETs result in remarkable accuracy with the order of the approximation error ranging from $1.0E-05$ to $1.0E-07$ for problems up to 500 dimensions, and of the order of $1.0E-04$ to $1.0E-03$ for 1,000 to 2,000 dimensions, with a relatively low number (up to 15,000) of features.

Paperid: 215, https://arxiv.org/pdf/2511.00117.pdf

Abstract:
The increasing energy demands and carbon footprint of large-scale AI require intelligent workload management in globally distributed data centers. Yet progress is limited by the absence of benchmarks that realistically capture the interplay of time-varying environmental factors (grid carbon intensity, electricity prices, weather), detailed data center physics (CPUs, GPUs, memory, HVAC energy), and geo-distributed network dynamics (latency and transmission costs). To bridge this gap, we present DCcluster-Opt: an open-source, high-fidelity simulation benchmark for sustainable, geo-temporal task scheduling. DCcluster-Opt combines curated real-world datasets, including AI workload traces, grid carbon intensity, electricity markets, weather across 20 global regions, cloud transmission costs, and empirical network delay parameters with physics-informed models of data center operations, enabling rigorous and reproducible research in sustainable computing. It presents a challenging scheduling problem where a top-level coordinating agent must dynamically reassign or defer tasks that arrive with resource and service-level agreement requirements across a configurable cluster of data centers to optimize multiple objectives. The environment also models advanced components such as heat recovery. A modular reward system enables an explicit study of trade-offs among carbon emissions, energy costs, service level agreements, and water use. It provides a Gymnasium API with baseline controllers, including reinforcement learning and rule-based strategies, to support reproducible ML research and a fair comparison of diverse algorithms. By offering a realistic, configurable, and accessible testbed, DCcluster-Opt accelerates the development and validation of next-generation sustainable computing solutions for geo-distributed data centers.

Paperid: 216, https://arxiv.org/pdf/2510.23140.pdf

Abstract:
Tracer kinetic modeling serves a vital role in diagnosis, treatment planning, tracer development and oncology, but burdens practitioners with complex and invasive arterial input function estimation (AIF). We adopt a physics-informed CycleGAN showing promise in DCE-MRI quantification to dynamic PET quantification. Our experiments demonstrate sound AIF predictions and parameter maps closely resembling the reference.

Paperid: 217, https://arxiv.org/pdf/2506.18332.pdf

Abstract:
Inspired by the attention mechanism, we develop an attention-enhanced physics-informed neural networks (AE-PINNs) for solving elliptic interface equations. In AE-PINNs, we decompose the solution into two complementary components: a continuous component and a component with discontinuities across the interface. The continuous component is approximated by a fully connected neural network in the whole domain, while the discontinuous component is approximated by an interface-attention neural network in each subdomain separated by the interface. The interface-attention neural network adopts a network structure similar to the attention mechanism to focus on the interface, with its key extension is to introduce a neural network that transmits interface information. Some numerical experiments have confirmed the effectiveness of the AE-PINNs, demonstrating higher accuracy compared with PINNs, I-PINNs and M-PINNs.

Paperid: 218, https://arxiv.org/pdf/2506.17654.pdf

Abstract:
This paper proposes a rank inspired neural network (RINN) to tackle the initialization sensitivity issue of physics informed extreme learning machines (PIELM) when numerically solving partial differential equations (PDEs). Unlike PIELM which randomly initializes the parameters of its hidden layers, RINN incorporates a preconditioning stage. In this stage, covariance-driven regularization is employed to optimize the orthogonality of the basis functions generated by the last hidden layer. The key innovation lies in minimizing the off-diagonal elements of the covariance matrix derived from the hidden-layer output. By doing so, pairwise orthogonality constraints across collocation points are enforced which effectively enhances both the numerical stability and the approximation ability of the optimized function space.The RINN algorithm unfolds in two sequential stages. First, it conducts a non-linear optimization process to orthogonalize the basis functions. Subsequently, it solves the PDE constraints using linear least-squares method. Extensive numerical experiments demonstrate that RINN significantly reduces performance variability due to parameter initialization compared to PIELM. Incorporating an early stopping mechanism based on PDE loss further improves stability, ensuring consistently high accuracy across diverse initialization settings.

Paperid: 219, https://arxiv.org/pdf/2504.14174.pdf

Abstract:
This position paper argues that the next generation of artificial intelligence in meteorological and climate sciences must transition from fragmented hybrid heuristics toward a unified paradigm of physics-guided multimodal transformers. While purely data-driven models have achieved significant gains in predictive accuracy, they often treat atmospheric processes as mere visual patterns, frequently producing results that lack scientific consistency or violate fundamental physical laws. We contend that current ``hybrid'' attempts to bridge this gap remain ad-hoc and struggle to scale across the heterogeneous nature of meteorological data ranging from satellite imagery to sparse sensor measurements. We argue that the transformer architecture, through its inherent capacity for cross-modal alignment, provides the only viable foundation for a systematic integration of domain knowledge via physical constraint embedding and physics-informed loss functions. By advocating for this unified architectural shift, we aim to steer the community away from ``black-box'' curve fitting and toward AI systems that are inherently falsifiable, scientifically grounded, and robust enough to address the existential challenges of extreme weather and climate change.

Paperid: 220, https://arxiv.org/pdf/2502.14432.pdf

Abstract:
Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering systems is often challenged by practical issues, including the presence of external inputs, dissipation, and noisy measurements. This paper introduces a novel framework that enhances the capabilities of HNNs to address these real-life factors. We integrate port-Hamiltonian theory into the neural network structure, allowing for the inclusion of external inputs and dissipation, while mitigating the impact of measurement noise through an output-error (OE) model structure. The resulting output error port-Hamiltonian neural networks (OE-pHNNs) can be adapted to tackle modeling complex engineering systems with noisy measurements. Furthermore, we propose the identification of OE-pHNNs based on the subspace encoder approach (SUBNET), which efficiently approximates the complete simulation loss using subsections of the data and uses an encoder function to predict initial states. By integrating SUBNET with OE-pHNNs, we achieve consistent models of complex engineering systems under noisy measurements. In addition, we perform a consistency analysis to ensure the reliability of the proposed data-driven model learning method. We demonstrate the effectiveness of our approach on system identification benchmarks, showing its potential as a powerful tool for modeling dynamic systems in real-world applications.

Paperid: 221, https://arxiv.org/pdf/2501.09935.pdf

Abstract:
Diffusion model shows remarkable potential on sparse-view computed tomography (SVCT) reconstruction. However, when a network is trained on a limited sample space, its generalization capability may be constrained, which degrades performance on unfamiliar data. For image generation tasks, this can lead to issues such as blurry details and inconsistencies between regions. To alleviate this problem, we propose a Sinogram-based Wavelet random decomposition And Random mask diffusion Model (SWARM) for SVCT reconstruction. Specifically, introducing a random mask strategy in the sinogram effectively expands the limited training sample space. This enables the model to learn a broader range of data distributions, enhancing its understanding and generalization of data uncertainty. In addition, applying a random training strategy to the high-frequency components of the sinogram wavelet enhances feature representation and improves the ability to capture details in different frequency bands, thereby improving performance and robustness. Two-stage iterative reconstruction method is adopted to ensure the global consistency of the reconstructed image while refining its details. Experimental results demonstrate that SWARM outperforms competing approaches in both quantitative and qualitative performance across various datasets.

Paperid: 222, https://arxiv.org/pdf/2412.00527.pdf

Abstract:
In this work we develop a novel algorithm, termed as mixed least-squares deep neural network (MLS-DNN), to recover an anisotropic conductivity tensor from the internal measurements of the solutions. It is based on applying the least-squares formulation to the mixed form of the elliptic problem, and approximating the internal flux and conductivity tensor simultaneously using deep neural networks. We provide error bounds on the approximations obtained via both population and empirical losses. The analysis relies on the canonical source condition, approximation theory of deep neural networks and statistical learning theory. We also present multiple numerical experiments to illustrate the performance of the method, and conduct a comparative study with the standard Galerkin finite element method and physics informed neural network. The results indicate that the method can accurately recover the anisotropic conductivity in both two- and three-dimensional cases, up to 10\% noise in the data.

Paperid: 223, https://arxiv.org/pdf/2410.14477.pdf

Abstract:
Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov semigroup. The unbounded nature of IGs complicates traditional methods such as vector-valued regression and Hilbert-Schmidt operator analysis. Existing techniques, including physics-informed kernel regression, are computationally expensive and limited in scope, with no recovery guarantees for transfer operator methods when the time-lag is small. We propose a novel method that leverages the IG's resolvent, characterized by the Laplace transform of transfer operators. This approach is robust to time-lag variations, ensuring accurate eigenvalue learning even for small time-lags. Our statistical analysis applies to a broader class of Markov processes than current methods while reducing computational complexity from quadratic to linear in the state dimension. Finally, we illustrate the behaviour of our method in two experiments.

Paperid: 224, https://arxiv.org/pdf/2601.05528.pdf

Abstract:
Combinatorial materials libraries are an efficient route to generate large families of candidate compositions, but their impact is often limited by the speed and depth of characterization and by the difficulty of extracting actionable structure-property relations from complex characterization data. Here we develop an autonomous scanning probe microscopy (SPM) framework that integrates automated atomic force and magnetic force microscopy (AFM/MFM) to rapidly explore magnetic and structural properties across combinatorial spread libraries. To enable automated exploration of systems without a clear optimization target, we introduce a combination of a static physics-informed bag-of-features (BoF) representation of measured surface morphology and magnetic structure with multi-objective Bayesian optimization (MOBO) to discover the relative significance and robustness of features. The resulting closed-loop workflow selectively samples the compositional gradient and reconstructs feature landscapes consistent with dense grid "ground truth" measurements. The resulting Pareto structure reveals where multiple nanoscale objectives are simultaneously optimized, where trade-offs between roughness, coherence, and magnetic contrast are unavoidable, and how families of compositions cluster into distinct functional regimes, thereby turning multi-feature imaging data into interpretable maps of competing structure-property trends. While demonstrated for Au-Co-Ni and AFM/MFM, the approach is general and can be extended to other combinatorial systems, imaging modalities, and feature sets, illustrating how feature-based MOBO and autonomous SPM can transform microscopy images from static data products into active feedback for real-time, multi-objective materials discovery.

Paperid: 225, https://arxiv.org/pdf/2601.03086.pdf

Abstract:
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics informed pretraining stage and an optional finetuning stage. In the pretraining stage, a neural operator based on the Transolver architecture is trained solely from governing partial differential equations, without relying on labeled solution data. The model operates directly on unstructured point clouds, jointly encoding geometric information, material properties, and boundary conditions, and produces physically consistent initial solutions with extremely high computational efficiency. PDE constraints are enforced through explicit finite element, based differentiation, avoiding the overhead associated with automatic differentiation. In the fine-tuning stage, the pretrained prediction is used as an initial guess for conventional FEM solvers, preserving their accuracy, convergence guarantees, and extrapolation capability while substantially reducing the number of iterations required to reach a prescribed tolerance. PFEM is validated on a broad range of benchmark problems, including linear elasticity and nonlinear hyperelasticity with complex geometries, heterogeneous materials, and arbitrary boundary conditions. Numerical results demonstrate strong generalization in the pretraining stage with relative errors on the order of 1\%, and speedups of up to one order of magnitude in the fine-tuning stage compared to FEM with zero initial guesses.

Paperid: 226, https://arxiv.org/pdf/2511.06948.pdf

Abstract:
Attenuation artifacts remain a significant challenge in cardiac Myocardial Perfusion Imaging (MPI) using Single-Photon Emission Computed Tomography (SPECT), often compromising diagnostic accuracy and reducing clinical interpretability. While hybrid SPECT/CT systems mitigate these artifacts through CT-derived attenuation maps, their high cost, limited accessibility, and added radiation exposure hinder widespread clinical adoption. In this study, we propose a novel CT-free solution to attenuation correction in cardiac SPECT. Specifically, we introduce Physics-aware Attenuation Correction Diffusion Model (PADM), a diffusion-based generative method that incorporates explicit physics priors via a teacher--student distillation mechanism. This approach enables attenuation artifact correction using only Non-Attenuation-Corrected (NAC) input, while still benefiting from physics-informed supervision during training. To support this work, we also introduce CardiAC, a comprehensive dataset comprising 424 patient studies with paired NAC and Attenuation-Corrected (AC) reconstructions, alongside high-resolution CT-based attenuation maps. Extensive experiments demonstrate that PADM outperforms state-of-the-art generative models, delivering superior reconstruction fidelity across both quantitative metrics and visual assessment.

Paperid: 227, https://arxiv.org/pdf/2510.20293.pdf

Abstract:
Movable antenna (MA) technology provides a promising avenue for actively shaping wireless channels through dynamic antenna positioning, thereby enabling electromagnetic radiation reconstruction to enhance physical layer security (PLS). However, its practical deployment is hindered by two major challenges: the high computational complexity of real time optimization and a critical temporal mismatch between slow mechanical movement and rapid channel variations. Although data driven methods have been introduced to alleviate online optimization burdens, they are still constrained by suboptimal training labels derived from conventional solvers or high sample complexity in reinforcement learning. More importantly, existing learning based approaches often overlook communication-specific domain knowledge, particularly the asymmetric roles and adversarial interactions between legitimate users and eavesdroppers, which are fundamental to PLS. To address these issues, this paper reformulates the MA positioning problem as a predictive task and introduces RoleAware-MAPP, a novel Transformer based framework that incorporates domain knowledge through three key components: role-aware embeddings that model user specific intentions, physics-informed semantic features that encapsulate channel propagation characteristics, and a composite loss function that strategically prioritizes secrecy performance over mere geometric accuracy. Extensive simulations under 3GPP-compliant scenarios show that RoleAware-MAPP achieves an average secrecy rate of 0.3569 bps/Hz and a strictly positive secrecy capacity of 81.52%, outperforming the strongest baseline by 48.4% and 5.39 percentage points, respectively, while maintaining robust performance across diverse user velocities and noise conditions.

Paperid: 228, https://arxiv.org/pdf/2510.09995.pdf

Abstract:
Lens flare occurs when shooting towards strong light sources, significantly degrading the visual quality of images. Due to the difficulty in capturing flare-corrupted and flare-free image pairs in the real world, existing datasets are typically synthesized in 2D by overlaying artificial flare templates onto background images. However, the lack of flare diversity in templates and the neglect of physical principles in the synthesis process hinder models trained on these datasets from generalizing well to real-world scenarios. To address these challenges, we propose a new physics-informed method for flare data generation, which consists of three stages: parameterized template creation, the laws of illumination-aware 2D synthesis, and physical engine-based 3D rendering, which finally gives us a mixed flare dataset that incorporates both 2D and 3D perspectives, namely FlareX. This dataset offers 9,500 2D templates derived from 95 flare patterns and 3,000 flare image pairs rendered from 60 3D scenes. Furthermore, we design a masking approach to obtain real-world flare-free images from their corrupted counterparts to measure the performance of the model on real-world images. Extensive experiments demonstrate the effectiveness of our method and dataset.

Paperid: 229, https://arxiv.org/pdf/2509.22411.pdf

Abstract:
The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle distribution functions (PDFs). Despite its success, solving the LBE numerically remains computationally intensive due to strict time-step restrictions imposed by collision kernels. Here, we introduce a physics-informed neural operator framework for the LBE that enables prediction over large time horizons without step-by-step integration, effectively bypassing the need to explicitly solve the collision kernel. We incorporate intrinsic moment-matching constraints of the LBE, along with global equivariance of the full distribution field, enabling the model to capture the complex dynamics of the underlying kinetic system. Our framework is discretization-invariant, enabling models trained on coarse lattices to generalise to finer ones (kinetic super-resolution). In addition, it is agnostic to the specific form of the underlying collision model, which makes it naturally applicable across different kinetic datasets regardless of the governing dynamics. Our results demonstrate robustness across complex flow scenarios, including von Karman vortex shedding, ligament breakup, and bubble adhesion. This establishes a new data-driven pathway for modelling kinetic systems.

Paperid: 230, https://arxiv.org/pdf/2507.16008.pdf

Abstract:
Physics-informed neural networks (PINNs) have gained prominence in recent years and are now effectively used in a number of applications. However, their performance remains unstable due to the complex landscape of the loss function. To address this issue, we reformulate PINN training as a nonconvex-strongly concave saddle-point problem. After establishing the theoretical foundation for this approach, we conduct an extensive experimental study, evaluating its effectiveness across various tasks and architectures. Our results demonstrate that the proposed method outperforms the current state-of-the-art techniques.

Paperid: 231, https://arxiv.org/pdf/2506.13961.pdf

Abstract:
Analysis of nonlinear autonomous systems typically involves estimating domains of attraction, which have been a topic of extensive research interest for decades. Despite that, accurately estimating domains of attraction for nonlinear systems remains a challenging task, where existing methods are conservative or limited to low-dimensional systems. The estimation becomes even more challenging when accounting for state constraints. In this work, we propose a framework to accurately estimate safe (state-constrained) domains of attraction for discrete-time autonomous nonlinear systems. In establishing this framework, we first derive a new Zubov equation, whose solution corresponds to the exact safe domain of attraction. The solution to the aforementioned Zubov equation is shown to be unique and continuous over the whole state space. We then present a physics-informed approach to approximating the solution of the Zubov equation using neural networks. To obtain certifiable estimates of the domain of attraction from the neural network approximate solutions, we propose a verification framework that can be implemented using standard verification tools (e.g., $Î±,\!Î²$-CROWN and dReal). To illustrate its effectiveness, we demonstrate our approach through numerical examples concerning nonlinear systems with state constraints.

Paperid: 232, https://arxiv.org/pdf/2505.16373.pdf

Abstract:
Panchromatic (PAN) -assisted Dual-Camera Compressive Hyperspectral Imaging (DCCHI) is a key technology in snapshot hyperspectral imaging. Existing research primarily focuses on exploring spectral information from 2D compressive measurements and spatial information from PAN images in an explicit manner, leading to a bottleneck in HSI reconstruction. Various physical factors, such as temperature, emissivity, and multiple reflections between objects, play a critical role in the process of a sensor acquiring hyperspectral thermal signals. Inspired by this, we attempt to investigate the interrelationships between physical properties to provide deeper theoretical insights for HSI reconstruction. In this paper, we propose a Physics-Informed Cross-Modal State Space Model Network (PCMamba) for DCCHI, which incorporates the forward physical imaging process of HSI into the linear complexity of Mamba to facilitate lightweight and high-quality HSI reconstruction. Specifically, we analyze the imaging process of hyperspectral thermal signals to enable the network to disentangle the three key physical properties-temperature, emissivity, and texture. By fully exploiting the potential information embedded in 2D measurements and PAN images, the HSIs are reconstructed through a physics-driven synthesis process. Furthermore, we design a Cross-Modal Scanning Mamba Block (CSMB) that introduces inter-modal pixel-wise interaction with positional inductive bias by cross-scanning the backbone features and PAN features. Extensive experiments conducted on both real and simulated datasets demonstrate that our method significantly outperforms SOTA methods in both quantitative and qualitative metrics.

Paperid: 233, https://arxiv.org/pdf/2502.00782.pdf

Abstract:
AI for PDEs has garnered significant attention, particularly Physics-Informed Neural Networks (PINNs). However, PINNs are typically limited to solving specific problems, and any changes in problem conditions necessitate retraining. Therefore, we explore the generalization capability of transfer learning in the strong and energy form of PINNs across different boundary conditions, materials, and geometries. The transfer learning methods we employ include full finetuning, lightweight finetuning, and Low-Rank Adaptation (LoRA). The results demonstrate that full finetuning and LoRA can significantly improve convergence speed while providing a slight enhancement in accuracy.

Paperid: 234, https://arxiv.org/pdf/2501.12053.pdf

Abstract:
Solving partial differential equations (PDEs) using neural methods has been a long-standing scientific and engineering research pursuit. Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative to traditional numerical methods for solving PDEs. However, the gap between domain-specific knowledge and deep learning expertise often limits the practical application of PINNs. Previous works typically involve manually conducting extensive PINNs experiments and summarizing heuristic rules for hyperparameter tuning. In this work, we introduce PINNsAgent, a novel surrogation framework that leverages large language models (LLMs) and utilizes PINNs as a foundation to bridge the gap between domain-specific knowledge and deep learning. Specifically, PINNsAgent integrates (1) Physics-Guided Knowledge Replay (PGKR), which encodes the essential characteristics of PDEs and their associated best-performing PINNs configurations into a structured format, enabling efficient knowledge transfer from solved PDEs to similar problems and (2) Memory Tree Reasoning, a strategy that effectively explores the search space for optimal PINNs architectures. By leveraging LLMs and exploration strategies, PINNsAgent enhances the automation and efficiency of PINNs-based solutions. We evaluate PINNsAgent on 14 benchmark PDEs, demonstrating its effectiveness in automating the surrogation process and significantly improving the accuracy of PINNs-based solutions.

Paperid: 235, https://arxiv.org/pdf/2412.08681.pdf

Abstract:
Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.

Paperid: 236, https://arxiv.org/pdf/2410.19843.pdf

Abstract:
In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields, especially integrating artificial intelligence and traditional science (AI for Science: Artificial intelligence for science), which has attracted widespread attention. In AI for Science, using artificial intelligence algorithms to solve partial differential equations (AI for PDEs: Artificial intelligence for partial differential equations) has become a focal point in computational mechanics. The core of AI for PDEs is the fusion of data and partial differential equations (PDEs), which can solve almost any PDEs. Therefore, this article provides a comprehensive review of the research on AI for PDEs, summarizing the existing algorithms and theories. The article discusses the applications of AI for PDEs in computational mechanics, including solid mechanics, fluid mechanics, and biomechanics. The existing AI for PDEs algorithms include those based on Physics-Informed Neural Networks (PINNs), Deep Energy Methods (DEM), Operator Learning, and Physics-Informed Neural Operator (PINO). AI for PDEs represents a new method of scientific simulation that provides approximate solutions to specific problems using large amounts of data, then fine-tuning according to specific physical laws, avoiding the need to compute from scratch like traditional algorithms. Thus, AI for PDEs is the prototype for future foundation models in computational mechanics, capable of significantly accelerating traditional numerical algorithms.

Paperid: 237, https://arxiv.org/pdf/2601.21363.pdf

Abstract:
Reinforcement learning (RL) is widely used for humanoid control, with on-policy methods such as Proximal Policy Optimization (PPO) enabling robust training via large-scale parallel simulation and, in some cases, zero-shot deployment to real robots. However, the low sample efficiency of on-policy algorithms limits safe adaptation to new environments. Although off-policy RL and model-based RL have shown improved sample efficiency, the gap between large-scale pretraining and efficient finetuning on humanoids still exists. In this paper, we find that off-policy Soft Actor-Critic (SAC), with large-batch update and a high Update-To-Data (UTD) ratio, reliably supports large-scale pretraining of humanoid locomotion policies, achieving zero-shot deployment on real robots. For adaptation, we demonstrate that these SAC-pretrained policies can be finetuned in new environments and out-of-distribution tasks using model-based methods. Data collection in the new environment executes a deterministic policy while stochastic exploration is instead confined to a physics-informed world model. This separation mitigates the risks of random exploration during adaptation while preserving exploratory coverage for improvement. Overall, the approach couples the wall-clock efficiency of large-scale simulation during pretraining with the sample efficiency of model-based learning during fine-tuning.

Paperid: 238, https://arxiv.org/pdf/2601.21284.pdf

Abstract:
Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be followed. This paper proposes Physics-Informed Learning via Diffusion (PILD), a framework that unifies diffusion modeling and first-principles physical constraints by introducing a virtual residual observation sampled from a Laplace distribution to supervise generation during training. To further integrate physical laws, a conditional embedding module is incorporated to inject physical information into the denoising network at multiple layers, ensuring consistent guidance throughout the diffusion process. The proposed PILD framework is concise, modular, and broadly applicable to problems governed by ordinary differential equations, partial differential equations, as well as algebraic equations or inequality constraints. Extensive experiments across engineering and scientific tasks including estimating vehicle trajectories, tire forces, Darcy flow and plasma dynamics, demonstrate that our PILD substantially improves accuracy, stability, and generalization over existing physics-informed and diffusion-based baselines.

Paperid: 239, https://arxiv.org/pdf/2510.17270.pdf

Abstract:
Grey-box methods for system identification combine deep learning with physics-informed constraints, capturing complex dependencies while improving out-of-distribution generalization. Yet, despite the growing importance of floating-base systems such as humanoids and quadrupeds, current grey-box models ignore their specific physical constraints. For instance, the inertia matrix is not only positive definite but also exhibits branch-induced sparsity and input independence. Moreover, the 6x6 composite spatial inertia of the floating base inherits properties of single-rigid-body inertia matrices. As we show, this includes the triangle inequality on the eigenvalues of the composite rotational inertia. To address the lack of physical consistency in deep learning models of floating-base systems, we introduce a parameterization of inertia matrices that satisfies all these constraints. Inspired by Deep Lagrangian Networks (DeLaN), we train neural networks to predict physically plausible inertia matrices that minimize inverse dynamics error under Lagrangian mechanics. For evaluation, we collected and released a dataset on multiple quadrupeds and humanoids. In these experiments, our Floating-Base Deep Lagrangian Networks (FeLaN) achieve highly competitive performance on both simulated and real robots, while providing greater physical interpretability.

Paperid: 240, https://arxiv.org/pdf/2509.24801.pdf

Abstract:
A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence.

Paperid: 241, https://arxiv.org/pdf/2509.13386.pdf

Abstract:
Demands for software-defined vehicles (SDV) are rising and electric vehicles (EVs) are increasingly being equipped with powerful computers. This enables onboard AI systems to optimize charge-aware path optimization customized to reflect vehicle's current condition and environment. We present VEGA, a charge-aware EV navigation agent that plans over a charger-annotated road graph using Proximal Policy Optimization (PPO) with budgeted A* teacher-student guidance under state-of-charge (SoC) feasibility. VEGA consists of two modules. First, a physics-informed neural operator (PINO), trained on real vehicle speed and battery-power logs, uses recent vehicle speed logs to estimate aerodynamic drag, rolling resistance, mass, motor and regenerative-braking efficiencies, and auxiliary load by learning a vehicle-custom dynamics. Second, a Reinforcement Learning (RL) agent uses these dynamics to optimize a path with optimal charging stops and dwell times under SoC constraints. VEGA requires no additional sensors and uses only vehicle speed signals. It may serve as a virtual sensor for power and efficiency to potentially reduce EV cost. In evaluation on long routes like San Francisco to New York, VEGA's stops, dwell times, SoC management, and total travel time closely track Tesla Trip Planner while being slightly more conservative, presumably due to real vehicle conditions such as vehicle parameter drift due to deterioration. Although trained only in U.S. regions, VEGA was able to compute optimal charge-aware paths in France and Japan, demonstrating generalizability. It achieves practical integration of physics-informed learning and RL for EV eco-routing.

Paperid: 242, https://arxiv.org/pdf/2509.09183.pdf

Abstract:
Low-light Object detection is crucial for many real-world applications but remains challenging due to degraded image quality. While recent studies have shown that RAW images offer superior potential over RGB images, existing approaches either use RAW-RGB images with information loss or employ complex frameworks. To address these, we propose a lightweight and self-adaptive Image Signal Processing (ISP) plugin, Dark-ISP, which directly processes Bayer RAW images in dark environments, enabling seamless end-to-end training for object detection. Our key innovations are: (1) We deconstruct conventional ISP pipelines into sequential linear (sensor calibration) and nonlinear (tone mapping) sub-modules, recasting them as differentiable components optimized through task-driven losses. Each module is equipped with content-aware adaptability and physics-informed priors, enabling automatic RAW-to-RGB conversion aligned with detection objectives. (2) By exploiting the ISP pipeline's intrinsic cascade structure, we devise a Self-Boost mechanism that facilitates cooperation between sub-modules. Through extensive experiments on three RAW image datasets, we demonstrate that our method outperforms state-of-the-art RGB- and RAW-based detection approaches, achieving superior results with minimal parameters in challenging low-light environments.

Paperid: 243, https://arxiv.org/pdf/2508.14807.pdf

Abstract:
Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

Paperid: 244, https://arxiv.org/pdf/2508.12602.pdf

Abstract:
We present a hybrid surrogate model for electric vehicle parameter estimation and power consumption. We combine our novel architecture Spectral Parameter Operator built on a Fourier Neural Operator backbone for global context and a differentiable physics module in the forward pass. From speed and acceleration alone, it outputs time-varying motor and regenerative braking efficiencies, as well as aerodynamic drag, rolling resistance, effective mass, and auxiliary power. These parameters drive a physics-embedded estimate of battery power, eliminating any separate physics-residual loss. The modular design lets representations converge to physically meaningful parameters that reflect the current state and condition of the vehicle. We evaluate on real-world logs from a Tesla Model 3, Tesla Model S, and the Kia EV9. The surrogate achieves a mean absolute error of 0.2kW (about 1% of average traction power at highway speeds) for Tesla vehicles and about 0.8kW on the Kia EV9. The framework is interpretable, and it generalizes well to unseen conditions, and sampling rates, making it practical for path optimization, eco-routing, on-board diagnostics, and prognostics health management.

Paperid: 245, https://arxiv.org/pdf/2506.18295.pdf

Abstract:
Neural ray tracing (RT) has emerged as a promising paradigm for channel modeling by combining physical propagation principles with neural networks. It enables high modeling accuracy and efficiency. However, current neural RT methods face two key limitations: constrained generalization capability due to strong spatial dependence, and weak adherence to electromagnetic laws. In this paper, we propose GeNeRT, a Generalizable Neural RT framework with enhanced generalization, accuracy and efficiency. GeNeRT supports both intra-scenario spatial transferability and inter-scenario zero-shot generalization. By incorporating Fresnel-inspired neural network design, it also achieves higher accuracy in multipath component (MPC) prediction. Furthermore, a GPU-tensorized acceleration strategy is introduced to improve runtime efficiency. Extensive experiments conducted in outdoor scenarios demonstrate that GeNeRT generalizes well across untrained regions within a scenario and entirely unseen environments, and achieves superior accuracy in MPC prediction compared to baselines. Moreover, it outperforms Wireless Insite in runtime efficiency, particularly in multi-transmitter settings. Ablation experiments validate the effectiveness of the network architecture and training strategy in capturing physical principles of ray-surface interactions.

Paperid: 246, https://arxiv.org/pdf/2506.08043.pdf

Abstract:
Fast and accurate simulation of soft tissue deformation is a critical factor for surgical robotics and medical training. In this paper, we introduce a novel physics-informed neural simulator that approximates soft tissue deformations in a realistic and real-time manner. Our framework integrates Kelvinlet-based priors into neural simulators, making it the first approach to leverage Kelvinlets for residual learning and regularization in data-driven soft tissue modeling. By incorporating large-scale Finite Element Method (FEM) simulations of both linear and nonlinear soft tissue responses, our method improves neural network predictions across diverse architectures, enhancing accuracy and physical consistency while maintaining low latency for real-time performance. We demonstrate the effectiveness of our approach by performing accurate surgical maneuvers that simulate the use of standard laparoscopic tissue grasping tools with high fidelity. These results establish Kelvinlet-augmented learning as a powerful and efficient strategy for real-time, physics-aware soft tissue simulation in surgical applications.

Paperid: 247, https://arxiv.org/pdf/2505.14555.pdf

Abstract:
Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization. We propose PhyDL-NWP, a physics-guided deep learning framework that integrates physical equations with latent force parameterization into data-driven models. It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics. PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170x faster inference with only 55K parameters. Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.

Paperid: 248, https://arxiv.org/pdf/2503.19333.pdf

Abstract:
Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify uncertainty in these networks. While approaches such as Bayesian PINNs (B-PINNs) provide a principled approach to capturing uncertainty through Bayesian inference, they can be computationally expensive for large-scale applications. In this work, we propose Epistemic Physics-Informed Neural Networks (E-PINNs), a framework that leverages a small network, the \emph{epinet}, to efficiently quantify uncertainty in PINNs. The proposed approach works as an add-on to existing, pre-trained PINNs with a small computational overhead. We demonstrate the applicability of the proposed framework in various test cases and compare the results with B-PINNs using Hamiltonian Monte Carlo (HMC) posterior estimation and dropout-equipped PINNs (Dropout-PINNs). Our experiments show that E-PINNs provide similar coverage to B-PINNs, with often comparable sharpness, while being computationally more efficient. This observation, combined with E-PINNs' more consistent uncertainty estimates and better calibration compared to Dropout-PINNs for the examples presented, indicates that E-PINNs offer a promising approach in terms of accuracy-efficiency trade-off.

Paperid: 249, https://arxiv.org/pdf/2503.06320.pdf

Abstract:
We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty is giving appropriate initial conditions or initial guesses, to which the widely used time-marching schemes and Newton's iteration method are very sensitive in finding solutions for complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first reveal that PINNs, when combined with random initialization and deep ensemble method -- originally developed for uncertainty quantification -- can effectively uncover multiple solutions to nonlinear ordinary and partial differential equations (ODEs/PDEs). Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen-Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear differential equations.

Paperid: 250, https://arxiv.org/pdf/2411.14691.pdf

Abstract:
An onboard prediction of dynamic parameters (e.g. Aerodynamic drag, rolling resistance) enables accurate path planning for EVs. This paper presents EV-PINN, a Physics-Informed Neural Network approach in predicting instantaneous battery power and cumulative energy consumption during cruising while generalizing to the nonlinear dynamics of an EV. Our method learns real-world parameters such as motor efficiency, regenerative braking efficiency, vehicle mass, coefficient of aerodynamic drag, and coefficient of rolling resistance using automatic differentiation based on dynamics and ensures consistency with ground truth vehicle data. EV-PINN was validated using 15 and 35 minutes of in-situ battery log data from the Tesla Model 3 Long Range and Tesla Model S, respectively. With only vehicle speed and time as inputs, our model achieves high accuracy and generalization to dynamics, with validation losses of 0.002195 and 0.002292, respectively. This demonstrates EV-PINN's effectiveness in estimating parameters and predicting battery usage under actual driving conditions without the need for additional sensors.

Paperid: 251, https://arxiv.org/pdf/2411.06651.pdf

Abstract:
Accurately characterizing migration velocity models is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional velocity model building methods such as Full-Waveform Inversion (FWI) are powerful but often struggle with the inherent complexities of the inverse problem, including noise, limited bandwidth, receiver aperture and computational constraints. To address these challenges, we propose a scalable methodology that integrates generative modeling, in the form of Diffusion networks, with physics-informed summary statistics, making it suitable for complicated imaging problems including field datasets. By defining these summary statistics in terms of subsurface-offset image volumes for poor initial velocity models, our approach allows for computationally efficient generation of Bayesian posterior samples for migration velocity models that offer a useful assessment of uncertainty. To validate our approach, we introduce a battery of tests that measure the quality of the inferred velocity models, as well as the quality of the inferred uncertainties. With modern synthetic datasets, we reconfirm gains from using subsurface-image gathers as the conditioning observable. For complex velocity model building involving salt, we propose a new iterative workflow that refines amortized posterior approximations with salt flooding and demonstrate how the uncertainty in the velocity model can be propagated to the final product reverse time migrated images. Finally, we present a proof of concept on field datasets to show that our method can scale to industry-sized problems.

Paperid: 252, https://arxiv.org/pdf/2411.06286.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov-Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov-Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Paperid: 253, https://arxiv.org/pdf/2410.14764.pdf

Abstract:
We develop a method for multifidelity Kolmogorov-Arnold networks (KANs), which use a low-fidelity model along with a small amount of high-fidelity data to train a model for the high-fidelity data accurately. Multifidelity KANs (MFKANs) reduce the amount of expensive high-fidelity data needed to accurately train a KAN by exploiting the correlations between the low- and high-fidelity data to give accurate and robust predictions in the absence of a large high-fidelity dataset. In addition, we show that multifidelity KANs can be used to increase the accuracy of physics-informed KANs (PIKANs), without the use of training data.

Paperid: 254, https://arxiv.org/pdf/2410.13228.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Finally, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Paperid: 255, https://arxiv.org/pdf/2410.06442.pdf

Abstract:
Large language models (LLMs), like ChatGPT, have shown that even trained with noisy prior data, they can generalize effectively to new tasks through in-context learning (ICL) and pre-training techniques. Motivated by this, we explore whether a similar approach can be applied to scientific foundation models (SFMs). Our methodology is structured as follows: (i) we collect low-cost physics-informed neural network (PINN)-based approximated prior data in the form of solutions to partial differential equations (PDEs) constructed through an arbitrary linear combination of mathematical dictionaries; (ii) we utilize Transformer architectures with self and cross-attention mechanisms to predict PDE solutions without knowledge of the governing equations in a zero-shot setting; (iii) we provide experimental evidence on the one-dimensional convection-diffusion-reaction equation, which demonstrate that pre-training remains robust even with approximated prior data, with only marginal impacts on test accuracy. Notably, this finding opens the path to pre-training SFMs with realistic, low-cost data instead of (or in conjunction with) numerical high-cost data. These results support the conjecture that SFMs can improve in a manner similar to LLMs, where fully cleaning the vast set of sentences crawled from the Internet is nearly impossible.

Paperid: 256, https://arxiv.org/pdf/2410.04001.pdf

Abstract:
We introduce Sparse Physics Informed Backpropagation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Rank Neural Representation (LRNR). The approach exploits the low rank structure within LRNR and constructs a reduced neural network approximation that is much smaller in size. We call the smaller network FastLRNR. We show that backpropagation of FastLRNR can be substituted for that of LRNR, enabling a significant reduction in complexity. We apply SPInProp to a physics informed neural networks framework and demonstrate how the solution of parametrized partial differential equations is accelerated.

Paperid: 257, https://arxiv.org/pdf/2409.03005.pdf

Abstract:
Self-supervised learning is a powerful approach for developing traversability models for off-road navigation, but these models often struggle with inputs unseen during training. Existing methods utilize techniques like evidential deep learning to quantify model uncertainty, helping to identify and avoid out-of-distribution terrain. However, always avoiding out-of-distribution terrain can be overly conservative, e.g., when novel terrain can be effectively analyzed using a physics-based model. To overcome this challenge, we introduce Physics-Informed Evidential Traversability (PIETRA), a self-supervised learning framework that integrates physics priors directly into the mathematical formulation of evidential neural networks and introduces physics knowledge implicitly through an uncertainty-aware, physics-informed training loss. Our evidential network seamlessly transitions between learned and physics-based predictions for out-of-distribution inputs. Additionally, the physics-informed loss regularizes the learned model, ensuring better alignment with the physics model. Extensive simulations and hardware experiments demonstrate that PIETRA improves both learning accuracy and navigation performance in environments with significant distribution shifts.

Paperid: 258, https://arxiv.org/pdf/2601.21570.pdf

Abstract:
The field of Embodied AI is witnessing a rapid evolution toward general-purpose robotic systems, fueled by high-fidelity simulation and large-scale data collection. However, this scaling capability remains severely bottlenecked by a reliance on labor-intensive manual oversight from intricate reward shaping to hyperparameter tuning across heterogeneous backends. Inspired by LLMs' success in software automation and science discovery, we introduce \textsc{EmboCoach-Bench}, a benchmark evaluating the capacity of LLM agents to autonomously engineer embodied policies. Spanning 32 expert-curated RL and IL tasks, our framework posits executable code as the universal interface. We move beyond static generation to assess a dynamic closed-loop workflow, where agents leverage environment feedback to iteratively draft, debug, and optimize solutions, spanning improvements from physics-informed reward design to policy architectures such as diffusion policies. Extensive evaluations yield three critical insights: (1) autonomous agents can qualitatively surpass human-engineered baselines by 26.5\% in average success rate; (2) agentic workflow with environment feedback effectively strengthens policy development and substantially narrows the performance gap between open-source and proprietary models; and (3) agents exhibit self-correction capabilities for pathological engineering cases, successfully resurrecting task performance from near-total failures through iterative simulation-in-the-loop debugging. Ultimately, this work establishes a foundation for self-evolving embodied intelligence, accelerating the paradigm shift from labor-intensive manual tuning to scalable, autonomous engineering in embodied AI field.

Paperid: 259, https://arxiv.org/pdf/2511.09475.pdf

Abstract:
Solar energetic particle (SEP) events, as one of the most prominent manifestations of solar activity, can generate severe hazardous radiation when accelerated by solar flares or shock waves formed aside from coronal mass ejections (CMEs). However, most existing data-driven methods used for SEP predictions are operated as black-box models, making it challenging for solar physicists to interpret the results and understand the underlying physical causes of such events rather than just obtain a prediction. To address this challenge, we propose a novel framework that integrates global explanations and ad-hoc feature mapping to enhance model transparency and provide deeper insights into the decision-making process. We validate our approach using a dataset of 341 SEP events, including 244 significant (>=10 MeV) proton events exceeding the Space Weather Prediction Center S1 threshold, spanning solar cycles 22, 23, and 24. Furthermore, we present an explainability-focused case study of major SEP events, demonstrating how our method improves explainability and facilitates a more physics-informed understanding of SEP event prediction.

Paperid: 260, https://arxiv.org/pdf/2511.05629.pdf

Abstract:
Sea Surface Temperature (SST) is crucial for understanding upper-ocean thermal dynamics and ocean-atmosphere interactions, which have profound economic and social impacts. While data-driven models show promise in SST prediction, their black-box nature often limits interpretability and overlooks key physical processes. Recently, physics-informed neural networks have been gaining momentum but struggle with complex ocean-atmosphere dynamics due to 1) inadequate characterization of seawater movement (e.g., coastal upwelling) and 2) insufficient integration of external SST drivers (e.g., turbulent heat fluxes). To address these challenges, we propose SSTODE, a physics-informed Neural Ordinary Differential Equations (Neural ODEs) framework for SST prediction. First, we derive ODEs from fluid transport principles, incorporating both advection and diffusion to model ocean spatiotemporal dynamics. Through variational optimization, we recover a latent velocity field that explicitly governs the temporal dynamics of SST. Building upon ODE, we introduce an Energy Exchanges Integrator (EEI)-inspired by ocean heat budget equations-to account for external forcing factors. Thus, the variations in the components of these factors provide deeper insights into SST dynamics. Extensive experiments demonstrate that SSTODE achieves state-of-the-art performances in global and regional SST forecasting benchmarks. Furthermore, SSTODE visually reveals the impact of advection dynamics, thermal diffusion patterns, and diurnal heating-cooling cycles on SST evolution. These findings demonstrate the model's interpretability and physical consistency.

Paperid: 261, https://arxiv.org/pdf/2510.12335.pdf

Abstract:
Electric Vehicles (EVs) offer substantial flexibility for grid services, yet large-scale, uncoordinated charging can threaten voltage stability in distribution networks. Existing Reinforcement Learning (RL) approaches for smart charging often disregard physical grid constraints or have limited performance for complex large-scale tasks, limiting their scalability and real-world applicability. This paper introduces a physics-informed (PI) RL algorithm that integrates a differentiable power flow model and voltage-based reward design into the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, enabling EVs to deliver real-time voltage support while meeting user demands. The resulting PI-TD3 algorithm achieves faster convergence, improved sample efficiency, and reliable voltage magnitude regulation under uncertain and overloaded conditions. Benchmarks on the IEEE 34-bus and 123-bus networks show that the proposed PI-TD3 outperforms both model-free RL and optimization-based baselines in grid constraint management, user satisfaction, and economic metrics, even as the system scales to hundreds of EVs. These advances enable robust, scalable, and practical EV charging strategies that enhance grid resilience and support distribution networks operation.

Paperid: 262, https://arxiv.org/pdf/2509.07634.pdf

Abstract:
This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly integrate partially known physics-based models, improving parameter estimation and overall model accuracy. The proposed method enhances traditional modeling approaches by integrating a parametric model, which provides physical interpretability, with a kernel-based function, which accounts for unmodelled dynamics. The two model's components are identified from data simultaneously, minimizing a suitable cost that balances the relative importance of the physical and the black-box parts of the model. Additionally, nonlinear state smoothing is employed to address scenarios involving state-space models with not fully measurable states. Numerical simulations on an experimental benchmark system demonstrate the effectiveness of the proposed approach, with performance comparisons against state-of-the-art identification techniques.

Paperid: 263, https://arxiv.org/pdf/2507.22493.pdf

Abstract:
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the input to a high-dimensional latent representation, enabling uncertainty-aware prediction of the solution. Specifically, the architecture consists of a confidence-aware encoder and a probabilistic decoder. The encoder implements a high-dimensional latent variable model based on a Gaussian process (LVM-GP), where the latent representation is constructed by interpolating between a learnable deterministic feature and a Gaussian process prior, with the interpolation strength adaptively controlled by a confidence function learned from data. The decoder defines a conditional Gaussian distribution over the solution field, where the mean is predicted by a neural operator applied to the latent representation, allowing the model to learn flexible function-to-function mapping. Moreover, physical laws are enforced as soft constraints in the loss function to ensure consistency with the underlying PDE structure. Compared to existing approaches such as Bayesian physics-informed neural networks (B-PINNs) and deep ensembles, the proposed framework can efficiently capture functional dependencies via merging a latent Gaussian process and neural operator, resulting in competitive predictive accuracy and robust uncertainty quantification. Numerical experiments demonstrate the effectiveness and reliability of the method.

Paperid: 264, https://arxiv.org/pdf/2502.20772.pdf

Abstract:
State estimation for Multi-Input Multi-Output (MIMO) systems with noise, such as vehicle chassis systems, presents a significant challenge due to the imperfect and complex relationship between inputs and outputs. To solve this problem, we design a Damper characteristics-based Bayesian Physics-Informed Neural Network (Damper-B-PINN). First, we introduce a neuron forward process inspired by the mechanical properties of dampers, which limits abrupt jumps in neuron values between epochs while maintaining search capability. Additionally, we apply an optimized Bayesian dropout layer to the MIMO system to enhance robustness against noise and prevent non-convergence issues. Physical information is incorporated into the loss function to serve as a physical prior for the neural network. The effectiveness of our Damper-B-PINN architecture is then validated across ten datasets and fourteen vehicle types, demonstrating superior accuracy, computational efficiency, and convergence in vehicle state estimation (i.e., dynamic wheel load) compared to other state-of-the-art benchmarks.

Paperid: 265, https://arxiv.org/pdf/2502.11382.pdf

Abstract:
Accurate blur estimation is essential for high-performance imaging across various applications. Blur is typically represented by the point spread function (PSF). In this paper, we propose a physics-informed PSF learning framework for imaging systems, consisting of a simple calibration followed by a learning process. Our framework could achieve both high accuracy and universal applicability. Inspired by the Seidel PSF model for representing spatially varying PSF, we identify its limitations in optimization and introduce a novel wavefront-based PSF model accompanied by an optimization strategy, both reducing optimization complexity and improving estimation accuracy. Moreover, our wavefront-based PSF model is independent of lens parameters, eliminate the need for prior knowledge of the lens. To validate our approach, we compare it with recent PSF estimation methods (Degradation Transfer and Fast Two-step) through a deblurring task, where all the estimated PSFs are used to train state-of-the-art deblurring algorithms. Our approach demonstrates improvements in image quality in simulation and also showcases noticeable visual quality improvements on real captured images.

Paperid: 266, https://arxiv.org/pdf/2502.04719.pdf

Abstract:
Deep optics has emerged as a promising approach by co-designing optical elements with deep learning algorithms. However, current research typically overlooks the analysis and optimization of manufacturing and assembly tolerances. This oversight creates a significant performance gap between designed and fabricated optical systems. To address this challenge, we present the first end-to-end tolerance-aware optimization framework that incorporates multiple tolerance types into the deep optics design pipeline. Our method combines physics-informed modelling with data-driven training to enhance optical design by accounting for and compensating for structural deviations in manufacturing and assembly. We validate our approach through computational imaging applications, demonstrating results in both simulations and real-world experiments. We further examine how our proposed solution improves the robustness of optical systems and vision algorithms against tolerances through qualitative and quantitative analyses. Code and additional visual results are available at openimaginglab.github.io/LensTolerance.

Paperid: 267, https://arxiv.org/pdf/2501.12654.pdf

Abstract:
Off-road navigation is essential for a wide range of applications in field robotics such as planetary exploration and disaster response. However, it remains an unresolved challenge due to the unstructured environments and inherent complexity of terrain-vehicle interactions. Traditional physics-based methods struggle to accurately model the nonlinear dynamics of these interactions, while data-driven approaches often suffer from overfitting to specific motion patterns, vehicle sizes, and types, limiting their generalizability. To overcome these challenges, we introduce a vision-based friction estimation framework grounded in neuro-symbolic principles, integrating neural networks for visual perception with symbolic reasoning for physical modeling. This enables significantly improved generalization abilities through explicit physical reasoning incorporating the predicted friction. Additionally, we develop a physics-informed planner that leverages the learned friction coefficient to generate physically feasible and efficient paths, along with corresponding speed profiles. We refer to our approach as AnyNav and evaluate it in both simulation and real-world experiments, demonstrating its utility and robustness across various off-road scenarios and multiple types of four-wheeled vehicles. These results mark an important step toward developing neuro-symbolic spatial intelligence to reason about complex, unstructured environments and enable autonomous off-road navigation in challenging scenarios. Video demonstrations are available at https://sairlab.org/anynav/, where the source code will also be released.

Paperid: 268, https://arxiv.org/pdf/2501.01000.pdf

Abstract:
Flight test analysis often requires predefined test points with arbitrarily tight tolerances, leading to extensive and resource-intensive experimental campaigns. To address this challenge, we propose a novel approach to flight test analysis using Gaussian processes (GPs) with physics-informed mean functions to estimate aerodynamic quantities from arbitrary flight test data, validated using real T-38 aircraft data collected in collaboration with the United States Air Force Test Pilot School. We demonstrate our method by estimating the pitching moment coefficient without requiring predefined or repeated flight test points, significantly reducing the need for extensive experimental campaigns. Our approach incorporates aerodynamic models as priors within the GP framework, enhancing predictive accuracy across diverse flight conditions and providing robust uncertainty quantification. Key contributions include the integration of physics-based priors in a probabilistic model, which allows for precise computation from arbitrary flight test maneuvers, and the demonstration of our method capturing relevant dynamic characteristics such as short-period mode behavior. The proposed framework offers a scalable and generalizable solution for efficient data-driven flight test analysis and is able to accurately predict the short period frequency and damping for the T-38 across several Mach and dynamic pressure profiles.

Paperid: 269, https://arxiv.org/pdf/2412.07637.pdf

Abstract:
Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC literature, which is given by the linear interpolation in the space of energies. Inspired by Sequential Monte Carlo, we alternate between deterministic time steps from the TT representation of the flow field and stochastic steps, which include Langevin and resampling steps. These adjust the relative weights of the different modes of the target distribution and anneal to the correct path distribution. We showcase the efficiency of our method on multiple numerical examples.

Paperid: 270, https://arxiv.org/pdf/2411.14214.pdf

Abstract:
LLM-based autonomous agents have demonstrated outstanding performance in solving complex industrial tasks. However, in the pursuit of carbon neutrality and high-performance renewable energy systems, existing AI-assisted design automation faces significant limitations in explainability, scalability, and usability. To address these challenges, we propose LP-COMDA, an LLM-based, physics-informed autonomous agent that automates the modulation design of power converters in Power Electronics Systems with minimal human supervision. Unlike traditional AI-assisted approaches, LP-COMDA contains an LLM-based planner that gathers and validates design specifications through a user-friendly chat interface. The planner then coordinates with physics-informed design and optimization tools to iteratively generate and refine modulation designs autonomously. Through the chat interface, LP-COMDA provides an explainable design process, presenting explanations and charts. Experiments show that LP-COMDA outperforms all baseline methods, achieving a 63.2% reduction in error compared to the second-best benchmark method in terms of standard mean absolute error. Furthermore, empirical studies with 20 experts conclude that design time with LP-COMDA is over 33 times faster than conventional methods, showing its significant improvement on design efficiency over the current processes.

Paperid: 271, https://arxiv.org/pdf/2409.18423.pdf

Abstract:
Perceiving the global field from sparse sensors has been a grand challenge in the monitoring, analysis, and design of physical systems. In this context, sensor placement optimization is a crucial issue. Most existing works require large and sufficient data to construct data-based criteria, which are intractable in data-free scenarios without numerical and experimental data. To this end, we propose a novel physics-driven sensor placement optimization (PSPO) method for temperature field reconstruction using a physics-based criterion to optimize sensor locations. In our methodological framework, we firstly derive the theoretical upper and lower bounds of the reconstruction error under noise scenarios by analyzing the optimal solution, proving that error bounds correlate with the condition number determined by sensor locations. Furthermore, the condition number, as the physics-based criterion, is used to optimize sensor locations by the genetic algorithm. Finally, the best sensors are validated by reconstruction models, including non-invasive end-to-end models, non-invasive reduced-order models, and physics-informed models. Experimental results, both on a numerical and an application case, demonstrate that the PSPO method significantly outperforms random and uniform selection methods, improving the reconstruction accuracy by nearly an order of magnitude. Moreover, the PSPO method can achieve comparable reconstruction accuracy to the existing data-driven placement optimization methods.

Paperid: 272, https://arxiv.org/pdf/2601.01462.pdf

Abstract:
We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity constraints, and standard neural network approximations do not naturally enforce the associated spectral boundary conditions. To address this challenge, we introduce a spectrally-defined mollification strategy that preserves the structure of the nonlocal operator while ensuring boundary compatibility. This enables the derivation of rigorous energy estimates in Sobolev spaces. Our results rely on analytical tools from PDE theory, highlighting the compatibility of PINN approximations with classical energy estimates for nonlocal equations. We prove convergence of the PINN approximation in any space-time Sobolev norm $H^k$ (with $k \in \N)$. The analysis highlights the role of mollified residuals in enabling theoretical guarantees for neural-network-based solvers of nonlocal PDEs.

Paperid: 273, https://arxiv.org/pdf/2510.15400.pdf

Abstract:
Clinical adoption of multi-shot diffusion-weighted magnetic resonance imaging (multi-shot DWI) for body-wide tumor diagnostics is limited by severe motion-induced phase artifacts from respiration, peristalsis, and so on, compounded by multi-organ, multi-slice, multi-direction and multi-b-value complexities. Here, we introduce a reconstruction framework, LoSP-Prompt, that overcomes these challenges through physics-informed modeling and synthetic-data-driven prompt learning. We model inter-shot phase variations as a high-order Locally Smooth Phase (LoSP), integrated into a low-rank Hankel matrix reconstruction. Crucially, the algorithm's rank parameter is automatically set via prompt learning trained exclusively on synthetic abdominal DWI data emulating physiological motion. Validated across 10,000+ clinical images (43 subjects, 4 scanner models, 5 centers), LoSP-Prompt: (1) Achieved twice the spatial resolution of clinical single-shot DWI, enhancing liver lesion conspicuity; (2) Generalized to seven diverse anatomical regions (liver, kidney, sacroiliac, pelvis, knee, spinal cord, brain) with a single model; (3) Outperformed state-of-the-art methods in image quality, artifact suppression, and noise reduction (11 radiologists' evaluations on a 5-point scale, $p<0.05$), achieving 4-5 points (excellent) on kidney DWI, 4 points (good to excellent) on liver, sacroiliac and spinal cord DWI, and 3-4 points (good) on knee and tumor brain. The approach eliminates navigator signals and realistic data supervision, providing an interpretable, robust solution for high-resolution multi-organ multi-shot DWI. Its scanner-agnostic performance signifies transformative potential for precision oncology.

Paperid: 274, https://arxiv.org/pdf/2510.08924.pdf

Abstract:
We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt to the intrinsic features of the unknown solution. Drawing inspiration from classical mesh refinement techniques, we also modify the domain decomposition on-the-fly throughout training by introducing new subdomains in regions of high residual loss, thereby providing additional expressive power where the solution of the differential equation is challenging to represent. Our flexible approach to domain decomposition is well-suited for multiscale problems, as different subdomains can learn to capture different scales of the underlying solution. Moreover, the ability to introduce new subdomains during training helps prevent convergence to unwanted local minima and can reduce the need for extensive hyperparameter tuning compared to static domain decomposition approaches. Throughout, we present comprehensive numerical results which demonstrate the effectiveness of AB-PINNs at solving a variety of complex multiscale partial differential equations.

Paperid: 275, https://arxiv.org/pdf/2510.02982.pdf

Abstract:
Deep learning (DL) has demonstrated promise for accelerating and enhancing the accuracy of flow physics simulations, but progress is constrained by the scarcity of high-fidelity training data, which is costly to generate and inherently limited to a small set of flow conditions. Consequently, closures trained in the conventional offline paradigm tend to overfit and fail to generalise to new regimes. We introduce an online optimisation framework for DL-based Reynolds-averaged Navier--Stokes (RANS) closures which seeks to address the challenge of limited high-fidelity datasets. Training data is dynamically generated by embedding a direct numerical simulation (DNS) within a subdomain of the RANS domain. The RANS solution supplies boundary conditions to the DNS, while the DNS provides mean velocity and turbulence statistics that are used to update a DL closure model during the simulation. This feedback loop enables the closure to adapt to the embedded DNS target flow, avoiding reliance on precomputed datasets and improving out-of-distribution performance. The approach is demonstrated for the stochastically forced Burgers equation and for turbulent channel flow at $Re_τ=180$, $270$, $395$ and $590$ with varying embedded domain lengths $1\leq L_0/L\leq 8$. Online-optimised RANS models significantly outperform both offline-trained and literature-calibrated closures, with accurate training achieved using modest DNS subdomains. Performance degrades primarily when boundary-condition contamination dominates or when domains are too short to capture low-wavenumber modes. This framework provides a scalable route to physics-informed machine learning closures, enabling data-adaptive reduced-order models that generalise across flow regimes without requiring large precomputed training datasets.

Paperid: 276, https://arxiv.org/pdf/2510.01206.pdf

Abstract:
Efficient molecular dynamics (MD) simulation is vital for understanding atomic-scale processes in materials science and biophysics. Traditional density functional theory (DFT) methods are computationally expensive, which limits the feasibility of long-term simulations. We propose a novel approach that formulates MD simulation as a time-series forecasting problem, enabling advanced forecasting models to predict atomic trajectories via displacements rather than absolute positions. We incorporate a physics-informed loss and inference mechanism based on DFT-parametrised pair-wise Morse potential functions that penalize unphysical atomic proximity to enforce physical plausibility. Our method consistently surpasses standard baselines in simulation accuracy across diverse materials. The results highlight the importance of incorporating physics knowledge to enhance the reliability and precision of atomic trajectory forecasting. Remarkably, it enables stable modeling of thousands of MD steps in minutes, offering a scalable alternative to costly DFT simulations.

Paperid: 277, https://arxiv.org/pdf/2508.19052.pdf

Abstract:
Graph Neural Networks (GNNs) have deeply modified the landscape of numerical simulations by demonstrating strong capabilities in approximating solutions of physical systems. However, their ability to extrapolate beyond their training domain (\textit{e.g.} larger or structurally different graphs) remains uncertain. In this work, we establish that GNNs can serve purposes beyond their traditional role, and be exploited to generate numerical schemes, in conjunction with symbolic regression. First, we show numerically and theoretically that a GNN trained on a dataset consisting solely of two-node graphs can extrapolate a first-order Finite Volume (FV) scheme for the heat equation on out-of-distribution, unstructured meshes. Specifically, if a GNN achieves a loss $\varepsilon$ on such a dataset, it implements the FV scheme with an error of $\mathcal{O}(\varepsilon)$. Using symbolic regression, we show that the network effectively rediscovers the exact analytical formulation of the standard first-order FV scheme. We then extend this approach to an unsupervised context: the GNN recovers the first-order FV scheme using only a residual loss similar to Physics-Informed Neural Networks (PINNs) with no access to ground-truth data. Finally, we push the methodology further by considering higher-order schemes: we train (i) a 2-hop and (ii) a 2-layers GNN using the same PINN loss, that autonomously discover (i) a second-order correction term to the initial scheme using a 2-hop stencil, and (ii) the classic second-order midpoint scheme. These findings follows a recent paradigm in scientific computing: GNNs are not only strong approximators, but can be active contributors to the development of novel numerical methods.

Paperid: 278, https://arxiv.org/pdf/2506.13950.pdf

Abstract:
We propose a hybrid machine learning scheme to learn -- in physics-informed and numerical analysis-informed fashion -- invariant manifolds (IM) of discrete maps for constructing reduced-order models (ROMs) for dynamical systems. The proposed scheme combines polynomial series with shallow neural networks, exploiting the complementary strengths of both approaches. Polynomials enable an efficient and accurate modeling of ROMs with guaranteed local exponential convergence rate around the fixed point, where, under certain assumptions, the IM is demonstrated to be analytic. Neural networks provide approximations to more complex structures beyond the reach of the polynomials' convergence. We evaluate the efficiency of the proposed scheme using three benchmark examples, examining convergence behavior, numerical approximation accuracy, and computational training cost. Additionally, we compare the IM approximations obtained solely with neural networks and with polynomial expansions. We demonstrate that the proposed hybrid scheme outperforms both pure polynomial approximations (power series, Legendre and Chebyshev polynomials) and standalone shallow neural network approximations in terms of numerical approximation accuracy.

Paperid: 279, https://arxiv.org/pdf/2506.13678.pdf

Abstract:
Human activity intensity prediction is crucial to many location-based services. Despite tremendous progress in modeling dynamics of human activity, most existing methods overlook physical constraints of spatial interaction, leading to uninterpretable spatial correlations and over-smoothing phenomenon. To address these limitations, this work proposes a physics-informed deep learning framework, namely Gravity-informed Spatiotemporal Transformer (Gravityformer) by integrating the universal law of gravitation to refine transformer attention. Specifically, it (1) estimates two spatially explicit mass parameters based on spatiotemporal embedding feature, (2) models the spatial interaction in end-to-end neural network using proposed adaptive gravity model to learn the physical constraint, and (3) utilizes the learned spatial interaction to guide and mitigate the over-smoothing phenomenon in transformer attention. Moreover, a parallel spatiotemporal graph convolution transformer is proposed for achieving a balance between coupled spatial and temporal learning. Systematic experiments on six real-world large-scale activity datasets demonstrate the quantitative and qualitative superiority of our model over state-of-the-art benchmarks. Additionally, the learned gravity attention matrix can be not only disentangled and interpreted based on geographical laws, but also improved the generalization in zero-shot cross-region inference. This work provides a novel insight into integrating physical laws with deep learning for spatiotemporal prediction.

Paperid: 280, https://arxiv.org/pdf/2505.20300.pdf

Abstract:
We propose FMEnets, a physics-informed machine learning framework for the design and analysis of non-ideal plug flow reactors. FMEnets integrates the fundamental governing equations (Navier-Stokes for fluid flow, material balance for reactive species transport, and energy balance for temperature distribution) into a unified multi-scale network model. The framework is composed of three interconnected sub-networks with independent optimizers that enable both forward and inverse problem-solving. In the forward mode, FMEnets predicts velocity, pressure, species concentrations, and temperature profiles using only inlet and outlet information. In the inverse mode, FMEnets utilizes sparse multi-residence-time measurements to simultaneously infer unknown kinetic parameters and states. FMEnets can be implemented either as FME-PINNs, which employ conventional multilayer perceptrons, or as FME-KANs, based on Kolmogorov-Arnold Networks. Comprehensive ablation studies highlight the critical role of the FMEnets architecture in achieving accurate predictions. Specifically, FME-KANs are more robust to noise than FME-PINNs, although both representations are comparable in accuracy and speed in noise-free conditions. The proposed framework is applied to three different sets of reaction scenarios and is compared with finite element simulations. FMEnets effectively captures the complex interactions, achieving relative errors less than 2.5% for the unknown kinetic parameters. The new network framework not only provides a computationally efficient alternative for reactor design and optimization, but also opens new avenues for integrating empirical correlations, limited and noisy experimental data, and fundamental physical equations to guide reactor design.

Paperid: 281, https://arxiv.org/pdf/2504.17968.pdf

Abstract:
This paper presents a digital-twin platform for active safety analysis in mixed traffic environments. The platform is built using a multi-modal data-enabled traffic environment constructed from drone-based aerial LiDAR, OpenStreetMap, and vehicle sensor data (e.g., GPS and inclinometer readings). High-resolution 3D road geometries are generated through AI-powered semantic segmentation and georeferencing of aerial LiDAR data. To simulate real-world driving scenarios, the platform integrates the CAR Learning to Act (CARLA) simulator, Simulation of Urban MObility (SUMO) traffic model, and NVIDIA PhysX vehicle dynamics engine. CARLA provides detailed micro-level sensor and perception data, while SUMO manages macro-level traffic flow. NVIDIA PhysX enables accurate modeling of vehicle behaviors under diverse conditions, accounting for mass distribution, tire friction, and center of mass. This integrated system supports high-fidelity simulations that capture the complex interactions between autonomous and conventional vehicles. Experimental results demonstrate the platform's ability to reproduce realistic vehicle dynamics and traffic scenarios, enhancing the analysis of active safety measures. Overall, the proposed framework advances traffic safety research by enabling in-depth, physics-informed evaluation of vehicle behavior in dynamic and heterogeneous traffic environments.

Paperid: 282, https://arxiv.org/pdf/2504.07379.pdf

Abstract:
Physics-Informed Kolmogorov-Arnold Networks (PIKANs) are gaining attention as an effective counterpart to the original multilayer perceptron-based Physics-Informed Neural Networks (PINNs). Both representation models can address inverse problems and facilitate gray-box system identification. However, a comprehensive understanding of their performance in terms of accuracy and speed remains underexplored. In particular, we introduce a modified PIKAN architecture, tanh-cPIKAN, which is based on Chebyshev polynomials for parametrization of the univariate functions with an extra nonlinearity for enhanced performance. We then present a systematic investigation of how choices of the optimizer, representation, and training configuration influence the performance of PINNs and PIKANs in the context of systems pharmacology modeling. We benchmark a wide range of first-order, second-order, and hybrid optimizers, including various learning rate schedulers. We use the new Optax library to identify the most effective combinations for learning gray-boxes under ill-posed, non-unique, and data-sparse conditions. We examine the influence of model architecture (MLP vs. KAN), numerical precision (single vs. double), the need for warm-up phases for second-order methods, and sensitivity to the initial learning rate. We also assess the optimizer scalability for larger models and analyze the trade-offs introduced by JAX in terms of computational efficiency and numerical accuracy. Using two representative systems pharmacology case studies - a pharmacokinetics model and a chemotherapy drug-response model - we offer practical guidance on selecting optimizers and representation models/architectures for robust and efficient gray-box discovery. Our findings provide actionable insights for improving the training of physics-informed networks in biomedical applications and beyond.

Paperid: 283, https://arxiv.org/pdf/2502.20858.pdf

Abstract:
Imitating how humans move their gaze in a visual scene is a vital research problem for both visual understanding and psychology, kindling crucial applications such as building alive virtual characters. Previous studies aim to predict gaze trajectories when humans are free-viewing an image, searching for required targets, or looking for clues to answer questions in an image. While these tasks focus on visual-centric scenarios, humans move their gaze also along with audio signal inputs in more common scenarios. To fill this gap, we introduce a new task that predicts human gaze trajectories in a visual scene with synchronized audio inputs and provide a new dataset containing 20k gaze points from 8 subjects. To effectively integrate audio information and simulate the dynamic process of human gaze motion, we propose a novel learning framework called EyEar (Eye moving while Ear listening) based on physics-informed dynamics, which considers three key factors to predict gazes: eye inherent motion tendency, vision salient attraction, and audio semantic attraction. We also propose a probability density score to overcome the high individual variability of gaze trajectories, thereby improving the stabilization of optimization and the reliability of the evaluation. Experimental results show that EyEar outperforms all the baselines in the context of all evaluation metrics, thanks to the proposed components in the learning model.

Paperid: 284, https://arxiv.org/pdf/2502.17209.pdf

Abstract:
Purpose: T2* quantification from gradient echo magnetic resonance imaging is particularly affected by subject motion due to the high sensitivity to magnetic field inhomogeneities, which are influenced by motion and might cause signal loss. Thus, motion correction is crucial to obtain high-quality T2* maps. Methods: We extend our previously introduced learning-based physics-informed motion correction method, PHIMO, by utilizing acquisition knowledge to enhance the reconstruction performance for challenging motion patterns and increase PHIMO's robustness to varying strengths of magnetic field inhomogeneities across the brain. We perform comprehensive evaluations regarding motion detection accuracy and image quality for data with simulated and real motion. Results: Our extended version of PHIMO outperforms the learning-based baseline methods both qualitatively and quantitatively with respect to line detection and image quality. Moreover, PHIMO performs on-par with a conventional state-of-the-art motion correction method for T2* quantification from gradient echo MRI, which relies on redundant data acquisition. Conclusion: PHIMO's competitive motion correction performance, combined with a reduction in acquisition time by over 40% compared to the state-of-the-art method, make it a promising solution for motion-robust T2* quantification in research settings and clinical routine.

Paperid: 285, https://arxiv.org/pdf/2502.04947.pdf

Abstract:
In this work, we present a preliminary study combining two approaches in the context of solving PDEs: the classical finite element method (FEM) and more recent techniques based on neural networks. Indeed, in recent years, physics-informed neural networks (PINNs) have become particularly interesting for rapidly solving such problems, especially in high dimensions. However, their lack of accuracy is a significant drawback in this context, hence the interest in combining them with FEM, for which error estimators are already known. The complete pipeline proposed here, therefore, consists of modifying classical FEM approximation spaces by taking information from a prior, chosen here as the prediction of a neural network. On the one hand, this combination improves and certifies the prediction of neural networks to obtain a fast and accurate solution. On the other hand, error estimates are proven, showing that such strategies outperform classical ones by a factor that depends only on the quality of the prior. We validate our approach with numerical results obtained for this preliminary work on parametric problems with one- and two-dimensional geometries. They demonstrate that to achieve a fixed error target, a coarser mesh can be used with our enhanced FEM compared to the standard one, leading to reduced computation time, particularly for parametric problems.

Paperid: 286, https://arxiv.org/pdf/2502.04406.pdf

Abstract:
Simulating complex physical systems is crucial for understanding and predicting phenomena across diverse fields, such as fluid dynamics and heat transfer, as well as plasma physics and structural mechanics. Traditional approaches rely on solving partial differential equations (PDEs) using numerical methods, which are computationally expensive and often prohibitively slow for real-time applications or large-scale simulations. Neural PDEs have emerged as efficient alternatives to these costly numerical solvers, offering significant computational speed-ups. However, their lack of robust uncertainty quantification (UQ) limits deployment in critical applications. We introduce a model-agnostic, physics-informed conformal prediction (CP) framework that provides guaranteed uncertainty estimates without requiring labelled data. By utilising a physics-based approach, we can quantify and calibrate the model's inconsistencies with the physics rather than the uncertainty arising from the data. Our approach utilises convolutional layers as finite-difference stencils and leverages physics residual errors as nonconformity scores, enabling data-free UQ with marginal and joint coverage guarantees across prediction domains for a range of complex PDEs. We further validate the efficacy of our method on neural PDE models for plasma modelling and shot design in fusion reactors.

Paperid: 287, https://arxiv.org/pdf/2501.16371.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network's training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly non-linear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self-Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers using both PINNs and PIKANs on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs.

Paperid: 288, https://arxiv.org/pdf/2411.01665.pdf

Abstract:
Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network (PINN [1]) based approach for solving the inverse source problems in robotics, jointly identifying unknown source functions and the complete state of a system given partial and noisy observations. Our approach demonstrates several advantages over prior works (Finite Element Methods (FEM) and data-driven approaches): it offers flexibility in integrating diverse constraints and boundary conditions; eliminates the need for complex discretizations (e.g., meshing); easily accommodates gradients from real measurements; and does not limit performance based on the diversity and quality of training data. We validate our method across three simulation and real-world scenarios involving up to 4th order partial differential equations (PDEs), constraints such as Signorini and Dirichlet, and various regression losses including Chamfer distance and L2 norm.

Paperid: 289, https://arxiv.org/pdf/2409.20528.pdf

Abstract:
Control Lyapunov functions are a central tool in the design and analysis of stabilizing controllers for nonlinear systems. Constructing such functions, however, remains a significant challenge. In this paper, we investigate physics-informed learning and formal verification of neural network control Lyapunov functions. These neural networks solve a transformed Hamilton-Jacobi-Bellman equation, augmented by data generated using Pontryagin's maximum principle. Similar to how Zubov's equation characterizes the domain of attraction for autonomous systems, this equation characterizes the null-controllability set of a controlled system. This principled learning of neural network control Lyapunov functions outperforms alternative approaches, such as sum-of-squares and rational control Lyapunov functions, as demonstrated by numerical examples. As an intermediate step, we also present results on the formal verification of quadratic control Lyapunov functions, which, aided by satisfiability modulo theories solvers, can perform surprisingly well compared to more sophisticated approaches and efficiently produce global certificates of null-controllability.

Paperid: 290, https://arxiv.org/pdf/2601.20361.pdf

Abstract:
Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take time as an input but reuse a single network with shared weights across all times, forcing the same features to represent markedly different dynamics. This coupling degrades accuracy and can destabilize training when enforcing PDE, boundary, and initial constraints jointly. We propose Time-Induced Neural Networks (TINNs), a novel architecture that parameterizes the network weights as a learned function of time, allowing the effective spatial representation to evolve over time while maintaining shared structure. The resulting formulation naturally yields a nonlinear least-squares problem, which we optimize efficiently using a Levenberg--Marquardt method. Experiments on various time-dependent PDEs show up to $4\times$ improved accuracy and $10\times$ faster convergence compared to PINNs and strong baselines.

Paperid: 291, https://arxiv.org/pdf/2601.07436.pdf

Abstract:
Realistic visual simulations are omnipresent, yet their creation requires computing time, rendering, and expert animation knowledge. Open-vocabulary visual effects generation from text inputs emerges as a promising solution that can unlock immense creative potential. However, current pipelines lack both physical realism and effective language interfaces, requiring slow offline optimization. In contrast, PhysTalk takes a 3D Gaussian Splatting (3DGS) scene as input and translates arbitrary user prompts into real time, physics based, interactive 4D animations. A large language model (LLM) generates executable code that directly modifies 3DGS parameters through lightweight proxies and particle dynamics. Notably, PhysTalk is the first framework to couple 3DGS directly with a physics simulator without relying on time consuming mesh extraction. While remaining open vocabulary, this design enables interactive 3D Gaussian animation via collision aware, physics based manipulation of arbitrary, multi material objects. Finally, PhysTalk is train-free and computationally lightweight: this makes 4D animation broadly accessible and shifts these workflows from a "render and wait" paradigm toward an interactive dialogue with a modern, physics-informed pipeline.

Paperid: 293, https://arxiv.org/pdf/2512.24205.pdf

Abstract:
Plasma kinetic equations exhibit pronounced sensitivity to microscopic perturbations in model parameters and data, making reliable and efficient uncertainty quantification (UQ) essential for predictive simulations. However, the cost of uncertainty sampling, the high-dimensional phase space, and multiscale stiffness pose severe challenges to both computational efficiency and error control in traditional numerical methods. These aspects are further emphasized in presence of collisions where the high-dimensional nonlocal collision integrations and conservation properties pose severe constraints. To overcome this, we present a variance-reduced Monte Carlo framework for UQ in the Vlasov--Poisson--Landau (VPL) system, in which neural network surrogates replace the multiple costly evaluations of the Landau collision term. The method couples a high-fidelity, asymptotic-preserving VPL solver with inexpensive, strongly correlated surrogates based on the Vlasov--Poisson--Fokker--Planck (VPFP) and Euler--Poisson (EP) equations. For the surrogate models, we introduce a generalization of the separable physics-informed neural network (SPINN), developing a class of tensor neural networks based on an anisotropic micro-macro decomposition, to reduce velocity-moment costs, model complexity, and the curse of dimensionality. To further increase correlation with VPL, we calibrate the VPFP model and design an asymptotic-preserving SPINN whose small- and large-Knudsen limits recover the EP and VP systems, respectively. Numerical experiments show substantial variance reduction over standard Monte Carlo, accurate statistics with far fewer high-fidelity samples, and lower wall-clock time, while maintaining robustness to stochastic dimension.

Paperid: 294, https://arxiv.org/pdf/2512.14010.pdf

Abstract:
The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed neural network framework for solving two-phase Stefan problems. The proposed method explicitly tracks the interface motion and enforces the discontinuity in the temperature gradient across the interface while maintaining global consistency of the temperature field. Our approach employs two neural networks: one representing the moving interface and the other for the temperature field. The interface network allows rapid categorization of thermal diffusivity in the spatial domain, which is a crucial step for selecting training points for the temperature network. The temperature network's input is augmented with a modified zero-level set function to accurately capture the jump in its normal derivative across the interface. Numerical experiments on two-phase dynamical Stefan problems demonstrate the superior accuracy and effectiveness of our proposed method compared with the ones obtained by other neural network methodology in literature. The results indicate that the proposed framework offers a robust and flexible alternative to traditional numerical methods for solving phase-change problems governed by moving boundaries. In addition, the proposed method can capture an unstable interface evolution associated with the Mullins-Sekerka instability.

Paperid: 295, https://arxiv.org/pdf/2512.06315.pdf

Abstract:
We survey classical, machine learning, and data-driven system identification approaches to learn control-relevant and physics-informed models of dynamical systems. Recently, machine learning approaches have enabled system identification from noisy, high-dimensional, and complex data. However, their utility is limited by their ability to provide provable guarantees on control-relevant properties. Meanwhile, control theory has identified several properties that are useful in analysis and control synthesis, such as dissipativity, monotonicity, energy conservation, and symmetry-preserving structures. We posit that merging system identification with such control-relevant or physics-informed properties can provide useful inductive bias, enhance explainability, enable control synthesis with provable guarantees, and improve sample complexity. We formulate system identification as an optimization problem where control-relevant properties can be enforced through direct parameterization (constraining the model structure to satisfy a desired property by construction), soft constraints (encouraging control-relevant properties through regularization or penalty terms), and hard constraints (imposing control-relevant properties as constraints in the optimization problem). Through this lens, we survey methods to learn physics-informed and control-relevant models spanning classical linear and nonlinear system identification, machine learning approaches, and direct identification through data-driven and behavioral representations. We also provide several expository examples that are accompanied by code and brief tutorials on a public Github repository. We also describe challenging directions for future research, including identification in networked, switched, and time-varying systems, experiment design, and bridging the gaps between data-driven, learning-based, and control-oriented approaches.

Paperid: 296, https://arxiv.org/pdf/2510.17143.pdf

Abstract:
Existing approaches for transporting and manipulating cable-suspended loads using multiple UAVs along reference trajectories typically rely on either centralized control architectures or reliable inter-agent communication. In this work, we propose a novel machine learning based method for decentralized kinodynamic planning that operates effectively under partial observability and without inter-agent communication. Our method leverages imitation learning to train a decentralized student policy for each UAV by imitating a centralized kinodynamic motion planner with access to privileged global observations. The student policy generates smooth trajectories using physics-informed neural networks that respect the derivative relationships in motion. During training, the student policies utilize the full trajectory generated by the teacher policy, leading to improved sample efficiency. Moreover, each student policy can be trained in under two hours on a standard laptop. We validate our method in both simulation and real-world environments to follow an agile reference trajectory, demonstrating performance comparable to that of centralized approaches.

Paperid: 297, https://arxiv.org/pdf/2510.09670.pdf

Abstract:
Modeling shock-to-detonation phenomena in energetic materials (EMs) requires capturing complex physical processes such as strong shocks, rapid changes in microstructural morphology, and nonlinear dynamics of chemical reaction fronts. These processes participate in energy localization at hotspots, which initiate chemical energy release leading to detonation. This study addresses the formation of hotspots in crystalline EMs subjected to weak-to-moderate shock loading, which, despite its critical relevance to the safe storage and handling of EMs, remains underexplored compared to the well-studied strong shock conditions. To overcome the computational challenges associated with direct numerical simulations, we advance the Physics-Aware Recurrent Convolutional Neural Network (PARCv2), which has been shown to be capable of predicting strong shock responses in EMs. We improved the architecture of PARCv2 to rapidly predict shear localizations and plastic heating, which play important roles in the weak-to-moderate shock regime. PARCv2 is benchmarked against two widely used physics-informed models, namely, Fourier neural operator and neural ordinary differential equation; we demonstrate its superior performance in capturing the spatiotemporal dynamics of shear band formation. While all models exhibit certain failure modes, our findings underscore the importance of domain-specific considerations in developing robust AI-accelerated simulation tools for reactive materials.

Paperid: 298, https://arxiv.org/pdf/2510.09192.pdf

Abstract:
In this work, we propose a data augmentation strategy aimed at improving the training phase of neural networks and, consequently, the accuracy of their predictions. Our approach relies on generating synthetic data through a suitable compartmental model combined with the incorporation of uncertainty. The available data are then used to calibrate the model, which is further integrated with deep learning techniques to produce additional synthetic data for training. The results show that neural networks trained on these augmented datasets exhibit significantly improved predictive performance. We focus in particular on two different neural network architectures: Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models. The NAR approach proves especially effective for short-term forecasting, providing accurate quantitative estimates by directly learning the dynamics from data and avoiding the additional computational cost of embedding physical constraints into the training. In contrast, PINNs yield less accurate quantitative predictions but capture the qualitative long-term behavior of the system, making them more suitable for exploring broader dynamical trends. Numerical simulations of the second phase of the COVID-19 pandemic in the Lombardy region (Italy) validate the effectiveness of the proposed approach.

Paperid: 299, https://arxiv.org/pdf/2510.08184.pdf

Abstract:
Increase in the number of space exploration missions has led to the accumulation of space debris, posing risk of collision with the operational satellites. Addressing this challenge is crucial for the sustainability of space operations. To plan a safe trajectory in the presence of moving space debris, an integrated approach of artificial potential field and sliding mode controller is proposed and implemented in this paper. The relative 6-DOF kinematics and dynamics of the spacecraft is modelled in the framework of geometric mechanics with the relative configuration expressed through exponential coordinates. Various collision avoidance guidance algorithms have been proposed in the literature but the Artificial Potential Field guidance algorithm is computationally efficient and enables real-time path adjustments to avoid collision with obstacles. However, it is prone to issues such as local minima. In literature, local minima issue is typically avoided by either redefining the potential function such as adding vorticity or by employing search techniques which are computationally expensive. To address these challenges, a physics-informed APF is proposed in this paper where Hamiltonian mechanics is used instead of the traditional Newtonian mechanics-based approach. In this approach, instead of relying on attractive and repulsive forces for path planning, the Hamiltonian approach uses the potential field to define a path of minimum potential. Additionally, to track the desired trajectory planned by the guidance algorithm within a fixed-time frame, a non-singular fixed-time sliding mode controller (FTSMC) is used. The proposed fixed-time sliding surface not only ensures fixed-time convergence of system states but also guarantees the global stability of the closed-loop system without singularity. The simulation results presented support the claims made.

Paperid: 300, https://arxiv.org/pdf/2510.06776.pdf

Abstract:
The COVID-19 pandemic has highlighted the need for quantitative modeling and analysis to understand real-world disease dynamics. In particular, post hoc analyses using compartmental models offer valuable insights into the effectiveness of public health interventions, such as vaccination strategies and containment policies. However, such compartmental models like SIR (Susceptible-Infectious-Recovered) often face limitations in directly incorporating noisy observational data. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve the inverse problem of the SIR model using infection data from the Robert Koch Institute (RKI). Our main contribution is a fine-grained, spatio-temporal analysis of COVID-19 dynamics across all German federal states over a three-year period. We estimate state-specific transmission and recovery parameters and time-varying reproduction number (R_t) to track the pandemic progression. The results highlight strong variations in transmission behavior across regions, revealing correlations with vaccination uptake and temporal patterns associated with major pandemic phases. Our findings demonstrate the utility of PINNs in localized, long-term epidemiological modeling.

Paperid: 301, https://arxiv.org/pdf/2509.23307.pdf

Abstract:
Accurate aircraft trajectory prediction is critical for air traffic management, airline operations, and environmental assessment. This paper introduces NODE-FDM, a Neural Ordinary Differential Equations-based Flight Dynamics Model trained on Quick Access Recorder (QAR) data. By combining analytical kinematic relations with data-driven components, NODE-FDM achieves a more accurate reproduction of recorded trajectories than state-of-the-art models such as a BADA-based trajectory generation methodology (BADA4 performance model combined with trajectory control routines), particularly in the descent phase of the flight. The analysis demonstrates marked improvements across altitude, speed, and mass dynamics. Despite current limitations, including limited physical constraints and the limited availability of QAR data, the results demonstrate the potential of physics-informed neural ordinary differential equations as a high-fidelity, data-driven approach to aircraft performance modelling. Future work will extend the framework to incorporate a full modelling of the lateral dynamics of the aircraft.

Paperid: 302, https://arxiv.org/pdf/2509.14437.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a promising machine learning approach for solving partial differential equations (PDEs). However, PINNs face significant challenges in balancing multi-objective losses, as multiple competing loss terms such as physics residuals, boundary conditions, and initial conditions must be appropriately weighted. While various loss balancing schemes have been proposed, they have been implemented within neural network architectures with fixed activation functions, and their effectiveness has been assessed using simpler PDEs. We hypothesize that the effectiveness of loss balancing schemes depends not only on the balancing strategy itself, but also on the loss function design and the neural network's inherent function approximation capabilities, which are influenced by the choice of activation function. In this paper, we extend existing solutions by incorporating trainable activation functions within the neural network architecture and evaluate the proposed approach on complex fluid flow applications modeled by the Navier-Stokes equations. Our evaluation across diverse Navier-Stokes problems demonstrates that this proposed solution achieves root mean square error (RMSE) improvements ranging from 7.4% to 95.2% across different scenarios. These findings highlight the importance of carefully designing the loss function and selecting activation functions for effective loss balancing.

Paperid: 303, https://arxiv.org/pdf/2509.08967.pdf

Abstract:
Full waveform inversion (FWI) is crucial for reconstructing high-resolution subsurface models, but it is often hindered, considering the limited data, by its null space resulting in low-resolution models, and more importantly, by its computational cost, especially if needed for real-time applications. Recent attempts to accelerate FWI using learned wavefield neural operators have shown promise in efficiency and differentiability, but typically suffer from noisy and unstable inversion performance. To address these limitations, we introduce a novel physics-informed FWI framework to enhance the inversion in accuracy while maintaining the efficiency of neural operator-based FWI. Instead of relying only on the L2 norm objective function via automatic differentiation, resulting in noisy model reconstruction, we integrate a physics constraint term in the loss function of FWI, improving the quality of the inverted velocity models. Specifically, starting with an initial model to simulate wavefields and then evaluating the loss over how much the resulting wavefield obeys the physical laws (wave equation) and matches the recorded data, we achieve a reduction in noise and artifacts. Numerical experiments using the OpenFWI and Overthrust models demonstrate our method's superior performance, offering cleaner and more accurate subsurface velocity than vanilla approaches. Considering the efficiency of the approach compared to FWI, this advancement represents a significant step forward in the practical application of FWI for real-time subsurface monitoring.

Paperid: 304, https://arxiv.org/pdf/2509.07579.pdf

Abstract:
Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs) relevant to multiscale modeling, but they often fail when applied to materials with discontinuous coefficients, such as media with piecewise constant properties. This paper introduces a dual formulation for the PINN framework to improve the reliability of the homogenization of periodic thermo-conductive composites, for both strong and variational (weak) formulations. The dual approach facilitates the derivation of guaranteed upper and lower error bounds, enabling more robust detection of PINN failure. We compare standard PINNs applied to smoothed material approximations with variational PINNs (VPINNs) using both spectral and neural network-based test functions. Our results indicate that while strong-form PINNs may outperform VPINNs in controlled settings, they are sensitive to material discontinuities and may fail without clear diagnostics. In contrast, VPINNs accommodate piecewise constant material parameters directly but require careful selection of test functions to avoid instability. Dual formulation serves as a reliable indicator of convergence quality, and its integration into PINN frameworks enhances their applicability to homogenization problems in micromechanics.

Paperid: 305, https://arxiv.org/pdf/2508.10555.pdf

Abstract:
Inverse scattering problems are critical in electromagnetic imaging and medical diagnostics but are challenged by their nonlinearity and diverse measurement scenarios. This paper proposes a physics-informed deep contrast source inversion framework (DeepCSI) for fast and accurate medium reconstruction across various measurement conditions. Inspired by contrast source inversion (CSI) and neural operator methods, a residual multilayer perceptron (ResMLP) is employed to model current distributions in the region of interest under different transmitter excitations, effectively linearizing the nonlinear inverse scattering problem and significantly reducing the computational cost of traditional full-waveform inversion. By modeling medium parameters as learnable tensors and utilizing a hybrid loss function that integrates state equation loss, data equation loss, and total variation regularization, DeepCSI establishes a fully differentiable framework for joint optimization of network parameters and medium properties. Compared with conventional methods, DeepCSI offers advantages in terms of simplicity and universal modeling capabilities for diverse measurement scenarios, including phase-less and multi-frequency observation. Simulations and experiments demonstrate that DeepCSI achieves high-precision, robust reconstruction under full-data, phaseless data, and multifrequency conditions, outperforming traditional CSI methods and providing an efficient and universal solution for complex inverse scattering problems.

Paperid: 306, https://arxiv.org/pdf/2508.08107.pdf

Abstract:
Hyperspectral imaging (HSI) is an advanced sensing modality that simultaneously captures spatial and spectral information, enabling non-invasive, label-free analysis of material, chemical, and biological properties. This Primer presents a comprehensive overview of HSI, from the underlying physical principles and sensor architectures to key steps in data acquisition, calibration, and correction. We summarize common data structures and highlight classical and modern analysis methods, including dimensionality reduction, classification, spectral unmixing, and AI-driven techniques such as deep learning. Representative applications across Earth observation, precision agriculture, biomedicine, industrial inspection, cultural heritage, and security are also discussed, emphasizing HSI's ability to uncover sub-visual features for advanced monitoring, diagnostics, and decision-making. Persistent challenges, such as hardware trade-offs, acquisition variability, and the complexity of high-dimensional data, are examined alongside emerging solutions, including computational imaging, physics-informed modeling, cross-modal fusion, and self-supervised learning. Best practices for dataset sharing, reproducibility, and metadata documentation are further highlighted to support transparency and reuse. Looking ahead, we explore future directions toward scalable, real-time, and embedded HSI systems, driven by sensor miniaturization, self-supervised learning, and foundation models. As HSI evolves into a general-purpose, cross-disciplinary platform, it holds promise for transformative applications in science, technology, and society.

Paperid: 307, https://arxiv.org/pdf/2507.03860.pdf

Abstract:
We study the problem of learning neural network models for Ordinary Differential Equations (ODEs) with parametric uncertainties. Such neural network models capture the solution to the ODE over a given set of parameters, initial conditions, and range of times. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for learning such models that combine data-driven deep learning with symbolic physics models in a principled manner. However, the accuracy of PINNs degrade when they are used to solve an entire family of initial value problems characterized by varying parameters and initial conditions. In this paper, we combine symbolic differentiation and Taylor series methods to propose a class of higher-order models for capturing the solutions to ODEs. These models combine neural networks and symbolic terms: they use higher order Lie derivatives and a Taylor series expansion obtained symbolically, with the remainder term modeled as a neural network. The key insight is that the remainder term can itself be modeled as a solution to a first-order ODE. We show how the use of these higher order PINNs can improve accuracy using interesting, but challenging ODE benchmarks. We also show that the resulting model can be quite useful for situations such as controlling uncertain physical systems modeled as ODEs.

Paperid: 308, https://arxiv.org/pdf/2505.22469.pdf

Abstract:
Efficient thermal and power management in modern multiprocessor systems-on-chip (MPSoCs) demands accurate power consumption estimation. One of the state-of-the-art approaches, Alternative Blind Power Identification (ABPI), theoretically eliminates the dependence on steady-state temperatures, addressing a major shortcoming of previous approaches. However, ABPI performance has remained unverified in actual hardware implementations. In this study, we conduct the first empirical validation of ABPI on commercial hardware using the NVIDIA Jetson Xavier AGX platform. Our findings reveal that, while ABPI provides computational efficiency and independence from steady-state temperature, it exhibits considerable accuracy deficiencies in real-world scenarios. To overcome these limitations, we introduce a novel approach that integrates Custom Physics-Informed Neural Networks (CPINNs) with the underlying thermal model of ABPI. Our approach employs a specialized loss function that harmonizes physical principles with data-driven learning, complemented by multi-objective genetic algorithm optimization to balance estimation accuracy and computational cost. In experimental validation, CPINN-ABPI achieves a reduction of 84.7\% CPU and 73.9\% GPU in the mean absolute error (MAE) relative to ABPI, with the weighted mean absolute percentage error (WMAPE) improving from 47\%--81\% to $\sim$12\%. The method maintains real-time performance with 195.3~$Î¼$s of inference time, with similar 85\%--99\% accuracy gains across heterogeneous SoCs.

Paperid: 309, https://arxiv.org/pdf/2505.18565.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a promising approach for solving complex fluid dynamics problems, yet their application to fluid-structure interaction (FSI) problems with moving boundaries remains largely unexplored. This work addresses the critical challenge of modeling FSI systems with deformable interfaces, where traditional unified PINN architectures struggle to capture the distinct physics governing fluid and structural domains simultaneously. We present an innovative Eulerian-Lagrangian PINN architecture that integrates immersed boundary method (IBM) principles to solve FSI problems with moving boundary conditions. Our approach fundamentally departs from conventional unified architectures by introducing domain-specific neural networks: an Eulerian network for fluid dynamics and a Lagrangian network for structural interfaces, coupled through physics-based constraints. Additionally, we incorporate learnable B-spline activation functions with SiLU to capture both localized high-gradient features near interfaces and global flow patterns. Empirical studies on a 2D cavity flow problem involving a moving solid structure show that while baseline unified PINNs achieve reasonable velocity predictions, they suffer from substantial pressure errors (12.9%) in structural regions. Our Eulerian-Lagrangian architecture with learnable activations (EL-L) achieves better performance across all metrics, improving accuracy by 24.1-91.4% and particularly reducing pressure errors from 12.9% to 2.39%. These results demonstrate that domain decomposition aligned with physical principles, combined with locality-aware activation functions, is essential for accurate FSI modeling within the PINN framework.

Paperid: 310, https://arxiv.org/pdf/2505.04018.pdf

Abstract:
Modal identification is crucial for structural health monitoring and structural control, providing critical insights into structural dynamics and performance. This study presents a novel deep learning framework that integrates graph neural networks (GNNs), transformers, and a physics-informed loss function to achieve modal decomposition and identification across a population of structures. The transformer module decomposes multi-degrees-of-freedom (MDOF) structural dynamic measurements into single-degree-of-freedom (SDOF) modal responses, facilitating the identification of natural frequencies and damping ratios. Concurrently, the GNN captures the structural configurations and identifies mode shapes corresponding to the decomposed SDOF modal responses. The proposed model is trained in a purely physics-informed and unsupervised manner, leveraging modal decomposition theory and the independence of structural modes to guide learning without the need for labeled data. Validation through numerical simulations and laboratory experiments demonstrates its effectiveness in accurately decomposing dynamic responses and identifying modal properties from sparse structural dynamic measurements, regardless of variations in external loads or structural configurations. Comparative analyses against established modal identification techniques and model variations further underscore its superior performance, positioning it as a favorable approach for population-based structural health monitoring.

Paperid: 311, https://arxiv.org/pdf/2503.16678.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as promising methods for solving partial differential equations (PDEs) by embedding physical laws within neural architectures. However, these classical approaches often require a large number of parameters to achieve reasonable accuracy, particularly for complex PDEs. In this paper, we present a quantum-classical physics-informed neural network (QCPINN) that combines quantum and classical components, allowing us to solve PDEs with significantly fewer parameters while maintaining comparable accuracy and convergence to classical PINNs. We systematically evaluated two quantum circuit architectures across various configurations on five benchmark PDEs to identify optimal QCPINN designs. Our results demonstrate that the QCPINN achieves stable convergence and comparable accuracy, while requiring approximately 10\% of the trainable parameters used in classical approaches. It also results in a 40\% reduction in the relative error $L_2$ for the convection-diffusion equation. These findings demonstrate the potential of parameter efficiency as a measurable quantum advantage in physics-informed machine learning, significantly reducing model complexity while preserving solution quality. This approach presents a promising solution to the computational challenges associated with solving PDEs.

Paperid: 312, https://arxiv.org/pdf/2502.21033.pdf

Abstract:
In this work, we integrate the predictive capabilities of compartmental disease dynamics models with machine learning ability to analyze complex, high-dimensional data and uncover patterns that conventional models may overlook. Specifically, we present a proof of concept demonstrating the application of data-driven methods and deep neural networks to a recently introduced Susceptible-Infected-Recovered type model with social features, including a saturated incidence rate, to improve epidemic prediction and forecasting. Our results show that a robust data augmentation strategy trough suitable data-driven models can improve the reliability of Feed-Forward Neural Networks and Nonlinear Autoregressive Networks, providing a complementary strategy to Physics-Informed Neural Networks, particularly in settings where data augmentation from mechanistic models can enhance learning. This approach enhances the ability to handle nonlinear dynamics and offers scalable, data-driven solutions for epidemic forecasting, prioritizing predictive accuracy over the constraints of physics-based models. Numerical simulations of the lockdown and post-lockdown phase of the COVID-19 epidemic in Italy and Spain validate our methodology.

Paperid: 313, https://arxiv.org/pdf/2412.13321.pdf

Abstract:
Modern machine learning often relies on optimizing a neural network's parameters using a loss function to learn complex features. Beyond training, examining the loss function with respect to a network's parameters (i.e., as a loss landscape) can reveal insights into the architecture and learning process. While the local structure of the loss landscape surrounding an individual solution can be characterized using a variety of approaches, the global structure of a loss landscape, which includes potentially many local minima corresponding to different solutions, remains far more difficult to conceptualize and visualize. To address this difficulty, we introduce LossLens, a visual analytics framework that explores loss landscapes at multiple scales. LossLens integrates metrics from global and local scales into a comprehensive visual representation, enhancing model diagnostics. We demonstrate LossLens through two case studies: visualizing how residual connections influence a ResNet-20, and visualizing how physical parameters influence a physics-informed neural network (PINN) solving a simple convection problem.

Paperid: 314, https://arxiv.org/pdf/2412.11967.pdf

Abstract:
Improving diesel engine efficiency and emission reduction have been critical research topics. Recent government regulations have shifted this focus to another important area related to engine health and performance monitoring. Although the advancements in the use of deep learning methods for system monitoring have shown promising results in this direction, designing efficient methods suitable for field systems remains an open research challenge. The objective of this study is to develop a computationally efficient neural network-based approach for identifying unknown parameters of a mean value diesel engine model to facilitate physics-based health monitoring and maintenance forecasting. We propose a hybrid method combining physics informed neural networks, PINNs, and a deep neural operator, DeepONet to predict unknown parameters and gas flow dynamics in a diesel engine. The operator network predicts independent actuator dynamics learnt through offline training, thereby reducing the PINNs online computational cost. To address PINNs need for retraining with changing input scenarios, we propose two transfer learning (TL) strategies. The first strategy involves multi-stage transfer learning for parameter identification. While this method is computationally efficient as compared to online PINN training, improvements are required to meet field requirements. The second TL strategy focuses solely on training the output weights and biases of a subset of multi-head networks pretrained on a larger dataset, substantially reducing computation time during online prediction. We also evaluate our model for epistemic and aleatoric uncertainty by incorporating dropout in pretrained networks and Gaussian noise in the training dataset. This strategy offers a tailored, computationally inexpensive, and physics-based approach for parameter identification in diesel engine sub systems.

Paperid: 315, https://arxiv.org/pdf/2411.15111.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs). However, they face challenges related to spectral bias (the tendency to learn low-frequency components while struggling with high-frequency features) and unstable convergence dynamics (mainly stemming from the multi-objective nature of the PINN loss function). These limitations impact their accuracy for problems involving rapid oscillations, sharp gradients, and complex boundary behaviors. We systematically investigate learnable activation functions as a solution to these challenges, comparing Multilayer Perceptrons (MLPs) using fixed and learnable activation functions against Kolmogorov-Arnold Networks (KANs) that employ learnable basis functions. Our evaluation spans diverse PDE types, including linear and non-linear wave problems, mixed-physics systems, and fluid dynamics. Using empirical Neural Tangent Kernel (NTK) analysis and Hessian eigenvalue decomposition, we assess spectral bias and convergence stability of the models. Our results reveal a trade-off between expressivity and training convergence stability. While learnable activation functions work well in simpler architectures, they encounter scalability issues in complex networks due to the higher functional dimensionality. Counterintuitively, we find that low spectral bias alone does not guarantee better accuracy, as functions with broader NTK eigenvalue spectra may exhibit convergence instability. We demonstrate that activation function selection remains inherently problem-specific, with different bases showing distinct advantages for particular PDE characteristics. We believe these insights will help in the design of more robust neural PDE solvers.

Paperid: 316, https://arxiv.org/pdf/2411.12136.pdf

Abstract:
In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights into the local structure of the so-called loss landscape (e.g., smoothness) as well as global properties of the underlying model (e.g., generalization performance). While various methods for visualizing the loss landscape have been proposed, many approaches limit sampling to just one or two directions, ignoring potentially relevant information in this extremely high-dimensional space. This paper introduces a new representation based on topological data analysis that enables the visualization of higher-dimensional loss landscapes. After describing this new topological landscape profile representation, we show how the shape of loss landscapes can reveal new details about model performance and learning dynamics, highlighting several use cases, including image segmentation (e.g., UNet) and scientific machine learning (e.g., physics-informed neural networks). Through these examples, we provide new insights into how loss landscapes vary across distinct hyperparameter spaces: we find that the topology of the loss landscape is simpler for better-performing models; and we observe greater variation in the shape of loss landscapes near transitions from low to high model performance.

Paperid: 317, https://arxiv.org/pdf/2411.09807.pdf

Abstract:
Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but less emphasis has been placed on quantifying and extracting actionable and reproducible insights from these complex representations. Inspired by powerful tools from topological data analysis (TDA) for summarizing the structure of high-dimensional data, here we characterize the underlying shape (or topology) of loss landscapes, quantifying the topology to reveal new insights about neural networks. To relate our findings to the machine learning (ML) literature, we compute simple performance metrics (e.g., accuracy, error), and we characterize the local structure of loss landscapes using Hessian-based metrics (e.g., largest eigenvalue, trace, eigenvalue spectral density). Following this approach, we study established models from image pattern recognition (e.g., ResNets) and scientific ML (e.g., physics-informed neural networks), and we show how quantifying the shape of loss landscapes can provide new insights into model performance and learning dynamics.

Paperid: 318, https://arxiv.org/pdf/2411.07239.pdf

Abstract:
We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for downstream tasks. Operator learning effectively approximates solution operators for PDEs and various PDE-related problems, yet it often struggles to generalize to new tasks. To address this, we investigate fine-tuning a pretrained model, while carefully selecting an initialization that enables rapid adaptation to new tasks with minimal data. Our approach combines distributed learning to integrate data from various operators in pre-training, while physics-informed methods enable zero-shot fine-tuning, minimizing the reliance on downstream data. We investigate standard fine-tuning and Low-Rank Adaptation fine-tuning, applying both to train complex nonlinear target operators that are difficult to learn only using random initialization. Through comprehensive numerical examples, we demonstrate the advantages of our approach, showcasing significant improvements in accuracy. Our findings provide a robust framework for advancing multi-operator learning and highlight the potential of transfer learning techniques in this domain.

Paperid: 319, https://arxiv.org/pdf/2601.17126.pdf

Abstract:
While deep learning is transforming data analysis in high-energy physics, computational challenges limit its potential. We address these challenges in the context of collider physics by introducing EveNet, an event-level foundation model pretrained on 500 million simulated collision events using a hybrid objective of self-supervised learning and physics-informed supervision. By leveraging a shared particle-cloud representation, EveNet outperforms state-of-the-art baselines across diverse tasks, including searches for heavy resonances and exotic Higgs decays, and demonstrates exceptional data efficiency in low-statistics regimes. Crucially, we validate the transferability of the model to experimental data by rediscovering the $Υ$ meson in CMS Open Data and show its capacity for precision physics through the robust extraction of quantum correlation observables stable against systematic uncertainties. These results indicate that EveNet can successfully encode the fundamental physical structure of particle interactions, which offers a unified and resource-efficient framework to accelerate discovery at current and future colliders.

Paperid: 320, https://arxiv.org/pdf/2512.23295.pdf

Abstract:
Physics-Informed Neural Networks with hard constraints (HC-PINNs) are increasingly favored for their ability to strictly enforce boundary conditions via a trial function ansatz $\tilde{u} = A + B \cdot N$, yet the theoretical mechanisms governing their training dynamics have remained unexplored. Unlike soft-constrained formulations where boundary terms act as additive penalties, this work reveals that the boundary function $B$ introduces a multiplicative spatial modulation that fundamentally alters the learning landscape. A rigorous Neural Tangent Kernel (NTK) framework for HC-PINNs is established, deriving the explicit kernel composition law. This relationship demonstrates that the boundary function $B(\vec{x})$ functions as a spectral filter, reshaping the eigenspectrum of the neural network's native kernel. Through spectral analysis, the effective rank of the residual kernel is identified as a deterministic predictor of training convergence, superior to classical condition numbers. It is shown that widely used boundary functions can inadvertently induce spectral collapse, leading to optimization stagnation despite exact boundary satisfaction. Validated across multi-dimensional benchmarks, this framework transforms the design of boundary functions from a heuristic choice into a principled spectral optimization problem, providing a solid theoretical foundation for geometric hard constraints in scientific machine learning.

Paperid: 321, https://arxiv.org/pdf/2511.13185.pdf

Abstract:
Coherent anti-Stokes Raman scattering (CARS) spectroscopy is a powerful and rapid technique widely used in medicine, material science, and chemical analyses. However, its effectiveness is hindered by the presence of a non-resonant background that interferes with and distorts the true Raman signal. Deep learning methods have been employed to reconstruct the true Raman spectrum from measured CARS data using labeled datasets. A more recent development integrates the domain knowledge of Kramers-Kronig relationships and smoothness constraints in the form of physics-informed loss functions. However, these deterministic models lack the ability to quantify uncertainty, an essential feature for reliable deployment in high-stakes scientific and biomedical applications. In this work, we evaluate and compare various uncertainty quantification (UQ) techniques within the context of CARS-to-Raman signal reconstruction. Furthermore, we demonstrate that incorporating physics-informed constraints into these models improves their calibration, offering a promising path toward more trustworthy CARS data analysis.

Paperid: 322, https://arxiv.org/pdf/2510.24577.pdf

Abstract:
We are very delighted to see the fast development of physics-informed extreme learning machine (PIELM) in recent years for higher computation efficiency and accuracy in physics-informed machine learning. As a summary or review on PIELM is currently not available, we would like to take this opportunity to show our perspective and experience for this promising research direction. We can see many efforts are made to solve PDEs with sharp gradients, nonlinearities, high-frequency behavior, hard constraints, uncertainty, multiphysics coupling. Despite the success, many urgent challenges remain to be tackled, which also provides us opportunities to develop more robust, interpretable, and generalizable PIELM frameworks with applications in science and engineering.

Paperid: 323, https://arxiv.org/pdf/2510.21426.pdf

Abstract:
The inverse Stefan problem, as a typical phase-change problem with moving boundaries, finds extensive applications in science and engineering. Recent years have seen the applications of physics-informed neural networks (PINNs) to solving Stefan problems, yet they still exhibit shortcomings in hyperparameter dependency, training efficiency, and prediction accuracy. To address this, this paper develops a physics-informed extreme learning machine (PIELM), a rapid physics-informed learning method framework for inverse Stefan problems. PIELM replaces conventional deep neural networks with an extreme learning machine network. The input weights are fixed in the PIELM framework, and the output weights are determined by optimizing a loss vector of physical laws composed by initial and boundary conditions and governing partial differential equations (PDEs). Then, solving inverse Stefan problems is transformed into finding the Moore-Penrose generalized inverse by the least squares method. Case studies show that the PIELM can increase the prediction accuracy by 3-7 order of magnitude in terms of the relative L2 error, and meanwhile saving more than 94% training time, compared to conventional PINNs.

Paperid: 324, https://arxiv.org/pdf/2510.12293.pdf

Abstract:
Conventional physics-informed extreme learning machine (PIELM) often faces challenges in solving partial differential equations (PDEs) involving high-frequency and variable-frequency behaviors. To address these challenges, we propose a general Fourier feature physics-informed extreme learning machine (GFF-PIELM). We demonstrate that directly concatenating multiple Fourier feature mappings (FFMs) and an extreme learning machine (ELM) network makes it difficult to determine frequency-related hyperparameters. Fortunately, we find an alternative to establish the GFF-PIELM in three main steps. First, we integrate a variation of FFM into ELM as the Fourier-based activation function, so there is still one hidden layer in the GFF-PIELM framework. Second, we assign a set of frequency coefficients to the hidden neurons, which enables ELM network to capture diverse frequency components of target solutions. Finally, we develop an innovative, straightforward initialization method for these hyperparameters by monitoring the distribution of ELM output weights. GFF-PIELM not only retains the high accuracy, efficiency, and simplicity of the PIELM framework but also inherits the ability of FFMs to effectively handle high-frequency problems. We carry out five case studies with a total of ten numerical examples to highlight the feasibility and validity of the proposed GFF-PIELM, involving high frequency, variable frequency, multi-scale behaviour, irregular boundary and inverse problems. Compared to conventional PIELM, the GFF-PIELM approach significantly improves predictive accuracy without additional cost in training time and architecture complexity. Our results confirm that that PIELM can be extended to solve high-frequency and variable-frequency PDEs with high accuracy, and our initialization strategy may further inspire advances in other physics-informed machine learning (PIML) frameworks.

Paperid: 325, https://arxiv.org/pdf/2510.11515.pdf

Abstract:
Batteries degrade with usage and continuous cycling. This aging is typically reflected through the resistance growth and the capacity fade of battery cells. Over the years, various charging methods have been presented in the literature that proposed current profiles in order to enable optimal, fast, and/or health-conscious charging. However, very few works have attempted to make the ubiquitous Constant Current Constant Voltage (CCCV) charging protocol adaptive to the changing battery health as it cycles. This work aims to address this gap and proposes a framework that optimizes the constant current part of the CCCV protocol adapting to long-term battery degradation. Specifically, a physics-informed Reinforcement Learning (RL) approach has been used that not only estimates a key battery degradation mechanism, namely, Loss of Active Material (LAM), but also adjusts the current magnitude of CCCV as a result of this particular degradation. The proposed framework has been implemented by combining PyBamm, an open-source battery modeling tool, and Stable-baselines where the RL agent was trained using a Proximal Policy Optimization (PPO) network. Simulation results show the potential of the proposed framework for enhancing the widely used CCCV protocol by embedding physics information in RL algorithm. A comparative study of this proposed agent has also been discussed with 2 other charging protocols generated by a non-physics-based RL agent and a constant CCCV for all the cycles.

Paperid: 326, https://arxiv.org/pdf/2510.06635.pdf

Abstract:
Symbolic regression aims to find interpretable analytical expressions by searching over mathematical formula spaces to capture underlying system behavior, particularly in scientific modeling governed by physical laws. However, traditional methods lack mechanisms for extracting structured physical priors from time series observations, making it difficult to capture symbolic expressions that reflect the system's global behavior. In this work, we propose a structure-aware symbolic regression framework, called StruSR, that leverages trained Physics-Informed Neural Networks (PINNs) to extract locally structured physical priors from time series data. By performing local Taylor expansions on the outputs of the trained PINN, we obtain derivative-based structural information to guide symbolic expression evolution. To assess the importance of expression components, we introduce a masking-based attribution mechanism that quantifies each subtree's contribution to structural alignment and physical residual reduction. These sensitivity scores steer mutation and crossover operations within genetic programming, preserving substructures with high physical or structural significance while selectively modifying less informative components. A hybrid fitness function jointly minimizes physics residuals and Taylor coefficient mismatch, ensuring consistency with both the governing equations and the local analytical behavior encoded by the PINN. Experiments on benchmark PDE systems demonstrate that StruSR improves convergence speed, structural fidelity, and expression interpretability compared to conventional baselines, offering a principled paradigm for physics-grounded symbolic discovery.

Paperid: 327, https://arxiv.org/pdf/2510.06020.pdf

Abstract:
Transferring the recent advancements in deep learning into scientific disciplines is hindered by the lack of the required large-scale datasets for training. We argue that in these knowledge-rich domains, the established body of scientific theory provides reliable inductive biases in the form of governing physical laws. We address the ill-posed inverse problem of recovering Raman spectra from noisy Coherent Anti-Stokes Raman Scattering (CARS) measurements, as the true Raman signal here is suppressed by a dominating non-resonant background. We propose RamPINN, a model that learns to recover Raman spectra from given CARS spectra. Our core methodological contribution is a physics-informed neural network that utilizes a dual-decoder architecture to disentangle resonant and non-resonant signals. This is done by enforcing the Kramers-Kronig causality relations via a differentiable Hilbert transform loss on the resonant and a smoothness prior on the non-resonant part of the signal. Trained entirely on synthetic data, RamPINN demonstrates strong zero-shot generalization to real-world experimental data, explicitly closing this gap and significantly outperforming existing baselines. Furthermore, we show that training with these physics-based losses alone, without access to any ground-truth Raman spectra, still yields competitive results. This work highlights a broader concept: formal scientific rules can act as a potent inductive bias, enabling robust, self-supervised learning in data-limited scientific domains.

Paperid: 328, https://arxiv.org/pdf/2510.00698.pdf

Abstract:
Physics-informed machine learning has been a promising data-driven and physics-informed approach in geotechnical engineering. This study proposes a physics-informed extreme learning machine (PIELM) framework for analyzing tunneling-induced soil-pile interactions. The pile foundation is modeled as an Euler-Bernoulli beam, and the surrounding soil is modeled as a Pasternak foundation. The soil-pile interaction is formulated into a fourth-order ordinary differential equation (ODE) that constitutes the physics-informed component, while measured data are incorporated into PIELM as the data-driven component. Combining physics and data yields a loss vector of the extreme learning machine (ELM) network, which is trained within 1 second by the least squares method. After validating the PIELM approach by the boundary element method (BEM) and finite difference method (FDM), parametric studies are carried out to examine the effects of ELM network architecture, data monitoring locations and numbers on the performance of PIELM. The results indicate that monitored data should be placed at positions where the gradients of pile deflections are significant, such as at the pile tip/top and near tunneling zones. Two application examples highlight the critical role of physics-informed and data-driven approach for tunnelling-induced soil-pile interactions. The proposed approach shows great potential for real-time monitoring and safety assessment of pile foundations, and benefits for intelligent early-warning systems in geotechnical engineering.

Paperid: 329, https://arxiv.org/pdf/2509.21541.pdf

Abstract:
Hair simulation and rendering are challenging due to complex strand dynamics, diverse material properties, and intricate light-hair interactions. Recent video diffusion models can generate high-quality videos, but they lack fine-grained control over hair dynamics. We present ControlHair, a hybrid framework that integrates a physics simulator with conditional video diffusion to enable controllable dynamic hair rendering. ControlHair adopts a three-stage pipeline: it first encodes physics parameters (e.g., hair stiffness, wind) into per-frame geometry using a simulator, then extracts per-frame control signals, and finally feeds control signals into a video diffusion model to generate videos with desired hair dynamics. This cascaded design decouples physics reasoning from video generation, supports diverse physics, and makes training the video diffusion model easy. Trained on a curated 10K video dataset, ControlHair outperforms text- and pose-conditioned baselines, delivering precisely controlled hair dynamics. We further demonstrate three use cases of ControlHair: dynamic hairstyle try-on, bullet-time effects, and cinemagraphic. ControlHair introduces the first physics-informed video diffusion framework for controllable dynamics. We provide a teaser video and experimental results on our website.

Paperid: 330, https://arxiv.org/pdf/2509.13620.pdf

Abstract:
Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In these applications, the fidelity of the surrogate's gradients with respect to system parameters is crucial, as the accuracy of downstream tasks, such as optimization and Bayesian inference, relies directly on the quality of the derivative information. Recent advances in physics-informed methods have leveraged derivative information to improve surrogate accuracy. However, incorporating explicit Jacobians can become computationally prohibitive, as the complexity typically scales quadratically with the number of input parameters. To address this limitation, we propose DeFINO (Derivative-based Fisher-score Informed Neural Operator), a reduced-order, derivative-informed training framework. DeFINO integrates Fourier neural operators (FNOs) with a novel derivative-based training strategy guided by the Fisher Information Matrix (FIM). By projecting Jacobians onto dominant eigen-directions identified by the FIM, DeFINO captures critical sensitivity information directly informed by observational data, significantly reducing computational expense. We validate DeFINO through synthetic experiments in the context of subsurface multi-phase fluid-flow, demonstrating improvements in gradient accuracy while maintaining robust forward predictions of underlying fluid dynamics. These results highlight DeFINO's potential to offer practical, scalable solutions for inversion problems in complex real-world scenarios, all at substantially reduced computational cost.

Paperid: 331, https://arxiv.org/pdf/2509.12226.pdf

Abstract:
This work introduces a physics-informed neural networks (PINNs)-based model predictive control (MPC) framework for susceptible-infected-recovered ($SIR$) spreading models. Existing studies in MPC design for epidemic control often assume either 1) measurable states of the dynamics, where the parameters are learned, or 2) known parameters of the model, where the states are learned. In this work, we address the joint real-time estimation of states and parameters within the MPC framework using only noisy infected states, under the assumption that 1) only the recovery rate is known, or 2) only the basic reproduction number is known. Under the first assumption, we propose MPC-PINNs and two novel PINNs algorithms, all of which are integrated into the MPC framework. First, we introduce MPC-PINNs, which are designed for $SIR$ models with control. We then propose log-scaled PINNs (MPC-LS-PINNs), which incorporate a log-scaled loss function to improve robustness against noise. Next, we present split-integral PINNs (MPC-SI-PINNs), which leverage integral operators and state coupling in the neural network training process to effectively reconstruct the complete epidemic state information. Building upon these methods, we further extend our framework for the second assumption. We establish the necessary conditions and extend our PINNs algorithms, where MPC-SI-PINNs are simplified as split-PINNs (MPC-S-PINNs). By incorporating these algorithms into the MPC framework, we simultaneously estimate the epidemic states and parameters while generating optimal control strategies. Experiment results demonstrate the effectiveness of the proposed methods under different settings.

Paperid: 332, https://arxiv.org/pdf/2508.08947.pdf

Abstract:
Traffic forecasting is essential for intelligent transportation systems. Accurate forecasting relies on continuous observations collected by traffic sensors. However, due to high deployment and maintenance costs, not all regions are equipped with such sensors. This paper aims to forecast for regions without traffic sensors, where the lack of historical traffic observations challenges the generalisability of existing models. We propose a model named GenCast, the core idea of which is to exploit external knowledge to compensate for the missing observations and to enhance generalisation. We integrate physics-informed neural networks into GenCast, enabling physical principles to regularise the learning process. We introduce an external signal learning module to explore correlations between traffic states and external signals such as weather conditions, further improving model generalisability. Additionally, we design a spatial grouping module to filter localised features that hinder model generalisability. Extensive experiments show that GenCast consistently reduces forecasting errors on multiple real-world datasets.

Paperid: 333, https://arxiv.org/pdf/2508.07536.pdf

Abstract:
Accurate and interpretable bearing fault classification is critical for ensuring the reliability of rotating machinery, particularly under variable operating conditions where domain shifts can significantly degrade model performance. This study proposes a physics-informed multimodal convolutional neural network (CNN) with a late fusion architecture, integrating vibration and motor current signals alongside a dedicated physics-based feature extraction branch. The model incorporates a novel physics-informed loss function that penalizes physically implausible predictions based on characteristic bearing fault frequencies - Ball Pass Frequency Outer (BPFO) and Ball Pass Frequency Inner (BPFI) - derived from bearing geometry and shaft speed. Comprehensive experiments on the Paderborn University dataset demonstrate that the proposed physics-informed approach consistently outperforms a non-physics-informed baseline, achieving higher accuracy, reduced false classifications, and improved robustness across multiple data splits. To address performance degradation under unseen operating conditions, three transfer learning (TL) strategies - Target-Specific Fine-Tuning (TSFT), Layer-Wise Adaptation Strategy (LAS), and Hybrid Feature Reuse (HFR) - are evaluated. Results show that LAS yields the best generalization, with additional performance gains when combined with physics-informed modeling. Validation on the KAIST bearing dataset confirms the framework's cross-dataset applicability, achieving up to 98 percent accuracy. Statistical hypothesis testing further verifies significant improvements (p < 0.01) in classification performance. The proposed framework demonstrates the potential of integrating domain knowledge with data-driven learning to achieve robust, interpretable, and generalizable fault diagnosis for real-world industrial applications.

Paperid: 334, https://arxiv.org/pdf/2507.02078.pdf

Abstract:
Accurate and scalable surrogate models for AC power flow are essential for real-time grid monitoring, contingency analysis, and decision support in increasingly dynamic and inverter-dominated power systems. However, most existing surrogates fall short of practical deployment due to their limited capacity to capture long-range nonlinear dependencies in meshed transmission networks and their weak enforcement of physical laws. These models often require extensive hyperparameter tuning, exhibit poor generalization under topology changes or large load swings, and typically do not quantify uncertainty or scale well beyond a few hundred buses. To address these challenges, this paper proposes a \textit{gated graph neural network (GGNN)} surrogate for AC power-flow estimation under topological uncertainty. The model is trained across multiple IEEE benchmark networks of varying size and complexity, each incorporating randomized line contingencies and up to 40\% load variation. To improve robustness and generalization, we explore both conventional supervised learning and physics-informed self-supervised training strategies. Comparative evaluations show that the proposed GGNN consistently outperforms prior GNN-based surrogates, achieving predictions closely aligned with Newton--Raphson solutions. By embedding operational constraints directly into the architecture and loss function, the model ensures physical consistency and delivers a lightweight, accurate, and scalable tool for real-time grid operations.

Paperid: 335, https://arxiv.org/pdf/2506.14786.pdf

Abstract:
Multimodal time series forecasting is foundational in various fields, such as utilizing satellite imagery and numerical data for predicting typhoons in climate science. However, existing multimodal approaches primarily focus on utilizing text data to help time series forecasting, leaving the visual data in existing time series datasets untouched. Furthermore, it is challenging for models to effectively capture the physical information embedded in visual data, such as satellite imagery's temporal and geospatial context, which extends beyond images themselves. To address this gap, we propose physics-informed positional encoding (PIPE), a lightweight method that embeds physical information into vision language models (VLMs). PIPE introduces two key innovations: (1) a physics-informed positional indexing scheme for mapping physics to positional IDs, and (2) a variant-frequency positional encoding mechanism for encoding frequency information of physical variables and sequential order of tokens within the embedding space. By preserving both the physical information and sequential order information, PIPE significantly improves multimodal alignment and forecasting accuracy. Through the experiments on the most representative and the largest open-sourced satellite image dataset, PIPE achieves state-of-the-art performance in both deep learning forecasting and climate domain methods, demonstrating superiority across benchmarks, including a 12% improvement in typhoon intensity forecasting over prior works. Our code is provided in the supplementary material.

Paperid: 336, https://arxiv.org/pdf/2506.12029.pdf

Abstract:
Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints, leading to forecasts that disobey vessel motion dynamics, such as in scenarios with limited or noisy data where sudden course changes or speed variations occur due to external factors. To address this limitation, we propose a Physics-Informed Neural Network (PINN) approach for trajectory prediction that integrates a streamlined kinematic model for vessel motion into the neural network training process via a first- and second-order, finite difference physics-based loss function. This loss function, discretized using the first-order forward Euler method, Heun's second-order approximation, and refined with a midpoint approximation based on Taylor series expansion, enforces fidelity to fundamental physical principles by penalizing deviations from expected kinematic behavior. We evaluated PINN using real-world AIS datasets that cover diverse maritime conditions and compared it with state-of-the-art models. Our results demonstrate that the proposed method reduces average displacement errors by up to 32% across models and datasets while maintaining physical consistency. These results enhance model reliability and adherence to mission-critical maritime activities, where precision translates into better situational awareness in the oceans.

Paperid: 337, https://arxiv.org/pdf/2506.08381.pdf

Abstract:
Accuracy and efficiency of the conventional physics-informed neural network (PINN) need to be improved before it can be a competitive alternative for soil consolidation analyses. This paper aims to overcome these limitations by proposing a highly accurate and efficient physics-informed machine learning (PIML) approach, termed time-stepping physics-informed extreme learning machine (TS-PIELM). In the TS-PIELM framework the consolidation process is divided into numerous time intervals, which helps overcome the limitation of PIELM in solving differential equations with sharp gradients. To accelerate network training, the solution is approximated by a single-layer feedforward extreme learning machine (ELM), rather than using a fully connected neural network in PINN. The input layer weights of the ELM network are generated randomly and fixed during the training process. Subsequently, the output layer weights are directly computed by solving a system of linear equations, which significantly enhances the training efficiency compared to the time-consuming gradient descent method in PINN. Finally, the superior performance of TS-PIELM is demonstrated by solving three typical Terzaghi consolidation problems. Compared to PINN, results show that the computational efficiency and accuracy of the novel TS-PIELM framework are improved by more than 1000 times and 100 times for one-dimensional cases, respectively. This paper provides compelling evidence that PIML can be a powerful tool for computational geotechnics.

Paperid: 338, https://arxiv.org/pdf/2506.01153.pdf

Abstract:
We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 5 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalisation capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

Paperid: 339, https://arxiv.org/pdf/2503.16850.pdf

Abstract:
This work investigates the feasibility of using Physics-Informed Neural Networks (PINNs) as surrogate models for river stage prediction, aiming to reduce computational cost while maintaining predictive accuracy. Our primary contribution demonstrates that PINNs can successfully approximate HEC-RAS numerical solutions when trained on a single river, achieving strong predictive accuracy with generally low relative errors, though some river segments exhibit higher deviations. By integrating the governing Saint-Venant equations into the learning process, the proposed PINN-based surrogate model enforces physical consistency and significantly improves computational efficiency compared to HEC-RAS. We evaluate the model's performance in terms of accuracy and computational speed, demonstrating that it closely approximates HEC-RAS predictions while enabling real-time inference. These results highlight the potential of PINNs as effective surrogate models for single-river hydrodynamics, offering a promising alternative for computationally efficient river stage forecasting. Future work will explore techniques to enhance PINN training stability and robustness across a more generalized multi-river model.

Paperid: 340, https://arxiv.org/pdf/2503.10253.pdf

Abstract:
Simulation of spatiotemporal systems governed by partial differential equations is widely applied in fields such as biology, chemistry, aerospace dynamics, and meteorology. Traditional numerical methods incur high computational costs due to the requirement of small time steps for accurate predictions. While machine learning has reduced these costs, long-term predictions remain challenged by error accumulation, particularly in scenarios with insufficient data or varying time scales, where stability and accuracy are compromised. Existing methods often neglect the effective utilization of multi-scale data, leading to suboptimal robustness in predictions. To address these issues, we propose a novel multi-scale learning framework, namely, the Physics-Informed Multi-Scale Recurrent Learning (PIMRL), to effectively leverage multi-scale data for spatiotemporal dynamics prediction. The PIMRL framework comprises two modules: the micro-scale module embeds physical knowledge into neural networks via pretraining, and the macro-scale module adopts a data-driven approach to learn the temporal evolution of physics in the latent space. Experimental results demonstrate that the PIMRL framework consistently achieves state-of-the-art performance across five benchmark datasets ranging from one to three dimensions, showing average improvements of over 9\% in both RMSE and MAE evaluation metrics, with maximum enhancements reaching up to 80%.

Paperid: 341, https://arxiv.org/pdf/2502.02682.pdf

Abstract:
Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applications. In such scenarios, detailed physical knowledge can be unavailable or difficult to obtain, and collecting extensive data is often prohibitively expensive. To mitigate this challenge, we propose the Pseudo Physics-Informed Neural Operator (PPI-NO) framework. PPI-NO constructs a surrogate physics system for the target system using partial differential equations (PDEs) derived from simple, rudimentary physics principles, such as basic differential operators. This surrogate system is coupled with a neural operator model, using an alternating update and learning process to iteratively enhance the model's predictive power. While the physics derived via PPI-NO may not mirror the ground-truth underlying physical laws -- hence the term ``pseudo physics'' -- this approach significantly improves the accuracy of standard operator learning models in data-scarce scenarios, which is evidenced by extensive evaluations across five benchmark tasks and a fatigue modeling application.

Paperid: 342, https://arxiv.org/pdf/2501.17110.pdf

Abstract:
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forcing or source terms, which commonly arise as pathwise solutions to stochastic PDEs. Kernel methods have recently been generalized to solve nonlinear PDEs by approximating their solutions as the maximum a posteriori estimator of GPs that are conditioned to satisfy the PDE at a finite set of collocation points. The convergence and error guarantees of these methods, however, rely on the PDE being defined in a classical sense and its solution possessing sufficient regularity to belong to the associated reproducing kernel Hilbert space. We propose a generalization of these methods to handle roughly forced nonlinear PDEs while preserving convergence guarantees with an oversmoothing GP kernel that is misspecified relative to the true solution's regularity. This is achieved by conditioning a regular GP to satisfy the PDE with a modified source term in a weak sense (when integrated against a finite number of test functions). This is equivalent to replacing the empirical $L^2$-loss on the PDE constraint by an empirical negative-Sobolev norm. We further show that this loss function can be used to extend physics-informed neural networks (PINNs) to stochastic equations, thereby resulting in a new NN-based variant termed Negative Sobolev Norm-PINN (NeS-PINN).

Paperid: 343, https://arxiv.org/pdf/2412.05197.pdf

Abstract:
Distance functions are crucial in robotics for representing spatial relationships between the robot and the environment. It provides an implicit representation of continuous and differentiable shapes, which can seamlessly be combined with control, optimization, and learning techniques. While standard distance fields rely on the Euclidean metric, many robotic tasks inherently involve non-Euclidean structures. To this end, we generalize the use of Euclidean distance fields to more general metric spaces by solving a Riemannian eikonal equation, a first-order partial differential equation, whose solution defines a distance field and its associated gradient flow on the manifold, enabling the computation of geodesics and globally length-minimizing paths. We show that this \emph{geodesic distance field} can also be exploited in the robot configuration space. To realize this concept, we exploit physics-informed neural networks to solve the eikonal equation for high-dimensional spaces, which provides a flexible and scalable representation without the need for discretization. Furthermore, a variant of our neural eikonal solver is introduced, which enables the gradient flow to march across both task and configuration spaces. As an example of application, we validate the proposed approach in an energy-aware motion generation task. This is achieved by considering a manifold defined by a Riemannian metric in configuration space, effectively taking the property of the robot's dynamics into account. Our approach produces minimal-energy trajectories for a 7-axis Franka robot by iteratively tracking geodesics through gradient flow backpropagation.

Paperid: 344, https://arxiv.org/pdf/2410.03573.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce HyResPINNs, a novel class of PINNs featuring adaptive hybrid residual blocks that integrate standard neural networks and radial basis function (RBF) networks. A distinguishing characteristic of HyResPINNs is the use of adaptive combination parameters within each residual block, enabling dynamic weighting of the neural and RBF network contributions. Our empirical evaluation of a diverse set of challenging PDE problems demonstrates that HyResPINNs consistently achieve superior accuracy to baseline methods. These results highlight the potential of HyResPINNs to bridge the gap between classical numerical methods and modern machine learning-based solvers, paving the way for more robust and adaptive approaches to physics-informed modeling.

Paperid: 345, https://arxiv.org/pdf/2410.03496.pdf

Abstract:
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale target solutions. To tackle this problem, we first study a strong Boundary Condition (BC) version of PINNs for Dirichlet BCs and observe a consistent decline in relative error compared to the standard PINNs. We then perform a theoretical analysis based on the Fourier transform and convolution theorem. We find that strong BC PINNs can better learn the amplitudes of high-frequency components of the target solutions. However, constructing the architecture for strong BC PINNs is difficult for many BCs and domain geometries. Enlightened by our theoretical analysis, we propose Fourier PINNs -- a simple, general, yet powerful method that augments PINNs with pre-specified, dense Fourier bases. Our proposed architecture likewise learns high-frequency components better but places no restrictions on the particular BCs or problem domains. We develop an adaptive learning and basis selection algorithm via alternating neural net basis optimization, Fourier and neural net basis coefficient estimation, and coefficient truncation. This scheme can flexibly identify the significant frequencies while weakening the nominal frequencies to better capture the target solution's power spectrum. We show the advantage of our approach through a set of systematic experiments.

Paperid: 346, https://arxiv.org/pdf/2601.07139.pdf

Abstract:
The surface pressure field of transportation systems, including cars, trains, and aircraft, is critical for aerodynamic analysis and design. In recent years, deep neural networks have emerged as promising and efficient methods for modeling surface pressure field, being alternatives to computationally expensive CFD simulations. Currently, large-scale public datasets are available for domains such as automotive aerodynamics. However, in many specialized areas, such as high-speed trains, data scarcity remains a fundamental challenge in aerodynamic modeling, severely limiting the effectiveness of standard neural network approaches. To address this limitation, we propose the Adaptive Field Learning Framework (AdaField), which pre-trains the model on public large-scale datasets to improve generalization in sub-domains with limited data. AdaField comprises two key components. First, we design the Semantic Aggregation Point Transformer (SAPT) as a high-performance backbone that efficiently handles large-scale point clouds for surface pressure prediction. Second, regarding the substantial differences in flow conditions and geometric scales across different aerodynamic subdomains, we propose Flow-Conditioned Adapter (FCA) and Physics-Informed Data Augmentation (PIDA). FCA enables the model to flexibly adapt to different flow conditions with a small set of trainable parameters, while PIDA expands the training data distribution to better cover variations in object scale and velocity. Our experiments show that AdaField achieves SOTA performance on the DrivAerNet++ dataset and can be effectively transferred to train and aircraft scenarios with minimal fine-tuning. These results highlight AdaField's potential as a generalizable and transferable solution for surface pressure field modeling, supporting efficient aerodynamic design across a wide range of transportation systems.

Paperid: 347, https://arxiv.org/pdf/2601.03113.pdf

Abstract:
This paper presents the first probabilistic Digital Twin of operational en route airspace, developed for the London Area Control Centre. The Digital Twin is intended to support the development and rigorous human-in-the-loop evaluation of AI agents for Air Traffic Control (ATC), providing a virtual representation of real-world airspace that enables safe exploration of higher levels of ATC automation. This paper makes three significant contributions: firstly, we demonstrate how historical and live operational data may be combined with a probabilistic, physics-informed machine learning model of aircraft performance to reproduce real-world traffic scenarios, while accurately reflecting the level of uncertainty inherent in ATC. Secondly, we develop a structured assurance case, following the Trustworthy and Ethical Assurance framework, to provide quantitative evidence for the Digital Twin's accuracy and fidelity. This is crucial to building trust in this novel technology within this safety-critical domain. Thirdly, we describe how the Digital Twin forms a unified environment for agent testing and evaluation. This includes fast-time execution (up to x200 real-time), a standardised Python-based ``gym'' interface that supports a range of AI agent designs, and a suite of quantitative metrics for assessing performance. Crucially, the framework facilitates competency-based assessment of AI agents by qualified Air Traffic Control Officers through a Human Machine Interface. We also outline further applications and future extensions of the Digital Twin architecture.

Paperid: 348, https://arxiv.org/pdf/2601.00427.pdf

Abstract:
This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the challenges inherent in sparse and noisy far-field data. The Fourier method provides a physics-informed, low-frequency approximation of the source, which serves as the input to a U-Net. The network is trained to map this coarse approximation to a high-fidelity source reconstruction, effectively suppressing truncation artifacts and recovering fine-scale geometric details. To enhance computational efficiency and robustness, we propose a high-to-low noise transfer learning strategy: a model pre-trained on high-noise regimes captures global topological features, offering a robust initialization for fine-tuning on lower-noise data. Numerical experiments demonstrate that the framework achieves accurate reconstructions with noise levels up to 100%, significantly outperforms traditional spectral methods under sparse measurement constraints, and generalizes well to unseen source geometries.

Paperid: 349, https://arxiv.org/pdf/2512.03476.pdf

Abstract:
Bridging the gap between theoretical conceptualization and computational implementation is a major bottleneck in Scientific Computing (SciC) and Scientific Machine Learning (SciML). We introduce ATHENA (Agentic Team for Hierarchical Evolutionary Numerical Algorithms), an agentic framework designed as an Autonomous Lab to manage the end-to-end computational research lifecycle. Its core is the HENA loop, a knowledge-driven diagnostic process framed as a Contextual Bandit problem. Acting as an online learner, the system analyzes prior trials to select structural `actions' ($A_n$) from combinatorial spaces guided by expert blueprints (e.g., Universal Approximation, Physics-Informed constraints). These actions are translated into executable code ($S_n$) to generate scientific rewards ($R_n$). ATHENA transcends standard automation: in SciC, it autonomously identifies mathematical symmetries for exact analytical solutions or derives stable numerical solvers where foundation models fail. In SciML, it performs deep diagnosis to tackle ill-posed formulations and combines hybrid symbolic-numeric workflows (e.g., coupling PINNs with FEM) to resolve multiphysics problems. The framework achieves super-human performance, reaching validation errors of $10^{-14}$. Furthermore, collaborative ``human-in-the-loop" intervention allows the system to bridge stability gaps, improving results by an order of magnitude. This paradigm shift focuses from implementation mechanics to methodological innovation, accelerating scientific discovery.

Paperid: 350, https://arxiv.org/pdf/2511.05452.pdf

Abstract:
Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and efficiency. In this work, we introduce a hybrid adaptive sampling and weighting method to enhance the performance of physics-informed neural networks (PINNs). The adaptive sampling component identifies training points in regions where the solution exhibits rapid variation, while the adaptive weighting component balances the convergence rate across training points. Numerical experiments show that applying only adaptive sampling or only adaptive weighting is insufficient to consistently achieve accurate predictions, particularly when training points are scarce. Since each method emphasizes different aspects of the solution, their effectiveness is problem dependent. By combining both strategies, the proposed framework consistently improves prediction accuracy and training efficiency, offering a more robust approach for solving PDEs with PINNs.

Paperid: 351, https://arxiv.org/pdf/2510.23501.pdf

Abstract:
Since their introduction, Kolmogorov-Arnold Networks (KANs) have been successfully applied across several domains, with physics-informed machine learning (PIML) emerging as one of the areas where they have thrived. In the PIML setting, Chebyshev-based physics-informed KANs (cPIKANs) have become the standard due to their computational efficiency. However, like their multilayer perceptron-based counterparts, cPIKANs face significant challenges when scaled to depth, leading to training instabilities that limit their applicability to several PDE problems. To address this, we propose a basis-agnostic, Glorot-like initialization scheme that preserves activation variance and yields substantial improvements in stability and accuracy over the default initialization of cPIKANs. Inspired by the PirateNet architecture, we further introduce Residual-Gated Adaptive KANs (RGA KANs), designed to mitigate divergence in deep cPIKANs where initialization alone is not sufficient. Through empirical tests and information bottleneck analysis, we show that RGA KANs successfully traverse all training phases, unlike baseline cPIKANs, which stagnate in the diffusion phase in specific PDE settings. Evaluations on seven standard forward PDE benchmarks under a fixed training pipeline with adaptive components demonstrate that RGA KANs consistently outperform parameter-matched cPIKANs and PirateNets - often by several orders of magnitude - while remaining stable in settings where the others diverge.

Paperid: 352, https://arxiv.org/pdf/2510.21796.pdf

Abstract:
The Madden-Julian Oscillation (MJO) is an important driver of global weather and climate extremes, but its prediction in operational dynamical models remains challenging, with skillful forecasts typically limited to 3-4 weeks. Here, we introduce a novel deep learning framework, the Physics-guided Cascaded Corrector for MJO (PCC-MJO), which acts as a universal post-processor to correct MJO forecasts from dynamical models. This two-stage model first employs a physics-informed 3D U-Net to correct spatial-temporal field errors, then refines the MJO's RMM index using an LSTM optimized for forecast skill. When applied to three different operational forecasts from CMA, ECMWF and NCEP, our unified framework consistently extends the skillful forecast range (bivariate correlation > 0.5) by 2-8 days. Crucially, the model effectively mitigates the "Maritime Continent barrier", enabling more realistic eastward propagation and amplitude. Explainable AI analysis quantitatively confirms that the model's decision-making is spatially congruent with observed MJO dynamics (correlation > 0.93), demonstrating that it learns physically meaningful features rather than statistical fittings. Our work provides a promising physically consistent, computationally efficient, and highly generalizable pathway to break through longstanding barriers in subseasonal forecasting.

Paperid: 353, https://arxiv.org/pdf/2510.17380.pdf

Abstract:
Optimizing the energy management within a smart grids scenario presents significant challenges, primarily due to the complexity of real-world systems and the intricate interactions among various components. Reinforcement Learning (RL) is gaining prominence as a solution for addressing the challenges of Optimal Power Flow in smart grids. However, RL needs to iterate compulsively throughout a given environment to obtain the optimal policy. This means obtaining samples from a, most likely, costly simulator, which can lead to a sample efficiency problem. In this work, we address this problem by substituting costly smart grid simulators with surrogate models built using Phisics-informed Neural Networks (PINNs), optimizing the RL policy training process by arriving to convergent results in a fraction of the time employed by the original environment.

Paperid: 354, https://arxiv.org/pdf/2510.11242.pdf

Abstract:
In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.

Paperid: 355, https://arxiv.org/pdf/2510.05433.pdf

Abstract:
Physics-informed machine learning (PIML) is emerging as a potentially transformative paradigm for modeling complex biomedical systems by integrating parameterized physical laws with data-driven methods. Here, we review three main classes of PIML frameworks: physics-informed neural networks (PINNs), neural ordinary differential equations (NODEs), and neural operators (NOs), highlighting their growing role in biomedical science and engineering. We begin with PINNs, which embed governing equations into deep learning models and have been successfully applied to biosolid and biofluid mechanics, mechanobiology, and medical imaging among other areas. We then review NODEs, which offer continuous-time modeling, especially suited to dynamic physiological systems, pharmacokinetics, and cell signaling. Finally, we discuss deep NOs as powerful tools for learning mappings between function spaces, enabling efficient simulations across multiscale and spatially heterogeneous biological domains. Throughout, we emphasize applications where physical interpretability, data scarcity, or system complexity make conventional black-box learning insufficient. We conclude by identifying open challenges and future directions for advancing PIML in biomedical science and engineering, including issues of uncertainty quantification, generalization, and integration of PIML and large language models.

Paperid: 356, https://arxiv.org/pdf/2510.05158.pdf

Abstract:
Physics-informed neural networks (PINNs) provide a powerful approach for solving partial differential equations (PDEs), but constructing a usable PINN remains labor-intensive and error-prone. Scientists must interpret problems as PDE formulations, design architectures and loss functions, and implement stable training pipelines. Existing large language model (LLM) based approaches address isolated steps such as code generation or architecture suggestion, but typically assume a formal PDE is already specified and therefore lack an end-to-end perspective. We present Lang-PINN, an LLM-driven multi-agent system that builds trainable PINNs directly from natural language task descriptions. Lang-PINN coordinates four complementary agents: a PDE Agent that parses task descriptions into symbolic PDEs, a PINN Agent that selects architectures, a Code Agent that generates modular implementations, and a Feedback Agent that executes and diagnoses errors for iterative refinement. This design transforms informal task statements into executable and verifiable PINN code. Experiments show that Lang-PINN achieves substantially lower errors and greater robustness than competitive baselines: mean squared error (MSE) is reduced by up to 3--5 orders of magnitude, end-to-end execution success improves by more than 50\%, and reduces time overhead by up to 74\%.

Paperid: 357, https://arxiv.org/pdf/2510.04490.pdf

Abstract:
Partial differential equation (PDE) solvers are fundamental to engineering simulation. Classical mesh-based approaches (finite difference/volume/element) are fast and accurate on high-quality meshes but struggle with higher-order operators and complex, hard-to-mesh geometries. Recently developed physics-informed neural networks (PINNs) and their variants are mesh-free and flexible, yet compute-intensive and often less accurate. This paper systematically benchmarks RBF-PIELM, a rapid PINN variant-an extreme learning machine with radial-basis activations-for higher-order PDEs. RBF-PIELM replaces PINNs' time-consuming gradient descent with a single-shot least-squares solve. We test RBF-PIELM on the fourth-order biharmonic equation using two benchmarks: lid-driven cavity flow (streamfunction formulation) and a manufactured oscillatory solution. Our results show up to $(350\times)$ faster training than PINNs and over $(10\times)$ fewer parameters for comparable solution accuracy. Despite surpassing PINNs, RBF-PIELM still lags mature mesh-based solvers and its accuracy degrades on highly oscillatory solutions, highlighting remaining challenges for practical deployment.

Paperid: 358, https://arxiv.org/pdf/2510.04322.pdf

Abstract:
Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and inverse problems of partial differential equations (PDEs) using deep learning. However they remain computationally expensive due to their iterative gradient descent based optimization and scale poorly with increasing model size. This paper introduces Physics-Informed Extreme Learning Machines (PIELMs) as fast alternative to PINNs for solving both forward and inverse problems in financial PDEs. PIELMs replace iterative optimization with a single least-squares solve, enabling deterministic and efficient training. We benchmark PIELM on the Black-Scholes and Heston-Hull-White models for forward pricing and demonstrate its capability in inverse model calibration to recover volatility and interest rate parameters from noisy data. From experiments we observe that PIELM achieve accuracy comparable to PINNs while being up to $30\times$ faster, highlighting their potential for real-time financial modeling.

Paperid: 359, https://arxiv.org/pdf/2509.25730.pdf

Abstract:
Ship traffic is an increasing source of underwater radiated noise in coastal waters, motivating real-time digital twins of ocean acoustics for operational noise mitigation. We present a physics-guided probabilistic framework to predict three-dimensional transmission loss in realistic ocean environments. As a case study, we consider the Salish Sea along shipping routes from the Pacific Ocean to the Port of Vancouver. A dataset of over 30 million source-receiver pairs was generated with a Gaussian beam solver across seasonal sound speed profiles and one-third-octave frequency bands spanning 12.5 Hz to 8 kHz. We first assess sparse variational Gaussian processes (SVGP) and then incorporate physics-based mean functions combining spherical spreading with frequency-dependent absorption. To capture nonlinear effects, we examine deep sigma-point processes and stochastic variational deep kernel learning. The final framework integrates four components: (i) a learnable physics-informed mean that represents dominant propagation trends, (ii) a convolutional encoder for bathymetry along the source-receiver track, (iii) a neural encoder for source, receiver, and frequency coordinates, and (iv) a residual SVGP layer that provides calibrated predictive uncertainty. This probabilistic digital twin facilitates the construction of sound-exposure bounds and worst-case scenarios for received levels. We further demonstrate the application of the framework to ship speed optimization, where predicted transmission loss combined with near-field source models provides sound exposure level estimates for minimizing acoustic impacts on marine mammals. The proposed framework advances uncertainty-aware digital twins for ocean acoustics and illustrates how physics-guided machine learning can support sustainable maritime operations.

Paperid: 360, https://arxiv.org/pdf/2509.06782.pdf

Abstract:
Offline Goal-Conditioned Reinforcement Learning (GCRL) holds great promise for domains such as autonomous navigation and locomotion, where collecting interactive data is costly and unsafe. However, it remains challenging in practice due to the need to learn from datasets with limited coverage of the state-action space and to generalize across long-horizon tasks. To improve on these challenges, we propose a \emph{Physics-informed (Pi)} regularized loss for value learning, derived from the Eikonal Partial Differential Equation (PDE) and which induces a geometric inductive bias in the learned value function. Unlike generic gradient penalties that are primarily used to stabilize training, our formulation is grounded in continuous-time optimal control and encourages value functions to align with cost-to-go structures. The proposed regularizer is broadly compatible with temporal-difference-based value learning and can be integrated into existing Offline GCRL algorithms. When combined with Hierarchical Implicit Q-Learning (HIQL), the resulting method, Eikonal-regularized HIQL (Eik-HIQL), yields significant improvements in both performance and generalization, with pronounced gains in stitching regimes and large-scale navigation tasks.

Paperid: 361, https://arxiv.org/pdf/2509.06574.pdf

Abstract:
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale collective effects. So we present a multi-scale framework that combines the three learning-driven tools to learn in concert within one pipeline. We use high-resolution Lattice Boltzmann snapshots of fluid velocity and particle stresses in a periodic box as input to the learning pipeline. the second step takes the morphology and positions orientations of particles to predict pairwise interaction forces between them with a E(2)-equivariant graph neural network that necessarily respect flat symmetries. Then, a physics-informed neural network further updates these local estimates by summing over them with a stress data using Fourier feature mappings and residual blocks that is additionally regularized with a topological term (introduced by persistent homology) to penalize unrealistically tangled or spurious connections. In concert, these stages deliver an holistic highly-data driven full force network prediction empathizing on the physical underpinnings together with emerging multi-scale structure typical for active matter.

Paperid: 362, https://arxiv.org/pdf/2509.02649.pdf

Abstract:
Kernel methods are powerful tools in statistical learning, but their cubic complexity in the sample size n limits their use on large-scale datasets. In this work, we introduce a scalable framework for kernel regression with O(n log n) complexity, fully leveraging GPU acceleration. The approach is based on a Fourier representation of kernels combined with non-uniform fast Fourier transforms (NUFFT), enabling exact, fast, and memory-efficient computations. We instantiate our framework in three settings: Sobolev kernel regression, physics-informed regression, and additive models. When known, the proposed estimators are shown to achieve minimax convergence rates, consistent with classical kernel theory. Empirical results demonstrate that our methods can process up to tens of billions of samples within minutes, providing both statistical accuracy and computational scalability. These contributions establish a flexible approach, paving the way for the routine application of kernel methods in large-scale learning tasks.

Paperid: 363, https://arxiv.org/pdf/2509.01679.pdf

Abstract:
Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the "vanilla" DeepONet is valued for its simplicity and efficiency, while the modified DeepONet achieves higher accuracy at the cost of increased training time. In this work, we propose a series of Transformer-inspired DeepONet variants that introduce bidirectional cross-conditioning between the branch and trunk networks in DeepONet. Query-point information is injected into the branch network and input-function information into the trunk network, enabling dynamic dependencies while preserving the simplicity and efficiency of the "vanilla" DeepONet in a non-intrusive manner. Experiments on four PDE benchmarks -- advection, diffusion-reaction, Burgers', and Korteweg-de Vries equations -- show that for each case, there exists a variant that matches or surpasses the accuracy of the modified DeepONet while offering improved training efficiency. Moreover, the best-performing variant for each equation aligns naturally with the equation's underlying characteristics, suggesting that the effectiveness of cross-conditioning depends on the characteristics of the equation and its underlying physics. To ensure robustness, we validate the effectiveness of our variants through a range of rigorous statistical analyses, among them the Wilcoxon Two One-Sided Test, Glass's Delta, and Spearman's rank correlation.

Paperid: 364, https://arxiv.org/pdf/2508.21559.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in conventional data-driven methods. This paper evaluates PINNs' capabilities as surrogate models for smart grid dynamics, comparing their performance against XGBoost, Random Forest, and Linear Regression across three key experiments: interpolation, cross-validation, and episodic trajectory prediction. By training PINNs exclusively through physics-based loss functions (enforcing power balance, operational constraints, and grid stability) we demonstrate their superior generalization, outperforming data-driven models in error reduction. Notably, PINNs maintain comparatively lower MAE in dynamic grid operations, reliably capturing state transitions in both random and expert-driven control scenarios, while traditional models exhibit erratic performance. Despite slight degradation in extreme operational regimes, PINNs consistently enforce physical feasibility, proving vital for safety-critical applications. Our results contribute to establishing PINNs as a paradigm-shifting tool for smart grid surrogation, bridging data-driven flexibility with first-principles rigor. This work advances real-time grid control and scalable digital twins, emphasizing the necessity of physics-aware architectures in mission-critical energy systems.

Paperid: 365, https://arxiv.org/pdf/2508.12681.pdf

Abstract:
Dynamic control of soft continuum robots (SCRs) holds great potential for expanding their applications, but remains a challenging problem due to the high computational demands of accurate dynamic models. While data-driven approaches like Koopman-operator-based methods have been proposed, they typically lack adaptability and cannot capture the full robot shape, limiting their applicability. This work introduces a real-time-capable nonlinear model-predictive control (MPC) framework for SCRs based on a domain-decoupled physics-informed neural network (DD-PINN) with adaptable bending stiffness. The DD-PINN serves as a surrogate for the dynamic Cosserat rod model with a speed-up factor of 44000. It is also used within an unscented Kalman filter for estimating the model states and bending compliance from end-effector position measurements. We implement a nonlinear evolutionary MPC running at 70 Hz on the GPU. In simulation, it demonstrates accurate tracking of dynamic trajectories and setpoint control with end-effector position errors below 3 mm (2.3% of the actuator's length). In real-world experiments, the controller achieves similar accuracy and accelerations up to 3.55 m/s2.

Paperid: 366, https://arxiv.org/pdf/2508.10322.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs), yet they often fail to achieve accurate convergence in the H1 norm, especially in the presence of boundary approximation errors. In this work, we propose a novel method called Sobolev-Stable Boundary Enforcement (SSBE), which redefines the boundary loss using Sobolev norms to incorporate boundary regularity directly into the training process. We provide rigorous theoretical analysis demonstrating that SSBE ensures bounded H1 error via a stability guarantee and derive generalization bounds that characterize its robustness under finite-sample regimes. Extensive numerical experiments on linear and nonlinear PDEs, including Poisson, heat, and elliptic problems, show that SSBE consistently outperforms standard PINNs in terms of both relative L2 and H1 errors, even in high-dimensional settings. The proposed approach offers a principled and practical solution for improving gradient fidelity and overall solution accuracy in neural network based PDE solvers.

Paperid: 367, https://arxiv.org/pdf/2507.10241.pdf

Abstract:
This paper introduces the Kernel Adaptive Physics-Informed Extreme Learning Machine (KAPI-ELM), an adaptive Radial Basis Function (RBF)-based extension of PI-ELM designed to solve both forward and inverse Partial Differential Equation (PDE) problems involving localized sharp gradients. While PI-ELMs outperform the traditional Physics-Informed Neural Networks (PINNs) in speed due to their single-shot, least square optimization, this advantage comes at a cost: their fixed, randomly initialized input layer limits their ability to capture sharp gradients. To overcome this limitation, we introduce a lightweight Bayesian Optimization (BO) framework that, instead of adjusting each input layer parameter individually as in traditional backpropagation, learns a small set of hyperparameters defining the statistical distribution from which the input weights are drawn. This novel distributional optimization strategy -- combining BO for input layer distributional parameters with least-squares optimization for output layer network parameters -- enables KAPI-ELM to preserve PI-ELM's speed while matching or exceeding the expressiveness of PINNs. We validate the proposed methodology on several challenging forward and inverse PDE benchmarks, including a 1D singularly perturbed convection-diffusion equation, a 2D Poisson equation with sharp localized sources, and a time-dependent advection equation. Notably, KAPI-ELM achieves state-of-the-art accuracy in both forward and inverse settings. In stiff PDE regimes, it matches or even outperforms advanced methods such as the Extended Theory of Functional Connections (XTFC), while requiring nearly an order of magnitude fewer tunable parameters. These results establish the potential of KAPI-ELM as a scalable, interpretable, and generalizable physics-informed learning framework, especially in stiff PDE regimes.

Paperid: 368, https://arxiv.org/pdf/2506.21499.pdf

Abstract:
Ultrasound Coherent Plane Wave Compounding (CPWC) enhances image contrast by combining echoes from multiple steered transmissions. While increasing the number of angles generally improves image quality, it drastically reduces the frame rate and can introduce blurring artifacts in fast-moving targets. Moreover, compounded images remain susceptible to noise, particularly when acquired with a limited number of transmissions. We propose a zero-shot denoising framework tailored for low-angle CPWC acquisitions, which enhances contrast without relying on a separate training dataset. The method divides the available transmission angles into two disjoint subsets, each used to form compound images that include higher noise levels. The new compounded images are then used to train a deep model via a self-supervised residual learning scheme, enabling it to suppress incoherent noise while preserving anatomical structures. Because angle-dependent artifacts vary between the subsets while the underlying tissue response is similar, this physics-informed pairing allows the network to learn to disentangle the inconsistent artifacts from the consistent tissue signal. Unlike supervised methods, our model requires no domain-specific fine-tuning or paired data, making it adaptable across anatomical regions and acquisition setups. The entire pipeline supports efficient training with low computational cost due to the use of a lightweight architecture, which comprises only two convolutional layers. Evaluations on simulation, phantom, and in vivo data demonstrate superior contrast enhancement and structure preservation compared to both classical and deep learning-based denoising methods.

Paperid: 369, https://arxiv.org/pdf/2505.06810.pdf

Abstract:
To mitigate the barren plateau problem, effective parameter initialization is crucial for optimizing the Quantum Approximate Optimization Algorithm (QAOA) in the near-term Noisy Intermediate-Scale Quantum (NISQ) era. Prior physics-driven approaches leveraged the optimal parameter concentration phenomenon, utilizing medium values of previously optimized QAOA parameters stored in databases as initialization for new graphs. However, this medium-value-based strategy lacks generalization capability. Conversely, prior computer-science-based approaches employed graph neural networks (GNNs) trained on previously optimized QAOA parameters to predict initialization values for new graphs. However, these approaches neglect key physics-informed QAOA principles, such as parameter concentration, symmetry, and adiabatic evolution, resulting in suboptimal parameter predictions and limited performance improvements. Furthermore, no existing GNN-based methods support parameter initialization for QAOA circuits with variable depths or for solving weighted Max-Cut problems. This paper introduces QSeer, a quantum-inspired GNN designed for accurate QAOA parameter prediction. Compared to prior physics- and computer-science-driven methods, QSeer improves the initial approximation ratio and convergence speed of QAOA circuits across diverse graphs by 6%-68% and 5x-10x, respectively.

Paperid: 370, https://arxiv.org/pdf/2504.15311.pdf

Abstract:
Due to its ability to work in non-line-of-sight and low-light environments, radio frequency (RF) imaging technology is expected to bring new possibilities for embodied intelligence and multimodal sensing. However, widely used RF devices (such as Wi-Fi) often struggle to provide high-precision electromagnetic measurements and large-scale datasets, hindering the application of RF imaging technology. In this paper, we combine the ideas of PINN to design the RINN network, using physical constraints instead of true value comparison constraints and adapting it with the characteristics of ubiquitous RF signals, allowing the RINN network to achieve RF imaging using only one sample without phase and with amplitude noise. Our numerical evaluation results show that compared with 5 classic algorithms based on phase data for imaging results, RINN's imaging results based on phaseless data are good, with indicators such as RRMSE (0.11) performing similarly well. RINN provides new possibilities for the universal development of radio frequency imaging technology.

Paperid: 371, https://arxiv.org/pdf/2504.02529.pdf

Abstract:
This paper presents a method for generating probabilistic descent trajectories in simulations of real-world airspace. A dataset of 116,066 trajectories harvested from Mode S radar returns in UK airspace was used to train and test the model. Thirteen aircraft types with varying performance characteristics were investigated. It was found that the error in the mean prediction of time to reach the bottom of descent for the proposed method was less than that of the the Base of Aircraft Data (BADA) model by a factor of 10. Furthermore, the method was capable of generating a range of trajectories that were similar to the held out test dataset when analysed in distribution. The proposed method is hybrid, with aircraft drag and calibrated airspeed functions generated probabilistically to parameterise the BADA equations, ensuring the physical plausibility of generated trajectories.

Paperid: 372, https://arxiv.org/pdf/2503.08482.pdf

Abstract:
Outdoor thermal comfort is a critical determinant of urban livability, particularly in hot desert climates where extreme heat poses challenges to public health, energy consumption, and urban planning. Mean Radiant Temperature ($T_{mrt}$) is a key parameter for evaluating outdoor thermal comfort, especially in urban environments where radiation dynamics significantly impact human thermal exposure. Traditional methods of estimating $T_{mrt}$ rely on field measurements and computational simulations, both of which are resource intensive. This study introduces a Physics-Informed Neural Network (PINN) approach that integrates shortwave and longwave radiation modeling with deep learning techniques. By leveraging a multimodal dataset that includes meteorological data, built environment characteristics, and fisheye image-derived shading information, our model enhances predictive accuracy while maintaining physical consistency. Our experimental results demonstrate that the proposed PINN framework outperforms conventional deep learning models, with the best-performing configurations achieving an RMSE of 3.50 and an $R^2$ of 0.88. This approach highlights the potential of physics-informed machine learning in bridging the gap between computational modeling and real-world applications, offering a scalable and interpretable solution for urban thermal comfort assessments.

Paperid: 373, https://arxiv.org/pdf/2502.12164.pdf

Abstract:
Water distribution systems (WDSs) are an important part of critical infrastructure becoming increasingly significant in the face of climate change and urban population growth. We propose a robust and scalable surrogate deep learning (DL) model to enable efficient planning, expansion, and rehabilitation of WDSs. Our approach incorporates an improved graph neural network architecture, an adapted physics-informed algorithm, an innovative training scheme, and a physics-preserving data normalization method. Evaluation results on a number of WDSs demonstrate that our model outperforms the current state-of-the-art DL model. Moreover, our method allows us to scale the model to bigger and more realistic WDSs. Furthermore, our approach makes the model more robust to out-of-distribution input features (demands, pipe diameters). Hence, our proposed method constitutes a significant step towards bridging the simulation-to-real gap in the use of artificial intelligence for WDSs.

Paperid: 374, https://arxiv.org/pdf/2502.01916.pdf

Abstract:
Soft robots can revolutionize several applications with high demands on dexterity and safety. When operating these systems, real-time estimation and control require fast and accurate models. However, prediction with first-principles (FP) models is slow, and learned black-box models have poor generalizability. Physics-informed machine learning offers excellent advantages here, but it is currently limited to simple, often simulated systems without considering changes after training. We propose physics-informed neural networks (PINNs) for articulated soft robots (ASRs) with a focus on data efficiency. The amount of expensive real-world training data is reduced to a minimum -- one dataset in one system domain. Two hours of data in different domains are used for a comparison against two gold-standard approaches: In contrast to a recurrent neural network, the PINN provides a high generalizability. The prediction speed of an accurate FP model is exceeded with the PINN by up to a factor of 467 at slightly reduced accuracy. This enables nonlinear model predictive control (MPC) of a pneumatic ASR. Accurate position tracking with the MPC running at 47 Hz is achieved in six dynamic experiments.

Paperid: 375, https://arxiv.org/pdf/2501.15057.pdf

Abstract:
Recent advancements in machine learning-based methods have demonstrated great potential for improved property prediction in material science. However, reliable estimation of the confidence intervals for the predicted values remains a challenge, due to the inherent complexities in material modeling. This study introduces a novel approach for uncertainty quantification in fatigue life prediction of metal materials based on integrating knowledge from physics-based fatigue life models and machine learning models. The proposed approach employs physics-based input features estimated using the Basquin fatigue model to augment the experimentally collected data of fatigue life. Furthermore, a physics-informed loss function that enforces boundary constraints for the estimated fatigue life of considered materials is introduced for the neural network models. Experimental validation on datasets comprising collected data from fatigue life tests for Titanium alloys and Carbon steel alloys demonstrates the effectiveness of the proposed approach. The synergy between physics-based models and data-driven models enhances the consistency in predicted values and improves uncertainty interval estimates.

Paperid: 376, https://arxiv.org/pdf/2501.11937.pdf

Abstract:
Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address this challenge, physics-informed intelligent learning methods have recently emerged, significantly improving generation efficiency while maintaining high mesh quality. However, physics-informed methods fail to generalize when applied to previously unseen geometries, as even small changes in the boundary shape necessitate burdensome retraining to adapt to new geometric variations. In this paper, we introduce MeshONet, the first generalizable intelligent learning method for structured mesh generation. The method transforms the mesh generation task into an operator learning problem with multiple input and solution functions. To effectively overcome the multivariable mapping restriction of operator learning methods, we propose a dual-branch, shared-trunk architecture to approximate the mapping between function spaces based on input-output pairs. Experimental results show that MeshONet achieves a speedup of up to four orders of magnitude in generation efficiency over traditional methods. It also enables generalization to different geometries without retraining, greatly enhancing the practicality of intelligent methods.

Paperid: 377, https://arxiv.org/pdf/2412.16738.pdf

Abstract:
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines robust multi-layer perceptron (MLP) based inner functions with flexible linear combinations of basis functions as outer functions. We first prove that KKAN is a universal approximator, and then we demonstrate its versatility across scientific machine-learning applications, including function regression, physics-informed machine learning (PIML), and operator-learning frameworks. The benchmark results show that KKANs outperform MLPs and the original Kolmogorov-Arnold Networks (KANs) in function approximation and operator learning tasks and achieve performance comparable to fully optimized MLPs for PIML. To better understand the behavior of the new representation models, we analyze their geometric complexity and learning dynamics using information bottleneck theory, identifying three universal learning stages, fitting, transition, and diffusion, across all types of architectures. We find a strong correlation between geometric complexity and signal-to-noise ratio (SNR), with optimal generalization achieved during the diffusion stage. Additionally, we propose self-scaled residual-based attention weights to maintain high SNR dynamically, ensuring uniform convergence and prolonged learning.

Paperid: 378, https://arxiv.org/pdf/2410.15336.pdf

Abstract:
Recent success of diffusion models has inspired a surge of interest in developing sampling techniques using reverse diffusion processes. However, accurately estimating the drift term in the reverse stochastic differential equation (SDE) solely from the unnormalized target density poses significant challenges, hindering existing methods from achieving state-of-the-art performance. In this paper, we introduce the Diffusion-PINN Sampler (DPS), a novel diffusion-based sampling algorithm that estimates the drift term by solving the governing partial differential equation of the log-density of the underlying SDE marginals via physics-informed neural networks (PINN). We prove that the error of log-density approximation can be controlled by the PINN residual loss, enabling us to establish convergence guarantees of DPS. Experiments on a variety of sampling tasks demonstrate the effectiveness of our approach, particularly in accurately identifying mixing proportions when the target contains isolated components.

Paperid: 379, https://arxiv.org/pdf/2409.15595.pdf

Abstract:
Linear control models have gained extensive application in vehicle control due to their simplicity, ease of use, and support for stability analysis. However, these models lack adaptability to the changing environment and multi-objective settings. Reinforcement learning (RL) models, on the other hand, offer adaptability but suffer from a lack of interpretability and generalization capabilities. This paper aims to develop a family of RL-based controllers enhanced by physics-informed policies, leveraging the advantages of both physics-based models (data-efficient and interpretable) and RL methods (flexible to multiple objectives and fast computing). We propose the Physics-Enhanced Residual Policy Learning (PERPL) framework, where the physics component provides model interpretability and stability. The learning-based Residual Policy adjusts the physics-based policy to adapt to the changing environment, thereby refining the decisions of the physics model. We apply our proposed model to decentralized control to mixed traffic platoon of Connected and Automated Vehicles (CAVs) and Human-driven Vehicles (HVs) using a constant time gap (CTG) strategy for cruising and incorporating actuator and communication delays. Experimental results demonstrate that our method achieves smaller headway errors and better oscillation dampening than linear models and RL alone in scenarios with artificially extreme conditions and real preceding vehicle trajectories. At the macroscopic level, overall traffic oscillations are also reduced as the penetration rate of CAVs employing the PERPL scheme increases.

Paperid: 380, https://arxiv.org/pdf/2409.13786.pdf

Abstract:
Physics-informed machine learning typically integrates physical priors into the learning process by minimizing a loss function that includes both a data-driven term and a partial differential equation (PDE) regularization. Building on the formulation of the problem as a kernel regression task, we use Fourier methods to approximate the associated kernel, and propose a tractable estimator that minimizes the physics-informed risk function. We refer to this approach as physics-informed kernel learning (PIKL). This framework provides theoretical guarantees, enabling the quantification of the physical prior's impact on convergence speed. We demonstrate the numerical performance of the PIKL estimator through simulations, both in the context of hybrid modeling and in solving PDEs. In particular, we show that PIKL can outperform physics-informed neural networks in terms of both accuracy and computation time. Additionally, we identify cases where PIKL surpasses traditional PDE solvers, particularly in scenarios with noisy boundary conditions.

Paperid: 381, https://arxiv.org/pdf/2409.05569.pdf

Abstract:
Neural network approaches have been demonstrated to work quite well to solve partial differential equations in practice. In this context approaches like physics-informed neural networks and the Deep Ritz method have become popular. In this paper, we propose a similar approach to solve an infinite-dimensional total variation minimization problem using neural networks. We illustrate that the resulting neural network problem does not have a solution in general. To circumvent this theoretic issue, we consider an auxiliary neural network problem, which indeed has a solution, and show that it converges in the sense of $Î$-convergence to the original problem. For computing a numerical solution we further propose a discrete version of the auxiliary neural network problem and again show its $Î$-convergence to the original infinite-dimensional problem. In particular, the $Î$-convergence proof suggests a particular discretization of the total variation. Moreover, we connect the discrete neural network problem to a finite difference discretization of the infinite-dimensional total variation minimization problem. Numerical experiments are presented supporting our theoretical findings.

Paperid: 382, https://arxiv.org/pdf/2409.01222.pdf

Abstract:
The coordinated dispatch of power and gas in the electricity-gas integrated energy system (EG-IES) is fundamental for ensuring operational security. However, the gas dynamics in the natural gas system (NGS) are governed by the nonlinear partial differential equations (PDE), making the dispatch problem of the EG-IES a complicated optimization model constrained by nonlinear PDE. To address it, we propose a globally linearized gas network model based on the Koopman operator theory, avoiding the commonly used local linearization and spatial discretization. Particularly, we propose a data-driven Koopman operator approximation approach for the globally linearized gas network model based on the extended dynamic mode decomposition, in which a physics-informed stability constraint is derived and embedded to improve the generalization ability and accuracy of the model. Based on this, we develop an optimal dispatch model for the EG-IES that first considers the nonlinear gas dynamics in the NGS. The case study verifies the effectiveness of this work. Simulation results reveal that the commonly used locally linearized gas network model fails to accurately capture the dynamic characteristics of NGS, bringing potential security threats to the system.

Paperid: 383, https://arxiv.org/pdf/2601.09595.pdf

Abstract:
We propose two globally continuous neural-based variants of the Neural Approximated Virtual Element Method (NAVEM), termed B-NAVEM and P-NAVEM. Both approaches construct local basis functions using pre-trained fully connected neural networks while ensuring exact continuity across adjacent mesh elements. B-NAVEM leverages a Physics-Informed Neural Network to approximately solve the local Laplace problem that defines the virtual element basis functions, whereas P-NAVEM directly enforces polynomial reproducibility via a tailored loss function, without requiring harmonicity within the element interior. Numerical experiments assess the methods in terms of computational cost, memory usage, and accuracy during both training and testing phases.

Paperid: 384, https://arxiv.org/pdf/2601.06156.pdf

Abstract:
The efficient construction of accurate channel knowledge maps (CKMs) is crucial for unleashing the full potential of environment-aware wireless networks, yet it remains a difficult ill-posed problem due to the sparsity of available location-specific channel knowledge data. Although diffusion-based methods such as denoising diffusion probabilistic models (DDPMs) have been exploited for CKM construction, they rely on iterative stochastic sampling, rendering them too slow for real-time wireless applications. To bridge the gap between high fidelity and efficient CKM construction, this letter introduces a novel framework based on linear transport guided flow matching (LT-GFM). Deviating from the noise-removal paradigm of diffusion models, our approach models the CKM generation process as a deterministic ordinary differential equation (ODE) that follows linear optimal transport paths, thereby drastically reducing the number of required inference steps. We propose a unified architecture that is applicable to not only the conventional channel gain map (CGM) construction, but also the more challenging spatial correlation map (SCM) construction. To achieve physics-informed CKM constructions, we integrate environmental semantics (e.g., building masks) for edge recovery and enforce Hermitian symmetry for property of the SCM. Simulation results verify that LT-GFM achieves superior distributional fidelity with significantly lower Fréchet Inception Distance (FID) and accelerates inference speed by a factor of 25 compared to DDPMs.

Paperid: 385, https://arxiv.org/pdf/2512.03795.pdf

Abstract:
Autonomous Driving (AD) vehicles still struggle to exhibit human-like behavior in highly dynamic and interactive traffic scenarios. The key challenge lies in AD's limited ability to interact with surrounding vehicles, largely due to a lack of understanding the underlying mechanisms of social interaction. To address this issue, we introduce MPCFormer, an explainable socially-aware autonomous driving approach with physics-informed and data-driven coupled social interaction dynamics. In this model, the dynamics are formulated into a discrete space-state representation, which embeds physics priors to enhance modeling explainability. The dynamics coefficients are learned from naturalistic driving data via a Transformer-based encoder-decoder architecture. To the best of our knowledge, MPCFormer is the first approach to explicitly model the dynamics of multi-vehicle social interactions. The learned social interaction dynamics enable the planner to generate manifold, human-like behaviors when interacting with surrounding traffic. By leveraging the MPC framework, the approach mitigates the potential safety risks typically associated with purely learning-based methods. Open-looped evaluation on NGSIM dataset demonstrates that MPCFormer achieves superior social interaction awareness, yielding the lowest trajectory prediction errors compared with other state-of-the-art approach. The prediction achieves an ADE as low as 0.86 m over a long prediction horizon of 5 seconds. Close-looped experiments in highly intense interaction scenarios, where consecutive lane changes are required to exit an off-ramp, further validate the effectiveness of MPCFormer. Results show that MPCFormer achieves the highest planning success rate of 94.67%, improves driving efficiency by 15.75%, and reduces the collision rate from 21.25% to 0.5%, outperforming a frontier Reinforcement Learning (RL) based planner.

Paperid: 386, https://arxiv.org/pdf/2511.23046.pdf

Abstract:
This paper puts forward a framework to accelerate Electromagnetic Transient (EMT) simulations by replacing individual components with trained Physics-Informed Neural Networks (PINNs). EMT simulations are considered the cornerstone of transient stability assessment of power systems with high shares of Inverter-Based Resources (IBRs), and, although accurate, they are notorious for their slow simulation speed. Taking a deeper dive into the EMT simulation algorithms, this paper identifies the most computationally expensive components of the simulation and replaces them with fast and accurate PINNs. The proposed novel PINN formulation enables a modular and scalable integration into the simulation algorithm. Using a type-4 wind turbine EMT model, we demonstrate a 4--6x simulation speedup by capturing the Phase-Locked Loop (PLL) with a PINN. We validate all our results with PSCAD software.

Paperid: 387, https://arxiv.org/pdf/2510.21051.pdf

Abstract:
Deep neural networks (DNNs) are powerful black-box function approximators which have been shown to yield improved performance compared to traditional neural network (NN) architectures. However, black-box algorithms do not incorporate known physics of the system and can yield results which are physically implausible. Physics-informed neural networks (PINNs) have grown in popularity due to their ability to leverage known physical principles in the learning process which has been empirically shown to improve performance compared to traditional black-box methods. This paper introduces the first physics-informed DNN controller for an Euler-Lagrange dynamic system where the adaptation laws are designed using a Lyapunov-based stability analysis to account for the skew-symmetry property of the inertia matrix and centripetal-Coriolis matrix. A Lyapunov-based stability analysis is provided to guarantee asymptotic convergence of the tracking error and the skew-symmetric prediction error. Simulations indicate that the developed update law demonstrates improvement in individual and overall function approximation capabilities when compared to a physics-informed adaptation law which does not incorporate knowledge of system symmetries.

Paperid: 388, https://arxiv.org/pdf/2510.18648.pdf

Abstract:
Water is essential for agricultural productivity. Assessing water shortages and reduced yield potential is a critical factor in decision-making for ensuring agricultural productivity and food security. Crop simulation models, which align with physical processes, offer intrinsic explainability but often perform poorly. Conversely, machine learning models for crop yield modeling are powerful and scalable, yet they commonly operate as black boxes and lack adherence to the physical principles of crop growth. This study bridges this gap by coupling the advantages of both worlds. We postulate that the crop yield is inherently defined by the water availability. Therefore, we formulate crop yield as a function of temporal water scarcity and predict both the crop drought stress and the sensitivity to water scarcity at fine-scale resolution. Sequentially modeling the crop yield response to water enables accurate yield prediction. To enforce physical consistency, a novel physics-informed loss function is proposed. We leverage multispectral satellite imagery, meteorological data, and fine-scale yield data. Further, to account for the uncertainty within the model, we build upon a deep ensemble approach. Our method surpasses state-of-the-art models like LSTM and Transformers in crop yield prediction with a coefficient of determination ($R^2$-score) of up to 0.82 while offering high explainability. This method offers decision support for industry, policymakers, and farmers in building a more resilient agriculture in times of changing climate conditions.

Paperid: 389, https://arxiv.org/pdf/2510.02503.pdf

Abstract:
Cyberattacks on pipeline operational technology systems pose growing risks to energy infrastructure. This study develops a physics-informed simulation and optimization framework for analyzing cyber-physical threats in petroleum pipeline networks. The model integrates networked hydraulic dynamics, SCADA-based state estimation, model predictive control (MPC), and a bi-level formulation for stealthy false-data injection (FDI) attacks. Pipeline flow and pressure dynamics are modeled on a directed graph using nodal pressure evolution and edge-based Weymouth-type relations, including control-aware equipment such as valves and compressors. An extended Kalman filter estimates the full network state from partial SCADA telemetry. The controller computes pressure-safe control inputs via MPC under actuator constraints and forecasted demands. Adversarial manipulation is formalized as a bi-level optimization problem where an attacker perturbs sensor data to degrade throughput while remaining undetected by bad-data detectors. This attack-control interaction is solved via Karush-Kuhn-Tucker (KKT) reformulation, which results in a tractable mixed-integer quadratic program. Test gas pipeline case studies demonstrate the covert reduction of service delivery under attack. Results show that undetectable attacks can cause sustained throughput loss with minimal instantaneous deviation. This reveals the need for integrated detection and control strategies in cyber-physical infrastructure.

Paperid: 390, https://arxiv.org/pdf/2510.00401.pdf

Abstract:
Long-horizon motion forecasting for multiple autonomous robots is challenging due to non-linear agent interactions, compounding prediction errors, and continuous-time evolution of dynamics. Learned dynamics of such a system can be useful in various applications such as travel time prediction, prediction-guided planning and generative simulation. In this work, we aim to develop an efficient trajectory forecasting model conditioned on multi-agent goals. Motivated by the recent success of physics-guided deep learning for partially known dynamical systems, we develop a model based on neural Controlled Differential Equations (CDEs) for long-horizon motion forecasting. Unlike discrete-time methods such as RNNs and transformers, neural CDEs operate in continuous time, allowing us to combine physics-informed constraints and biases to jointly model multi-robot dynamics. Our approach, named PINCoDE (Physics-Informed Neural Controlled Differential Equations), learns differential equation parameters that can be used to predict the trajectories of a multi-agent system starting from an initial condition. PINCoDE is conditioned on future goals and enforces physics constraints for robot motion over extended periods of time. We adopt a strategy that scales our model from 10 robots to 100 robots without the need for additional model parameters, while producing predictions with an average ADE below 0.5 m for a 1-minute horizon. Furthermore, progressive training with curriculum learning for our PINCoDE model results in a 2.7X reduction of forecasted pose error over 4 minute horizons compared to analytical models.

Paperid: 391, https://arxiv.org/pdf/2509.25222.pdf

Abstract:
We propose a physics-informed machine-learned framework for sensor-based flow estimation for drone trajectories in complex urban terrain. The input is a rich set of flow simulations at many wind conditions. The outputs are velocity and uncertainty estimates for a target domain and subsequent sensor optimization for minimal uncertainty. The framework has three innovations compared to traditional flow estimators. First, the algorithm scales proportionally to the domain complexity, making it suitable for flows that are too complex for any monolithic reduced-order representation. Second, the framework extrapolates beyond the training data, e.g., smaller and larger wind velocities. Last, and perhaps most importantly, the sensor location is a free input, significantly extending the vast majority of the literature. The key enablers are (1) a Reynolds number-based scaling of the flow variables, (2) a physics-based domain decomposition, (3) a cluster-based flow representation for each subdomain, (4) an information entropy correlating the subdomains, and (5) a multi-variate probability function relating sensor input and targeted velocity estimates. This framework is demonstrated using drone flight paths through a three-building cluster as a simple example. We anticipate adaptations and applications for estimating complete cities and incorporating weather input.

Paperid: 392, https://arxiv.org/pdf/2508.12226.pdf

Abstract:
Ultrasound computed tomography (USCT) is a radiation-free, high-resolution modality but remains limited for musculoskeletal imaging due to conventional ray-based reconstructions that neglect strong scattering. We propose a generative neural physics framework that couples generative networks with physics-informed neural simulation for fast, high-fidelity 3D USCT. By learning a compact surrogate of ultrasonic wave propagation from only dozens of cross-modality images, our method merges the accuracy of wave modeling with the efficiency and stability of deep learning. This enables accurate quantitative imaging of in vivo musculoskeletal tissues, producing spatial maps of acoustic properties beyond reflection-mode images. On synthetic and in vivo data (breast, arm, leg), we reconstruct 3D maps of tissue parameters in under ten minutes, with sensitivity to biomechanical properties in muscle and bone and resolution comparable to MRI. By overcoming computational bottlenecks in strongly scattering regimes, this approach advances USCT toward routine clinical assessment of musculoskeletal disease.

Paperid: 393, https://arxiv.org/pdf/2508.02976.pdf

Abstract:
Object manipulation skills are necessary for robots operating in various daily-life scenarios, ranging from warehouses to hospitals. They allow the robots to manipulate the given object to their desired arrangement in the cluttered environment. The existing approaches to solving object manipulations are either inefficient sampling based techniques, require expert demonstrations, or learn by trial and error, making them less ideal for practical scenarios. In this paper, we propose a novel, multimodal physics-informed neural network (PINN) for solving object manipulation tasks. Our approach efficiently learns to solve the Eikonal equation without expert data and finds object manipulation trajectories fast in complex, cluttered environments. Our method is multimodal as it also reactively replans the robot's grasps during manipulation to achieve the desired object poses. We demonstrate our approach in both simulation and real-world scenarios and compare it against state-of-the-art baseline methods. The results indicate that our approach is effective across various objects, has efficient training compared to previous learning-based methods, and demonstrates high performance in planning time, trajectory length, and success rates. Our demonstration videos can be found at https://youtu.be/FaQLkTV9knI.

Paperid: 394, https://arxiv.org/pdf/2508.01315.pdf

Abstract:
This work addresses the critical challenge of guaranteeing safety for complex dynamical systems where precise mathematical models are uncertain and data measurements are corrupted by noise. We develop a physics-informed, direct data-driven framework for synthesizing robust safety controllers (R-SCs) for both discrete- and continuous-time nonlinear polynomial systems that are subject to unknown-but-bounded disturbances. To do so, we introduce a notion of safety through robust control barrier certificates (R-CBCs), which ensure avoidance of (potentially multiple) unsafe regions, offering a less conservative alternative to existing methods based on robust invariant sets. Our core innovation lies in integrating the fundamental physical principles with observed noisy data which drastically reduces data requirements, enabling robust safety analysis with significantly shorter trajectories, compared to purely data-driven methods. To achieve this, the proposed synthesis procedure is formulated as a sum-of-squares (SOS) optimization program that systematically designs the R-CBC and its associated R-SC by leveraging both collected data and underlying physical laws. The efficacy of our framework is demonstrated on four benchmark systems, three discrete-time and one continuous-time nonlinear polynomial systems, confirming its ability to offer robust safety guarantees with reduced data demands.

Paperid: 395, https://arxiv.org/pdf/2507.15386.pdf

Abstract:
Gridization, the process of partitioning space into grids where users share similar channel characteristics, serves as a fundamental prerequisite for efficient large-scale network optimization. However, existing methods like Geographical or Beam Space Gridization (GSG or BSG) are limited by reliance on unavailable location data or the flawed assumption that similar signal strengths imply similar channel properties. We propose Channel Space Gridization (CSG), a pioneering framework that unifies channel estimation and gridization for the first time. Formulated as a joint optimization problem, CSG uses only beam-level reference signal received power (RSRP) to estimate Channel Angle Power Spectra (CAPS) and partition samples into grids with homogeneous channel characteristics. To perform CSG, we develop the CSG Autoencoder (CSG-AE), featuring a trainable RSRP-to-CAPS encoder, a learnable sparse codebook quantizer, and a physics-informed decoder based on the Localized Statistical Channel Model. On recognizing the limitations of naive training scheme, we propose a novel Pretraining-Initialization-Detached-Asynchronous (PIDA) training scheme for CSG-AE, ensuring stable and effective training by systematically addressing the common pitfalls of the naive training paradigm. Evaluations reveal that CSG-AE excels in CAPS estimation accuracy and clustering quality on synthetic data. On real-world datasets, it reduces Active Mean Absolute Error (MAE) by 30\% and Overall MAE by 65\% on RSRP prediction accuracy compared to salient baselines using the same data, while improving channel consistency, cluster sizes balance, and active ratio, advancing the development of gridization for large-scale network optimization.

Paperid: 396, https://arxiv.org/pdf/2507.11070.pdf

Abstract:
We propose a transfer learning framework for sound source reconstruction in Near-field Acoustic Holography (NAH), which adapts a well-trained data-driven model from one type of sound source to another using a physics-informed procedure. The framework comprises two stages: (1) supervised pre-training of a complex-valued convolutional neural network (CV-CNN) on a large dataset, and (2) purely physics-informed fine-tuning on a single data sample based on the Kirchhoff-Helmholtz integral. This method follows the principles of transfer learning by enabling generalization across different datasets through physics-informed adaptation. The effectiveness of the approach is validated by transferring a pre-trained model from a rectangular plate dataset to a violin top plate dataset, where it shows improved reconstruction accuracy compared to the pre-trained model and delivers performance comparable to that of Compressive-Equivalent Source Method (C-ESM). Furthermore, for successful modes, the fine-tuned model outperforms both the pre-trained model and C-ESM in accuracy.

Paperid: 397, https://arxiv.org/pdf/2507.05184.pdf

Abstract:
Characterizing quantum flakes is a critical step in quantum hardware engineering because the quality of these flakes directly influences qubit performance. Although computer vision methods for identifying two-dimensional quantum flakes have emerged, they still face significant challenges in estimating flake thickness. These challenges include limited data, poor generalization, sensitivity to domain shifts, and a lack of physical interpretability. In this paper, we introduce one of the first Physics-informed Adaptation Learning approaches to overcome these obstacles. We focus on two main issues, i.e., data scarcity and generalization. First, we propose a new synthetic data generation framework that produces diverse quantum flake samples across various materials and configurations, reducing the need for time-consuming manual collection. Second, we present $Ï$-Adapt, a physics-informed adaptation method that bridges the performance gap between models trained on synthetic data and those deployed in real-world settings. Experimental results show that our approach achieves state-of-the-art performance on multiple benchmarks, outperforming existing methods. Our proposed approach advances the integration of physics-based modeling and domain adaptation. It also addresses a critical gap in leveraging synthesized data for real-world 2D material analysis, offering impactful tools for deep learning and materials science communities.

Paperid: 398, https://arxiv.org/pdf/2506.18812.pdf

Abstract:
Physics-informed deep learning has achieved remarkable progress by embedding geometric priors, such as Hamiltonian symmetries and variational principles, into neural networks, enabling structure-preserving models that extrapolate with high accuracy. However, in systems with dissipation and holonomic constraints, ubiquitous in legged locomotion and multibody robotics, the canonical symplectic form becomes degenerate, undermining the very invariants that guarantee stability and long-term prediction. In this work, we tackle this foundational limitation by introducing Presymplectification Networks (PSNs), the first framework to learn the symplectification lift via Dirac structures, restoring a non-degenerate symplectic geometry by embedding constrained systems into a higher-dimensional manifold. Our architecture combines a recurrent encoder with a flow-matching objective to learn the augmented phase-space dynamics end-to-end. We then attach a lightweight Symplectic Network (SympNet) to forecast constrained trajectories while preserving energy, momentum, and constraint satisfaction. We demonstrate our method on the dynamics of the ANYmal quadruped robot, a challenging contact-rich, multibody system. To the best of our knowledge, this is the first framework that effectively bridges the gap between constrained, dissipative mechanical systems and symplectic learning, unlocking a whole new class of geometric machine learning models, grounded in first principles yet adaptable from data.

Paperid: 399, https://arxiv.org/pdf/2506.12742.pdf

Abstract:
Physics-informed Neural Motion Planners (PiNMPs) provide a data-efficient framework for solving the Eikonal Partial Differential Equation (PDE) and representing the cost-to-go function for motion planning. However, their scalability remains limited by spectral bias and the complex loss landscape of PDE-driven training. Domain decomposition mitigates these issues by dividing the environment into smaller subdomains, but existing methods enforce continuity only at individual spatial points. While effective for function approximation, these methods fail to capture the spatial connectivity required for motion planning, where the cost-to-go function depends on both the start and goal coordinates rather than a single query point. We propose Finite Basis Neural Time Fields (FB-NTFields), a novel neural field representation for scalable cost-to-go estimation. Instead of enforcing continuity in output space, FB-NTFields construct a latent space representation, computing the cost-to-go as a distance between the latent embeddings of start and goal coordinates. This enables global spatial coherence while integrating domain decomposition, ensuring efficient large-scale motion planning. We validate FB-NTFields in complex synthetic and real-world scenarios, demonstrating substantial improvements over existing PiNMPs. Finally, we deploy our method on a Unitree B1 quadruped robot, successfully navigating indoor environments. The supplementary videos can be found at https://youtu.be/OpRuCbLNOwM.

Paperid: 400, https://arxiv.org/pdf/2506.08462.pdf

Abstract:
Industrial processes must be robust and adaptable, as environments and tasks are often unpredictable, while operational errors remain costly and difficult to detect. AI-based control systems offer a path forward, yet typically depend on supervised learning with extensive labelled datasets, which limits their ability to generalize across variable and data-scarce industrial settings. Foundation models could enable broader reasoning and knowledge integration, but rarely deliver the quantitative precision demanded by engineering applications. Here, we introduceControl and Interpretation of Production via Hybrid Expertise and Reasoning (CIPHER): a vision-language-action (VLA) model framework aiming to replicate human-like reasoning for industrial control, instantiated in a commercial-grade 3D printer. It integrates a process expert, a regression model enabling quantitative characterization of system states required for engineering tasks. CIPHER also incorporates retrieval-augmented generation to access external expert knowledge and support physics-informed, chain-of-thought reasoning. This hybrid architecture exhibits strong generalization to out-of-distribution tasks. It interprets visual or textual inputs from process monitoring, explains its decisions, and autonomously generates precise machine instructions, without requiring explicit annotations. CIPHER thus lays the foundations for autonomous systems that act with precision, reason with context, and communicate decisions transparently, supporting safe and trusted deployment in industrial settings.

Paperid: 401, https://arxiv.org/pdf/2506.02792.pdf

Abstract:
We propose a novel, lightweight, and physically inspired approach to modeling the dynamics of parallel distributed-memory programs. Inspired by the Kuramoto model, we represent MPI processes as coupled oscillators with topology-aware interactions, custom coupling potentials, and stochastic noise. The resulting system of nonlinear ordinary differential equations opens a path to modeling key performance phenomena of parallel programs, including synchronization, delay propagation and decay, bottlenecks, and self-desynchronization. This paper introduces interaction potentials to describe memory- and compute-bound workloads and employs multiple quantitative metrics -- such as an order parameter, synchronization entropy, phase gradients, and phase differences -- to evaluate phase coherence and disruption. We also investigate the role of local noise and show that moderate noise can accelerate resynchronization in scalable applications. Our simulations align qualitatively with MPI trace data, showing the potential of physics-informed abstractions to predict performance patterns, which offers a new perspective for performance modeling and software-hardware co-design in parallel computing.

Paperid: 402, https://arxiv.org/pdf/2505.22085.pdf

Abstract:
Averaging techniques such as Ruppert--Polyak averaging and exponential movering averaging (EMA) are powerful approaches to accelerate optimization procedures of stochastic gradient descent (SGD) optimization methods such as the popular ADAM optimizer. However, depending on the specific optimization problem under consideration, the type and the parameters for the averaging need to be adjusted to achieve the smallest optimization error. In this work we propose an averaging approach, which we refer to as parallel averaged ADAM (PADAM), in which we compute parallely different averaged variants of ADAM and during the training process dynamically select the variant with the smallest optimization error. A central feature of this approach is that this procedure requires no more gradient evaluations than the usual ADAM optimizer as each of the averaged trajectories relies on the same underlying ADAM trajectory and thus on the same underlying gradients. We test the proposed PADAM optimizer in 13 stochastic optimization and deep neural network (DNN) learning problems and compare its performance with known optimizers from the literature such as standard SGD, momentum SGD, Adam with and without EMA, and ADAMW. In particular, we apply the compared optimizers to physics-informed neural network, deep Galerkin, deep backward stochastic differential equation and deep Kolmogorov approximations for boundary value partial differential equation problems from scientific machine learning, as well as to DNN approximations for optimal control and optimal stopping problems. In nearly all of the considered examples PADAM achieves, sometimes among others and sometimes exclusively, essentially the smallest optimization error. This work thus strongly suggest to consider PADAM for scientific machine learning problems and also motivates further research for adaptive averaging procedures within the training of DNNs.

Paperid: 403, https://arxiv.org/pdf/2505.19566.pdf

Abstract:
We present a novel formulation for modeling phase-field fracture propagation based on the Integrated Finite Element Neural Network (IFENN) framework. IFENN is a hybrid solver scheme that utilizes neural networks as PDE solvers within FEM, preserving accuracy via residual minimization while achieving speed-up via swift network predictions and reduction of the size of system of equations in coupled problems. In this work, we introduce a radically new formulation of IFENN in which the phase-field variable is calculated using physics-informed convolutional networks (PICNNs), while the equilibrium equation is still solved using FEM to maintain the solver robustness. Unlike conventional approaches, which rely on sequence or time-dependent models, we eliminate the need to include temporal features in the training setup and inference stage. Instead, we show that it is sufficient to learn only the spatial coupling between the strain energy density and the phase-field variable in the vicinity of the fracture process zone, and utilize this information along the advancing crack simulation. We train a single CNN in a purely physics-based, unsupervised manner on just two load increments from a single-notch tension problem, with a total training time of only 5 minutes. Following this exceptionally minimal and fast training, we show that the same PICNN can (when embedded within IFENN) model crack propagation in a very wide range of unseen scenarios, including arbitrarily rectangular domains, single and multiple interacting cracks, varying mesh densities, and arbitrary loading paths. The proposed formulation delivers breakthroughs that address many of the limitations in the existing literature of hybrid modeling, introducing a new paradigm for the development of generalizable, physics-consistent hybrid models that are applicable to fracture and other coupled problems.

Paperid: 404, https://arxiv.org/pdf/2505.12302.pdf

Abstract:
Power flow estimation plays a vital role in ensuring the stability and reliability of electrical power systems, particularly in the context of growing network complexities and renewable energy integration. However, existing studies often fail to adequately address the unique characteristics of power systems, such as the sparsity of network connections and the critical importance of the unique Slack node, which poses significant challenges in achieving high-accuracy estimations. In this paper, we present SenseFlow, a novel physics-informed and self-ensembling iterative framework that integrates two main designs, the Physics-Informed Power Flow Network (FlowNet) and Self-Ensembling Iterative Estimation (SeIter), to carefully address the unique properties of the power system and thereby enhance the power flow estimation. Specifically, SenseFlow enforces the FlowNet to gradually predict high-precision voltage magnitudes and phase angles through the iterative SeIter process. On the one hand, FlowNet employs the Virtual Node Attention and Slack-Gated Feed-Forward modules to facilitate efficient global-local communication in the face of network sparsity and amplify the influence of the Slack node on angle predictions, respectively. On the other hand, SeIter maintains an exponential moving average of FlowNet's parameters to create a robust ensemble model that refines power state predictions throughout the iterative fitting process. Experimental results demonstrate that SenseFlow outperforms existing methods, providing a promising solution for high-accuracy power flow estimation across diverse grid configurations.

Paperid: 405, https://arxiv.org/pdf/2505.01399.pdf

Abstract:
Tool use enhances a robot's task capabilities. Recent advances in vision-language models (VLMs) have equipped robots with sophisticated cognitive capabilities for tool-use applications. However, existing methodologies focus on elementary quasi-static tool manipulations or high-level tool selection while neglecting the critical aspect of task-appropriate tool grasping. To address this limitation, we introduce inverse Tool-Use Planning (iTUP), a novel VLM-driven framework that enables grounded fine-grained planning for versatile robotic tool use. Through an integrated pipeline of VLM-based tool and contact point grounding, position-velocity trajectory planning, and physics-informed grasp generation and selection, iTUP demonstrates versatility across (1) quasi-static and more challenging (2) dynamic and (3) cluster tool-use tasks. To ensure robust planning, our framework integrates stable and safe task-aware grasping by reasoning over semantic affordances and physical constraints. We evaluate iTUP and baselines on a comprehensive range of realistic tool use tasks including precision hammering, object scooping, and cluster sweeping. Experimental results demonstrate that iTUP ensures a thorough grounding of cognition and planning for challenging robot tool use across diverse environments.

Paperid: 406, https://arxiv.org/pdf/2504.17112.pdf

Abstract:
Supervised machine learning involves approximating an unknown functional relationship from a limited dataset of features and corresponding labels. The classical approach to feature-based machine learning typically relies on applying linear regression to standardized features, without considering their physical meaning. This may limit model explainability, particularly in scientific applications. This study proposes a physics-informed approach to feature-based machine learning that constructs non-linear feature maps informed by physical laws and dimensional analysis. These maps enhance model interpretability and, when physical laws are unknown, allow for the identification of relevant mechanisms through feature ranking. The method aims to improve both predictive performance in regression tasks and classification skill scores by integrating domain knowledge into the learning process, while also enabling the potential discovery of new physical equations within the context of explainable machine learning.

Paperid: 407, https://arxiv.org/pdf/2504.13768.pdf

Abstract:
Accurate real-time modeling of multi-body dynamical systems is essential for enabling digital twin applications across industries. While many data-driven approaches aim to learn system dynamics, jointly predicting internal loads and system trajectories remains a key challenge. This dual prediction is especially important for fault detection and predictive maintenance, where internal loads-such as contact forces-act as early indicators of faults, reflecting wear or misalignment before affecting motion. These forces also serve as inputs to degradation models (e.g., crack growth), enabling damage prediction and remaining useful life estimation. We propose Equi-Euler GraphNet, a physics-informed graph neural network (GNN) that simultaneously predicts internal forces and global trajectories in multi-body systems. In this mesh-free framework, nodes represent system components and edges encode interactions. Equi-Euler GraphNet introduces two inductive biases: (1) an equivariant message-passing scheme, interpreting edge messages as interaction forces consistent under Euclidean transformations; and (2) a temporal-aware iterative node update mechanism, based on Euler integration, to capture influence of distant interactions over time. Tailored for cylindrical roller bearings, it decouples ring dynamics from constrained motion of rolling elements. Trained on high-fidelity multiphysics simulations, Equi-Euler GraphNet generalizes beyond the training distribution, accurately predicting loads and trajectories under unseen speeds, loads, and configurations. It outperforms state-of-the-art GNNs focused on trajectory prediction, delivering stable rollouts over thousands of time steps with minimal error accumulation. Achieving up to a 200x speedup over conventional solvers while maintaining comparable accuracy, it serves as an efficient reduced-order model for digital twins, design, and maintenance.

Paperid: 408, https://arxiv.org/pdf/2504.11650.pdf

Abstract:
Power flow (PF) calculations are fundamental to power system analysis to ensure stable and reliable grid operation. The Newton-Raphson (NR) method is commonly used for PF analysis due to its rapid convergence when initialized properly. However, as power grids operate closer to their capacity limits, ill-conditioned cases and convergence issues pose significant challenges. This work, therefore, addresses these challenges by proposing strategies to improve NR initialization, hence minimizing iterations and avoiding divergence. We explore three approaches: (i) an analytical method that estimates the basin of attraction using mathematical bounds on voltages, (ii) Two data-driven models leveraging supervised learning or physics-informed neural networks (PINNs) to predict optimal initial guesses, and (iii) a reinforcement learning (RL) approach that incrementally adjusts voltages to accelerate convergence. These methods are tested on benchmark systems. This research is particularly relevant for modern power systems, where high penetration of renewables and decentralized generation require robust and scalable PF solutions. In experiments, all three proposed methods demonstrate a strong ability to provide an initial guess for Newton-Raphson method to converge with fewer steps. The findings provide a pathway for more efficient real-time grid operations, which, in turn, support the transition toward smarter and more resilient electricity networks.

Paperid: 409, https://arxiv.org/pdf/2504.04562.pdf

Abstract:
Foundation models have demonstrated strong reasoning and generalization capabilities in driving-related tasks, including scene understanding, planning, and control. However, they still face challenges in hallucinations, uncertainty, and long inference latency. While existing foundation models have general knowledge of avoiding collisions, they often lack transportation-specific safety knowledge. To overcome these limitations, we introduce LetsPi, a physics-informed, dual-phase, knowledge-driven framework for safe, human-like trajectory planning. To prevent hallucinations and minimize uncertainty, this hybrid framework integrates Large Language Model (LLM) reasoning with physics-informed social force dynamics. LetsPi leverages the LLM to analyze driving scenes and historical information, providing appropriate parameters and target destinations (goals) for the social force model, which then generates the future trajectory. Moreover, the dual-phase architecture balances reasoning and computational efficiency through its Memory Collection phase and Fast Inference phase. The Memory Collection phase leverages the physics-informed LLM to process and refine planning results through reasoning, reflection, and memory modules, storing safe, high-quality driving experiences in a memory bank. Surrogate safety measures and physics-informed prompt techniques are introduced to enhance the LLM's knowledge of transportation safety and physical force, respectively. The Fast Inference phase extracts similar driving experiences as few-shot examples for new scenarios, while simplifying input-output requirements to enable rapid trajectory planning without compromising safety. Extensive experiments using the HighD dataset demonstrate that LetsPi outperforms baseline models across five safety metrics.See PDF for project Github link.

Paperid: 410, https://arxiv.org/pdf/2503.23348.pdf

Abstract:
We human rely on a wide range of commonsense knowledge to interact with an extensive number and categories of objects in the physical world. Likewise, such commonsense knowledge is also crucial for robots to successfully develop generalized object manipulation skills. While recent advancements in Large Language Models (LLM) have showcased their impressive capabilities in acquiring commonsense knowledge and conducting commonsense reasoning, effectively grounding this semantic-level knowledge produced by LLMs to the physical world to thoroughly guide robots in generalized articulated object manipulation remains a challenge that has not been sufficiently addressed. To this end, we introduce analytic concepts, procedurally defined upon mathematical symbolism that can be directly computed and simulated by machines. By leveraging the analytic concepts as a bridge between the semantic-level knowledge inferred by LLMs and the physical world where real robots operate, we are able to figure out the knowledge of object structure and functionality with physics-informed representations, and then use the physically grounded knowledge to instruct robot control policies for generalized, interpretable and accurate articulated object manipulation. Extensive experiments in both simulation and real-world environments demonstrate the superiority of our approach.

Paperid: 411, https://arxiv.org/pdf/2503.05201.pdf

Abstract:
Electromyography (EMG)--based computational musculoskeletal modeling is a non-invasive method for studying musculotendon function, human movement, and neuromuscular control, providing estimates of internal variables like muscle forces and joint torques. However, EMG signals from deeper muscles are often challenging to measure by placing the surface EMG electrodes and unfeasible to measure directly using invasive methods. The restriction to the access of EMG data from deeper muscles poses a considerable obstacle to the broad adoption of EMG-driven modeling techniques. A strategic alternative is to use an estimation algorithm to approximate the missing EMG signals from deeper muscle. A similar strategy is used in physics-informed deep learning, where the features of physical systems are learned without labeled data. In this work, we propose a hybrid deep learning algorithm, namely the neural musculoskeletal model (NMM), that integrates physics-informed and data-driven deep learning to approximate the EMG signals from the deeper muscles. While data-driven modeling is used to predict the missing EMG signals, physics-based modeling engraves the subject-specific information into the predictions. Experimental verifications on five test subjects are carried out to investigate the performance of the proposed hybrid framework. The proposed NMM is validated against the joint torque computed from 'OpenSim' software. The predicted deep EMG signals are also compared against the state-of-the-art muscle synergy extrapolation (MSE) approach, where the proposed NMM completely outperforms the existing MSE framework by a significant margin.

Paperid: 412, https://arxiv.org/pdf/2502.07209.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve even moderate accuracy, while recent work on feature engineering allows higher accuracy and faster convergence. This paper introduces SAFE-NET, a Single-layered Adaptive Feature Engineering NETwork that achieves orders-of-magnitude lower errors with far fewer parameters than baseline feature engineering methods. SAFE-NET returns to basic ideas in machine learning, using Fourier features, a simplified single hidden layer network architecture, and an effective optimizer that improves the conditioning of the PINN optimization problem. Numerical results show that SAFE-NET converges faster and typically outperforms deeper networks and more complex architectures. It consistently uses fewer parameters -- on average, 65% fewer than the competing feature engineering methods -- while achieving comparable accuracy in less than 30% of the training epochs. Moreover, each SAFE-NET epoch is 95% faster than those of competing feature engineering approaches. These findings challenge the prevailing belief that modern PINNs effectively learn features in these scientific applications and highlight the efficiency gains possible through feature engineering.

Paperid: 413, https://arxiv.org/pdf/2502.06412.pdf

Abstract:
This paper puts forward the vision of creating a library of neural-network-based models for power system simulations. Traditional numerical solvers struggle with the growing complexity of modern power systems, necessitating faster and more scalable alternatives. Physics-Informed Neural Networks (PINNs) offer promise to solve fast the ordinary differential equations (ODEs) governing power system dynamics. This is vital for the reliability, cost optimization, and real-time decision-making in the electricity grid. Despite their potential, standardized frameworks to train PINNs remain scarce. This poses a barrier for the broader adoption and reproducibility of PINNs; it also does not allow the streamlined creation of a PINN-based model library. This paper addresses these gaps. It introduces a Python-based toolbox for developing PINNs tailored to power system components, available on GitHub https://github. com/radiakos/PowerPINN. Using this framework, we capture the dynamic characteristics of a 9th-order system, which is probably the most complex power system component trained with a PINN to date, demonstrating the toolbox capabilities, limitations, and potential improvements. The toolbox is open and free to use by anyone interested in creating PINN-based models for power system components.

Paperid: 414, https://arxiv.org/pdf/2501.17621.pdf

Abstract:
The importance and cost of time-domain simulations when studying power systems have exponentially increased in the last decades. With the growing share of renewable energy sources, the slow and predictable responses from large turbines are replaced by the fast and unpredictable dynamics from power electronics. The current existing simulation tools require new solutions designed for faster dynamics. Physics-Informed Neural Networks (PINNs) have recently emerged in power systems to accelerate such simulations. By incorporating knowledge during the up-front training, PINNs provide more accurate results over larger time steps than traditional numerical methods. This paper introduces PINNs as an alternative approximation method that seamlessly integrates with the current simulation framework. We replace a synchronous machine for a trained PINN in the IEEE 9-, 14-, and 30-bus systems and simulate several network disturbances. Including PINNs systematically boosts the simulations' accuracy, providing more accurate results for both the PINN-modeled component and the whole multi-machine system states.

Paperid: 415, https://arxiv.org/pdf/2501.11222.pdf

Abstract:
This paper introduces Residual-based Smote (RSmote), an innovative local adaptive sampling technique tailored to improve the performance of Physics-Informed Neural Networks (PINNs) through imbalanced learning strategies. Traditional residual-based adaptive sampling methods, while effective in enhancing PINN accuracy, often struggle with efficiency and high memory consumption, particularly in high-dimensional problems. RSmote addresses these challenges by targeting regions with high residuals and employing oversampling techniques from imbalanced learning to refine the sampling process. Our approach is underpinned by a rigorous theoretical analysis that supports the effectiveness of RSmote in managing computational resources more efficiently. Through extensive evaluations, we benchmark RSmote against the state-of-the-art Residual-based Adaptive Distribution (RAD) method across a variety of dimensions and differential equations. The results demonstrate that RSmote not only achieves or exceeds the accuracy of RAD but also significantly reduces memory usage, making it particularly advantageous in high-dimensional scenarios. These contributions position RSmote as a robust and resource-efficient solution for solving complex partial differential equations, especially when computational constraints are a critical consideration.

Paperid: 416, https://arxiv.org/pdf/2501.07373.pdf

Abstract:
Accurate, interpretable, and real-time modeling of multi-body dynamical systems is essential for predicting behaviors and inferring physical properties in natural and engineered environments. Traditional physics-based models face scalability challenges and are computationally demanding, while data-driven approaches like Graph Neural Networks (GNNs) often lack physical consistency, interpretability, and generalization. In this paper, we propose Dynami-CAL GraphNet, a Physics-Informed Graph Neural Network that integrates the learning capabilities of GNNs with physics-based inductive biases to address these limitations. Dynami-CAL GraphNet enforces pairwise conservation of linear and angular momentum for interacting nodes using edge-local reference frames that are equivariant to rotational symmetries, invariant to translations, and equivariant to node permutations. This design ensures physically consistent predictions of node dynamics while offering interpretable, edge-wise linear and angular impulses resulting from pairwise interactions. Evaluated on a 3D granular system with inelastic collisions, Dynami-CAL GraphNet demonstrates stable error accumulation over extended rollouts, effective extrapolations to unseen configurations, and robust handling of heterogeneous interactions and external forces. Dynami-CAL GraphNet offers significant advantages in fields requiring accurate, interpretable, and real-time modeling of complex multi-body dynamical systems, such as robotics, aerospace engineering, and materials science. By providing physically consistent and scalable predictions that adhere to fundamental conservation laws, it enables the inference of forces and moments while efficiently handling heterogeneous interactions and external forces.

Paperid: 417, https://arxiv.org/pdf/2501.01587.pdf

Abstract:
We propose an entropy-enhanced Generative Pre-Trained Physics-Informed Neural Network with a transform layer (EGPT-PINN) for solving parameterized nonlinear conservation laws. The EGPT-PINN extends the traditional physics-informed neural networks and its recently proposed generative pre-trained strategy for linear model reduction to nonlinear model reduction and shock-capturing domains. By utilizing an adaptive meta-network, a simultaneously trained transform layer, entropy enhancement strategies, implementable shock interaction analysis, and a separable training process, the EGPT-PINN efficiently captures complex parameter-dependent shock formations and interactions. Numerical results of EGPT-PINN applied to the families of inviscid Burgers' equation and the Euler equations, parameterized by their initial conditions, demonstrate the robustness and accuracy of the proposed technique. It accurately solves the viscosity solution via very few neurons without leveraging any {\it a priori} knowledge of the equations or its initial condition. Moreover, via a simple augmentation of the loss function by model-data mismatch, we demonstrate the robustness of EGPT-PINN in solving inverse problems more accurately than the vanilla and entropy-enhanced versions of PINN.

Paperid: 418, https://arxiv.org/pdf/2501.00502.pdf

Abstract:
In response to climate change, assessing crop productivity under extreme weather conditions is essential to enhance food security. Crop simulation models, which align with physical processes, offer explainability but often perform poorly. Conversely, machine learning (ML) models for crop modeling are powerful and scalable yet operate as black boxes and lack adherence to crop growths physical principles. To bridge this gap, we propose a novel method that combines the strengths of both approaches by estimating the water use and the crop sensitivity to water scarcity at the pixel level. This approach enables yield loss estimation grounded in physical principles by sequentially solving the equation for crop yield response to water scarcity, using an enhanced loss function. Leveraging Sentinel-2 satellite imagery, climate data, simulated water use data, and pixel-level yield data, our model demonstrates high accuracy, achieving an R2 of up to 0.77, matching or surpassing state-of-the-art models like RNNs and Transformers. Additionally, it provides interpretable and physical consistent outputs, supporting industry, policymakers, and farmers in adapting to extreme weather conditions.

Paperid: 419, https://arxiv.org/pdf/2412.03932.pdf

Abstract:
This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing BCs often relies on an accurate dynamics model; however, such models are often imprecise due to the model complexity involved, particularly when dealing with highly nonlinear systems. In such cases, while scenario approaches effectively address the safety problem using collected data to construct a guaranteed BC for the dynamical system, they often require substantial amounts of data-sometimes millions of samples-due to exponential sample complexity. To address this, we propose a physics-informed scenario approach that selects data samples such that the outputs of the physics-based model and the observed data are sufficiently close (within a specified threshold). This approach guides the scenario optimization process to eliminate redundant samples and significantly reduce the required dataset size. We demonstrate the capability of our approach in mitigating the amount of data required for scenario optimizations with both deterministic (i.e., confidence 1) and probabilistic (i.e., confidence between 0 and 1) guarantees. We validate our physics-informed scenario approach through two physical case studies, showcasing its practical application in reducing the required data.

Paperid: 420, https://arxiv.org/pdf/2412.02807.pdf

Abstract:
Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vector space. However, providing stability guarantees while learning the continuous-time dynamics, especially under conditions of relatively low observation frequency, remains a challenge within the existing Koopman-based learning frameworks. To address this challenge, we propose an algorithmic framework to simultaneously learn the vector field and Lyapunov functions for unknown nonlinear systems, using a limited amount of data sampled across the state space and along the trajectories at a relatively low sampling frequency. The proposed framework builds upon recently developed high-accuracy Koopman generator learning for capturing transient system transitions and physics-informed neural networks for training Lyapunov functions. We show that the learned Lyapunov functions can be formally verified using a satisfiability modulo theories (SMT) solver and provide less conservative estimates of the region of attraction compared to existing methods.

Paperid: 421, https://arxiv.org/pdf/2412.00088.pdf

Abstract:
Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to $\mathcal{O}(d^{k})$ scaling of the derivative tensor size and the $\mathcal{O}(2^{k-1}L)$ scaling in the computation graph, where $d$ is the dimension of the domain, $L$ is the number of ops in the forward computation graph, and $k$ is the derivative order. In previous works, the polynomial scaling in $d$ was addressed by amortizing the computation over the optimization process via randomization. Separately, the exponential scaling in $k$ for univariate functions ($d=1$) was addressed with high-order auto-differentiation (AD). In this work, we show how to efficiently perform arbitrary contraction of the derivative tensor of arbitrary order for multivariate functions, by properly constructing the input tangents to univariate high-order AD, which can be used to efficiently randomize any differential operator. When applied to Physics-Informed Neural Networks (PINNs), our method provides >1000$\times$ speed-up and >30$\times$ memory reduction over randomization with first-order AD, and we can now solve \emph{1-million-dimensional PDEs in 8 minutes on a single NVIDIA A100 GPU}. This work opens the possibility of using high-order differential operators in large-scale problems.

Paperid: 422, https://arxiv.org/pdf/2410.20275.pdf

Abstract:
Alternative Current Optimal Power Flow (AC-OPF) is essential for efficient power system planning and real-time operation but remains an NP-hard and non-convex optimization problem with significant computational challenges. This paper proposes a novel hybrid classical-quantum deep learning framework for AC-OPF problem, integrating parameterized quantum circuits (PQCs) for feature extraction with classical deep learning for data encoding and decoding. The proposed framework integrates two types of residual connection structures to mitigate the ``barren plateau" problem in quantum circuits, enhancing training stability and convergence. Furthermore, a physics-informed neural network (PINN) module is incorporated to guarantee tolerable constraint violation, improving the physical consistency and reliability of AC-OPF solutions. Experimental evaluations on multiple IEEE test systems demonstrate that the proposed approach achieves superior accuracy, generalization, and robustness to quantum noise while requiring minimal quantum resources.

Paperid: 423, https://arxiv.org/pdf/2410.13962.pdf

Abstract:
Tele-operated driving (ToD) systems are special types of cyber-physical systems (CPSs) where the operator remotely controls the steering, acceleration, and braking actions of the vehicle. Malicious actors may inject false data in communication channels to manipulate the tele-operators driving commands to cause harm. Hence, protection of this communication is necessary for the safe operation of the target vehicle. However, according to the National Institute of Standards and Technology (NIST) cybersecurity framework, protection merely is not enough and the detection of an attack is necessary. Moreover, UN R155 mandates that security incidents across vehicle fleets be detected and logged. Thus, cyber-physical threats of ToD are modeled with an attack-centric approach in this paper. Then, an attack model with false data injection (FDI) on steering control commands is created from real vehicle data. The risk of this attack model is assessed for a last-mile delivery (LMD) application. Finally, a physics-informed context-aware anomaly detection system (PCADS) is proposed to detect such false injection attacks, and preliminary experimental results are presented to validate the model.

Paperid: 424, https://arxiv.org/pdf/2512.21475.pdf

Abstract:
The Reference Signal Received Power (RSRP) is a crucial factor that determines communication performance in mobile networks. Accurately predicting the RSRP can help network operators perceive user experiences and maximize throughput by optimizing wireless resources. However, existing research into RSRP prediction has limitations in accuracy and verisimilitude. Theoretical derivations and existing data-driven methods consider only easily quantifiable Large-Scale (LS) information, and struggle to effectively capture the intertwined LS and Small-Scale (SS) signal attenuation characteristics of the wireless channel. Moreover, the lack of prior physical knowledge leads to weak accuracy, interpretability, and transferability. In this paper, we propose a novel RSRP prediction framework, Channel-Diff. This framework physically models LS and SS attenuation using multimodal conditions and employs physics-informed conditional diffusion models as the prediction network. Channel-Diff extracts prior physical information that characterises the signal propagation process from network parameters and multi-attribute maps of the urban spatial environment. It provides LS physical priors through large-scale propagation modelling and shadow-occlusion modelling, and SS physical priors through multipath propagation modelling and urban microenvironment feature extraction. We design a physical-prior-guided two-stage training scheme with a noise prior guidance mechanism, enabling effective fusion of multi-scale physical knowledge with the diffusion models. Evaluations demonstrate Channel-Diff exhibits excellent performance on RSRP prediction, achieving at least 25.15%-37.19% improvement in accuracy relative to baseline methods. Additionally, the model also demonstrated outstanding performance in terms of transferability and training efficiency.

Paperid: 425, https://arxiv.org/pdf/2512.20813.pdf

Abstract:
As wildfires increasingly evolve into urban conflagrations, traditional risk models that treat structures as isolated assets fail to capture the non-linear contagion dynamics characteristic of the wildland urban interface (WUI). This research bridges the gap between mechanistic physics and data driven learning by establishing a novel dual specialist ensemble framework that disentangles vulnerability into two distinct vectors, environmental contagion and structural fragility. The architecture integrates two specialized predictive streams, an environmental specialist, implemented as a graph neural network (GNN) that operationalizes the community as a directed contagion graph weighted by physics informed convection, radiation, and ember probabilities, and enriched with high dimensional Google AlphaEarth Foundation embeddings, and a Structural Specialist, implemented via XGBoost to isolate granular asset level resilience. Applied to the 2025 Eaton Fire, the framework reveals a critical dichotomy in risk drivers. The GNN demonstrates that neighborhood scale environmental pressure overwhelmingly dominates intrinsic structural features in defining propagation pathways, while the XGBoost model identifies eaves as the primary micro scale ingress vector. By synthesizing these divergent signals through logistic stacking, the ensemble achieves robust classification and generates a diagnostic risk topology. This capability empowers decision makers to move beyond binary loss prediction and precisely target mitigation prioritizing vegetation management for high connectivity clusters and structural hardening for architecturally vulnerable nodes thereby operationalizing a proactive, data driven approach to community resilience.

Paperid: 426, https://arxiv.org/pdf/2512.15746.pdf

Abstract:
Inverse design of heterogeneous material microstructures is a fundamentally ill-posed and famously computationally expensive problem. This is exacerbated by the high-dimensional design spaces associated with finely resolved images, multimodal input property streams, and a highly nonlinear forward physics. Whilst modern generative models excel at accurately modeling such complex forward behavior, most of them are not intrinsically structured to support fast, stable \emph{deterministic} inversion with a physics-informed bias. This work introduces Janus, a unified generative-predictive framework to address this problem. Janus couples a deep encoder-decoder architecture with a predictive KHRONOS head, a separable neural architecture. Topologically speaking, Janus learns a latent manifold simultaneously isometric for generative inversion and pruned for physical prediction; the joint objective inducing \emph{disentanglement} of the latent space. Janus is first validated on the MNIST dataset, demonstrating high-fidelity reconstruction, accurate classification and diverse generative inversion of all ten target classes. It is then applied to the inverse design of heterogeneous microstructures labeled with thermal conductivity. It achieves a forward prediction accuracy $R^2=0.98$ (2\% relative error) and sub-5\% pixelwise reconstruction error. Inverse solutions satisfy target properties to within $1\%$ relative error. Inverting a sweep through properties reveal smooth traversal of the latent manifold, and UMAP visualization confirms the emergence of a low-dimensional, disentangled manifold. By unifying prediction and generation within a single latent space, Janus enables real-time, physics-informed inverse microstructure generation at a lower computational cost typically associated with classical optimization-based approaches.

Paperid: 427, https://arxiv.org/pdf/2512.14211.pdf

Abstract:
Physics-Informed Neural Networks (PINN) are emerging as a promising approach for quantitative parameter estimation of Magnetic Resonance Imaging (MRI). While existing deep learning methods can provide an accurate quantitative estimation of the T2 parameter, they still require large amounts of training data and lack theoretical support and a recognized gold standard. Thus, given the absence of PINN-based approaches for T2 estimation, we propose embedding the fundamental physics of MRI, the Bloch equation, in the loss of PINN, which is solely based on target scan data and does not require a pre-defined training database. Furthermore, by deriving rigorous upper bounds for both the T2 estimation error and the generalization error of the Bloch equation solution, we establish a theoretical foundation for evaluating the PINN's quantitative accuracy. Even without access to the ground truth or a gold standard, this theory enables us to estimate the error with respect to the real quantitative parameter T2. The accuracy of T2 mapping and the validity of the theoretical analysis are demonstrated on a numerical cardiac model and a water phantom, where our method exhibits excellent quantitative precision in the myocardial T2 range. Clinical applicability is confirmed in 94 acute myocardial infarction (AMI) patients, achieving low-error quantitative T2 estimation under the theoretical error bound, highlighting the robustness and potential of PINN.

Paperid: 428, https://arxiv.org/pdf/2512.10287.pdf

Abstract:
Surrogate models provide fast alternatives to costly aerodynamic simulations and are extremely useful in design and optimization applications. This study proposes the use of a recent kernel-based neural surrogate, KHRONOS. In this work, we blend sparse high-fidelity (HF) data with low-fidelity (LF) information to predict aerodynamic fields under varying constraints in computational resources. Unlike traditional approaches, KHRONOS is built upon variational principles, interpolation theory, and tensor decomposition. These elements provide a mathematical basis for heavy pruning compared to dense neural networks. Using the AirfRANS dataset as a high-fidelity benchmark and NeuralFoil to generate low-fidelity counterparts, this work compares the performance of KHRONOS with three contemporary model architectures: a multilayer perceptron (MLP), a graph neural network (GNN), and a physics-informed neural network (PINN). We consider varying levels of high-fidelity data availability (0%, 10%, and 30%) and increasingly complex geometry parameterizations. These are used to predict the surface pressure coefficient distribution over the airfoil. Results indicate that, whilst all models eventually achieve comparable predictive accuracy, KHRONOS excels in resource-constrained conditions. In this domain, KHRONOS consistently requires orders of magnitude fewer trainable parameters and delivers much faster training and inference than contemporary dense neural networks at comparable accuracy. These findings highlight the potential of KHRONOS and similar architectures to balance accuracy and efficiency in multi-fidelity aerodynamic field prediction.

Paperid: 429, https://arxiv.org/pdf/2512.09202.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on resource-constrained platforms is hindered by substantial computational and memory overhead, primarily stemming from higher-order automatic differentiation, intensive tensor operations, and reliance on full-precision arithmetic. To address these challenges, we present a framework that enables scalable and energy-efficient PINN training on edge devices. This framework integrates fully quantized training, Stein's estimator (SE)-based residual loss computation, and tensor-train (TT) decomposition for weight compression. It contributes three key innovations: (1) a mixed-precision training method that use a square-block MX (SMX) format to eliminate data duplication during backpropagation; (2) a difference-based quantization scheme for the Stein's estimator that mitigates underflow; and (3) a partial-reconstruction scheme (PRS) for TT-Layers that reduces quantization-error accumulation. We further design PINTA, a precision-scalable hardware accelerator, to fully exploit the performance of the framework. Experiments on the 2-D Poisson, 20-D Hamilton-Jacobi-Bellman (HJB), and 100-D Heat equations demonstrate that the proposed framework achieves accuracy comparable to or better than full-precision, uncompressed baselines while delivering 5.5x to 83.5x speedups and 159.6x to 2324.1x energy savings. This work enables real-time PDE solving on edge devices and paves the way for energy-efficient scientific computing at scale.

Paperid: 430, https://arxiv.org/pdf/2511.18270.pdf

Abstract:
Autonomous aerial vehicles (AAVs) have played a pivotal role in coverage operations and search missions. Recent advances in large language models (LLMs) offer promising opportunities to augment AAV intelligence. These advances help address complex challenges like area coverage optimization, dynamic path planning, and adaptive decision-making. However, the absence of physical grounding in LLMs leads to hallucination and reproducibility problems in spatial reasoning and decision-making. To tackle these issues, we present Skypilot, an LLM-enhanced two-stage framework that grounds language models in physical reality by integrating monte carlo tree search (MCTS). In the first stage, we introduce a diversified action space that encompasses generate, regenerate, fine-tune, and evaluate operations, coupled with physics-informed reward functions to ensure trajectory feasibility. In the second stage, we fine-tune Qwen3-4B on 23,000 MCTS-generated samples, achieving substantial inference acceleration while maintaining solution quality. Extensive numerical simulations and real-world flight experiments validate the efficiency and superiority of our proposed approach. Detailed information and experimental results are accessible at https://sky-pilot.top.

Paperid: 431, https://arxiv.org/pdf/2511.12053.pdf

Abstract:
Monitoring battery health is essential for ensuring safe and efficient operation. However, there is an inherent trade-off between assessment speed and diagnostic depth-specifically, between rapid overall health estimation and precise identification of internal degradation states. Capturing detailed internal battery information efficiently remains a major challenge, yet such insights are key to understanding the various degradation mechanisms. To address this, we develop a parameterized physics-informed neural network (P-PINNSPM) over the key aging-related parameter space for a single particle model. The model can accurately predict internal battery variables across the parameter space and identifies internal parameters in about 30 seconds-achieving a 47x speedup over the finite volume method-while maintaining high accuracy. These parameters improve the battery state-of-health (SOH) estimation accuracy by at least 60.61%, compared to models without parameter incorporation. Moreover, they enable extrapolation to unseen SOH levels and support robust estimation across diverse charging profiles and operating conditions. Our results demonstrate the strong potential of physics-informed machine learning to advance real-time, data-efficient, and physics-aware battery management systems.

Paperid: 432, https://arxiv.org/pdf/2511.10079.pdf

Abstract:
Friction modeling plays a crucial role in achieving high-precision motion control in robotic operating systems. Traditional static friction models (such as the Stribeck model) are widely used due to their simple forms; however, they typically require predefined functional assumptions, which poses significant challenges when dealing with unknown functional structures. To address this issue, this paper proposes a physics-inspired machine learning approach based on the Kolmogorov Arnold Network (KAN) for static friction modeling of robotic joints. The method integrates spline activation functions with a symbolic regression mechanism, enabling model simplification and physical expression extraction through pruning and attribute scoring, while maintaining both high prediction accuracy and interpretability. We first validate the method's capability to accurately identify key parameters under known functional models, and further demonstrate its robustness and generalization ability under conditions with unknown functional structures and noisy data. Experiments conducted on both synthetic data and real friction data collected from a six-degree-of-freedom industrial manipulator show that the proposed method achieves a coefficient of determination greater than 0.95 across various tasks and successfully extracts concise and physically meaningful friction expressions. This study provides a new perspective for interpretable and data-driven robotic friction modeling with promising engineering applicability.

Paperid: 433, https://arxiv.org/pdf/2511.03746.pdf

Abstract:
Modern power systems with high penetration of inverter-based resources exhibit complex dynamic behaviors that challenge the scalability and generalizability of traditional stability assessment methods. This paper presents a dynamic recurrent adjacency memory network (DRAMN) that combines physics-informed analysis with deep learning for real-time power system stability forecasting. The framework employs sliding-window dynamic mode decomposition to construct time-varying, multi-layer adjacency matrices from phasor measurement unit and sensor data to capture system dynamics such as modal participation factors, coupling strengths, phase relationships, and spectral energy distributions. As opposed to processing spatial and temporal dependencies separately, DRAMN integrates graph convolution operations directly within recurrent gating mechanisms, enabling simultaneous modeling of evolving dynamics and temporal dependencies. Extensive validations on modified IEEE 9-bus, 39-bus, and a multi-terminal HVDC network demonstrate high performance, achieving 99.85%, 99.90%, and 99.69% average accuracies, respectively, surpassing all tested benchmarks, including classical machine learning algorithms and recent graph-based models. The framework identifies optimal combinations of measurements that reduce feature dimensionality by 82% without performance degradation. Correlation analysis between dominant measurements for small-signal and transient stability events validates generalizability across different stability phenomena. DRAMN achieves state-of-the-art accuracy while providing enhanced interpretability for power system operators, making it suitable for real-time deployment in modern control centers.

Paperid: 434, https://arxiv.org/pdf/2510.22221.pdf

Abstract:
Simulating hybrid magnonic quantum systems remains a challenge due to the large disparity between the timescales of the two systems. We present a massively parallel GPU-based simulation framework that enables fully coupled, large-scale modeling of on-chip magnon-photon circuits. Our approach resolves the dynamic interaction between ferromagnetic and electromagnetic fields with high spatiotemporal fidelity. To accelerate design workflows, we develop a physics-informed machine learning surrogate trained on the simulation data, reducing computational cost while maintaining accuracy. This combined approach reveals real-time energy exchange dynamics and reproduces key phenomena such as anti-crossing behavior and the suppression of ferromagnetic resonance under strong electromagnetic fields. By addressing the multiscale and multiphysics challenges in magnon-photon modeling, our framework enables scalable simulation and rapid prototyping of next-generation quantum and spintronic devices.

Paperid: 435, https://arxiv.org/pdf/2510.18845.pdf

Abstract:
Hamilton-Jacobi (HJ) Reachability offers a framework for generating safe value functions and policies in the face of adversarial disturbance, but is limited by the curse of dimensionality. Physics-informed deep learning is able to overcome this infeasibility, but itself suffers from slow and inaccurate convergence, primarily due to weak PDE gradients and the complexity of self-supervised learning. A few works, recently, have demonstrated that enriching the self-supervision process with regular supervision (based on the nature of the optimal control problem), greatly accelerates convergence and solution quality, however, these have been limited to single player problems and simple games. In this work, we introduce MADR: MPC-guided Adversarial DeepReach, a general framework to robustly approximate the two-player, zero-sum differential game value function. In doing so, MADR yields the corresponding optimal strategies for both players in zero-sum games as well as safe policies for worst-case robustness. We test MADR on a multitude of high-dimensional simulated and real robotic agents with varying dynamics and games, finding that our approach significantly out-performs state-of-the-art baselines in simulation and produces impressive results in hardware.

Paperid: 436, https://arxiv.org/pdf/2510.00457.pdf

Abstract:
With rapid urbanization, predicting urban microclimates has become critical, as it affects building energy demand and public health risks. However, existing generative and homogeneous graph approaches fall short in capturing physical consistency, spatial dependencies, and temporal variability. To address this, we introduce UrbanGraph, a physics-informed framework integrating heterogeneous and dynamic spatio-temporal graphs. It encodes key physical processes -- vegetation evapotranspiration, shading, and convective diffusion -- while modeling complex spatial dependencies among diverse urban entities and their temporal evolution. We evaluate UrbanGraph on UMC4/12, a physics-based simulation dataset covering diverse urban configurations and climates. Results show that UrbanGraph improves $R^2$ by up to 10.8% and reduces FLOPs by 17.0% over all baselines, with heterogeneous and dynamic graphs contributing 3.5% and 7.1% gains. Our dataset provides the first high-resolution benchmark for spatio-temporal microclimate modeling, and our method extends to broader urban heterogeneous dynamic computing tasks.

Paperid: 437, https://arxiv.org/pdf/2509.25450.pdf

Abstract:
This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes patch-local neural networks that operate on the reference domain of isogeometric analysis. A custom output layer enables the strong imposition of Dirichlet boundary conditions. Solution conformity across interfaces between non-uniform rational B-spline patches is enforced using dedicated interface neural networks. Training is performed using the variational framework by minimizing the energy functional derived after the weak form of the partial differential equation. The effectiveness of the suggested method is demonstrated on two highly non-trivial and practically relevant use-cases, namely, a 2D magnetostatics model of a quadrupole magnet and a 3D nonlinear solid and contact mechanics model of a mechanical holder. The results show excellent agreement to reference solutions obtained with high-fidelity finite element solvers, thus highlighting the potential of the suggested neural solver to tackle complex engineering problems given the corresponding computer-aided design models.

Paperid: 438, https://arxiv.org/pdf/2509.17354.pdf

Abstract:
Lane-change maneuvers are a leading cause of highway accidents, underscoring the need for accurate intention prediction to improve the safety and decision-making of autonomous driving systems. While prior studies using machine learning and deep learning methods (e.g., SVM, CNN, LSTM, Transformers) have shown promise, most approaches remain limited by binary classification, lack of scenario diversity, and degraded performance under longer prediction horizons. In this study, we propose a physics-informed AI framework that explicitly integrates vehicle kinematics, interaction feasibility, and traffic-safety metrics (e.g., distance headway, time headway, time-to-collision, closing gap time) into the learning process. lane-change prediction is formulated as a three-class problem that distinguishes left change, right change, and no change, and is evaluated across both straight highway segments (highD) and complex ramp scenarios (exiD). By integrating vehicle kinematics with interaction features, our machine learning models, particularly LightGBM, achieve state-of-the-art accuracy and strong generalization. Results show up to 99.8% accuracy and 93.6% macro F1 on highD, and 96.1% accuracy and 88.7% macro F1 on exiD at a 1-second horizon, outperforming a two-layer stacked LSTM baseline. These findings demonstrate the practical advantages of a physics-informed and feature-rich machine learning framework for real-time lane-change intention prediction in autonomous driving systems.

Paperid: 439, https://arxiv.org/pdf/2509.07687.pdf

Abstract:
We present the Physics-Informed Low-Rank Neural Operator (PILNO), a neural operator framework for efficiently approximating solution operators of partial differential equations (PDEs) on point cloud data. PILNO combines low-rank kernel approximations with an encoder--decoder architecture, enabling fast, continuous one-shot predictions while remaining independent of specific discretizations. The model is trained using a physics-informed penalty framework, ensuring that PDE constraints and boundary conditions are satisfied in both supervised and unsupervised settings. We demonstrate its effectiveness on diverse problems, including function fitting, the Poisson equation, the screened Poisson equation with variable coefficients, and parameterized Darcy flow. The low-rank structure provides computational efficiency in high-dimensional parameter spaces, establishing PILNO as a scalable and flexible surrogate modeling tool for PDEs.

Paperid: 440, https://arxiv.org/pdf/2508.15300.pdf

Abstract:
Map matching and registration are essential tasks in robotics for localisation and integration of multi-session or multi-robot data. Traditional methods rely on cameras or LiDARs to capture visual or geometric information but struggle in challenging conditions like smoke or dust. Magnetometers, on the other hand, detect magnetic fields, revealing features invisible to other sensors and remaining robust in such environments. In this paper, we introduce Mag-Match, a novel method for extracting and describing features in 3D magnetic vector field maps to register different maps of the same area. Our feature descriptor, based on higher-order derivatives of magnetic field maps, is invariant to global orientation, eliminating the need for gravity-aligned mapping. To obtain these higher-order derivatives map-wide given point-wise magnetometer data, we leverage a physics-informed Gaussian Process to perform efficient and recursive probabilistic inference of both the magnetic field and its derivatives. We evaluate Mag-Match in simulated and real-world experiments against a SIFT-based approach, demonstrating accurate map-to-map, robot-to-map, and robot-to-robot transformations - even without initial gravitational alignment.

Paperid: 441, https://arxiv.org/pdf/2507.21710.pdf

Abstract:
Accurately forecasting commodity demand remains a critical challenge due to volatile market dynamics, nonlinear dependencies, and the need for economically consistent predictions. This paper introduces PREIG, a novel deep learning framework tailored for commodity demand forecasting. The model uniquely integrates a Gated Recurrent Unit (GRU) architecture with physics-informed neural network (PINN) principles by embedding a domain-specific economic constraint: the negative elasticity between price and demand. This constraint is enforced through a customized loss function that penalizes violations of the physical rule, ensuring that model predictions remain interpretable and aligned with economic theory. To further enhance predictive performance and stability, PREIG incorporates a hybrid optimization strategy that couples NAdam and L-BFGS with Population-Based Training (POP). Experiments across multiple commodities datasets demonstrate that PREIG significantly outperforms traditional econometric models (ARIMA,GARCH) and deep learning baselines (BPNN,RNN) in both RMSE and MAPE. When compared with GRU,PREIG maintains good explainability while still performing well in prediction. By bridging domain knowledge, optimization theory and deep learning, PREIG provides a robust, interpretable, and scalable solution for high-dimensional nonlinear time series forecasting in economy.

Paperid: 442, https://arxiv.org/pdf/2507.15259.pdf

Abstract:
This letter develops a novel physics-informed neural ordinary differential equations-based framework to emulate the proprietary dynamics of the inverters -- essential for improved accuracy in grid dynamic simulations. In current industry practice, the original equipment manufacturers (OEMs) often do not disclose the exact internal controls and parameters of the inverters, posing significant challenges in performing accurate dynamic simulations and other relevant studies, such as gain tunings for stability analysis and controls. To address this, we propose a Physics-Informed Latent Neural ODE Model (PI-LNM) that integrates system physics with neural learning layers to capture the unmodeled behaviors of proprietary units. The proposed method is validated using a grid-forming inverter (GFM) case study, demonstrating improved dynamic simulation accuracy over approaches that rely solely on data-driven learning without physics-based guidance.

Paperid: 443, https://arxiv.org/pdf/2507.08977.pdf

Abstract:
Scientific modeling faces a tradeoff between the interpretability of mechanistic theory and the predictive power of machine learning. While hybrid approaches like Physics-Informed Neural Networks (PINNs) embed domain knowledge as functional constraints, they can be brittle under model misspecification. We introduce Simulation-Grounded Neural Networks (SGNNs), a framework that instead embeds domain knowledge into the training data to establish a structural prior. By pretraining on synthetic corpora spanning diverse model structures and observational artifacts, SGNNs learn the broad patterns of physical possibility. This allows the model to internalize the underlying dynamics of a system without being forced to satisfy a single, potentially incorrect equation. We evaluated SGNNs across scientific disciplines and found that this approach confers significant robustness. In prediction tasks, SGNNs nearly tripled COVID-19 forecasting skill versus CDC baselines. In tests on dengue outbreaks, SGNNs outperformed physics-constrained models even when both were restricted to incorrect human-to-human transmission equations, demonstrating that SGNNs are potentially more robust to model misspecification. For inference, SGNNs extend the logic of simulation-based inference to enable supervised learning for unobservable targets, estimating early COVID-19 transmissibility more accurately than traditional methods. Finally, SGNNs enable back-to-simulation attribution, a form of mechanistic interpretability that maps real-world data back to the simulated manifold to identify underlying processes. By unifying these disparate simulation-based techniques into a single framework, we demonstrate that mechanistic simulations can serve as effective training data for robust scientific inference that generalizes beyond the limitations of fixed functional forms.

Paperid: 444, https://arxiv.org/pdf/2507.07237.pdf

Abstract:
Data driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as mutli-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. However, most studies rely on overly simple benchmarks that do not reflect the true complexity of the fracture processes where PFM excels as a method. To address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1,000 random initial crack configurations for a total of 6,000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO) and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.

Paperid: 445, https://arxiv.org/pdf/2507.02106.pdf

Abstract:
We present a hybrid machine learning framework that combines Physics-Informed Neural Operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic (MHD) turbulence across a broad range of Reynolds numbers ($\mathrm{Re}$). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with $\mathrm{Re} \in \{100, 250, 500, 750, 1000, 3000, 10000\}$, the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At $\mathrm{Re}=1000$ and $3000$, the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels ($\mathrm{Re}=10000$), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.

Paperid: 446, https://arxiv.org/pdf/2506.10778.pdf

Abstract:
Understanding and reasoning about dynamics governed by physical laws through visual observation, akin to human capabilities in the real world, poses significant challenges. Currently, object-centric dynamic simulation methods, which emulate human behavior, have achieved notable progress but overlook two critical aspects: 1) the integration of physical knowledge into models. Humans gain physical insights by observing the world and apply this knowledge to accurately reason about various dynamic scenarios; 2) the validation of model adaptability across diverse scenarios. Real-world dynamics, especially those involving fluids and objects, demand models that not only capture object interactions but also simulate fluid flow characteristics. To address these gaps, we introduce SlotPi, a slot-based physics-informed object-centric reasoning model. SlotPi integrates a physical module based on Hamiltonian principles with a spatio-temporal prediction module for dynamic forecasting. Our experiments highlight the model's strengths in tasks such as prediction and Visual Question Answering (VQA) on benchmark and fluid datasets. Furthermore, we have created a real-world dataset encompassing object interactions, fluid dynamics, and fluid-object interactions, on which we validated our model's capabilities. The model's robust performance across all datasets underscores its strong adaptability, laying a foundation for developing more advanced world models.

Paperid: 447, https://arxiv.org/pdf/2505.13241.pdf

Abstract:
Physics-informed machine learning (PIML) is crucial in modern traffic flow modeling because it combines the benefits of both physics-based and data-driven approaches. In conventional PIML, physical information is typically incorporated by constructing a hybrid loss function that combines data-driven loss and physics loss through linear scalarization. The goal is to find a trade-off between these two objectives to improve the accuracy of model predictions. However, from a mathematical perspective, linear scalarization is limited to identifying only the convex region of the Pareto front, as it treats data-driven and physics losses as separate objectives. Given that most PIML loss functions are non-convex, linear scalarization restricts the achievable trade-off solutions. Moreover, tuning the weighting coefficients for the two loss components can be both time-consuming and computationally challenging. To address these limitations, this paper introduces a paradigm shift in PIML by reformulating the training process as a multi-objective optimization problem, treating data-driven loss and physics loss independently. We apply several multi-gradient descent algorithms (MGDAs), including traditional multi-gradient descent (TMGD) and dual cone gradient descent (DCGD), to explore the Pareto front in this multi-objective setting. These methods are evaluated on both macroscopic and microscopic traffic flow models. In the macroscopic case, MGDAs achieved comparable performance to traditional linear scalarization methods. Notably, in the microscopic case, MGDAs significantly outperformed their scalarization-based counterparts, demonstrating the advantages of a multi-objective optimization approach in complex PIML scenarios.

Paperid: 448, https://arxiv.org/pdf/2505.11578.pdf

Abstract:
This research confronts the challenge of substantial physical equation discrepancies encountered in the generation of spatiotemporal physical fields through data-driven trained models. A spatiotemporal physical field generation model, named HMT-PF, is developed based on the hybrid Mamba-Transformer architecture, incorporating unstructured grid information as input. A fine-tuning block, enhanced with physical information, is introduced to effectively reduce the physical equation discrepancies. The physical equation residuals are computed through a point query mechanism for efficient gradient evaluation, then encoded into latent space for refinement. The fine-tuning process employs a self-supervised learning approach to achieve physical consistency while maintaining essential field characteristics. Results show that the hybrid Mamba-Transformer model achieves good performance in generating spatiotemporal fields, while the physics-informed fine-tuning mechanism further reduces significant physical errors effectively. A MSE-R evaluation method is developed to assess the accuracy and realism of physical field generation.

Paperid: 449, https://arxiv.org/pdf/2505.11491.pdf

Abstract:
This study investigates why physics-informed machine learning (PIML) can fail in macroscopic traffic flow modeling. We define failure as cases where a PIML model underperforms both purely data-driven and purely physics-based baselines by a given threshold. Unlike in other fields, physics residuals themselves do not hinder optimization in this setting. Instead, effective updates require both data and physics gradients to form acute angles with the true gradient, a condition difficult to satisfy with low-resolution loop data. In such cases, neural networks cannot accurately approximate density and speed, and the constructed physics residuals, already degraded by discrete sampling and temporal averaging, lose their ability to capture PDE dynamics, which directly leads to PIML failure. Theoretically, although LWR and ARZ solutions are weak solutions, for piecewise $C^k$ initial data they remain $C^k$ off the shock set under mild conditions, which has Lebesgue measure zero. Thus, almost all detector or collocation points lie in smooth regions where residuals are valid, and the MLP's inability to exactly represent discontinuities is immaterial. Finally, we establish MSE lower bounds of physics residuals: higher-order models such as ARZ have strictly larger consistency error bounds than LWR under mild conditions. This explains why LWR-based PIML can outperform ARZ-based PIML even with high-resolution data, with the gap shrinking as resolution increases, consistent with prior empirical findings.

Paperid: 450, https://arxiv.org/pdf/2505.08687.pdf

Abstract:
Kolmogorov-Arnold Networks (KANs) have recently shown promise for solving partial differential equations (PDEs). Yet their original formulation is computationally and memory intensive, motivating the introduction of Chebyshev Type-I-based KANs (Chebyshev1KANs). Although Chebyshev1KANs have outperformed the vanilla KANs architecture, our rigorous theoretical analysis reveals that they still suffer from rank collapse, ultimately limiting their expressive capacity. To overcome these limitations, we enhance Chebyshev1KANs by integrating wavelet-activated MLPs with learnable parameters and an internal attention mechanism. We prove that this design preserves a full-rank Jacobian and is capable of approximating solutions to PDEs of arbitrary order. Furthermore, to alleviate the loss instability and imbalance introduced by the Chebyshev polynomial basis, we externally incorporate a Residual Gradient Attention (RGA) mechanism that dynamically re-weights individual loss terms according to their gradient norms and residual magnitudes. By jointly leveraging internal and external attention, we present AC-PKAN, a novel architecture that constitutes an enhancement to weakly supervised Physics-Informed Neural Networks (PINNs) and extends the expressive power of KANs. Experimental results from nine benchmark tasks across three domains show that AC-PKAN consistently outperforms or matches state-of-the-art models such as PINNsFormer, establishing it as a highly effective tool for solving complex real-world engineering problems in zero-data or data-sparse regimes. The code will be made publicly available upon acceptance.

Paperid: 451, https://arxiv.org/pdf/2504.04982.pdf

Abstract:
Data centers (DCs) as mission-critical infrastructures are pivotal in powering the growth of artificial intelligence (AI) and the digital economy. The evolution from Internet DC to AI DC has introduced new challenges in operating and managing data centers for improved business resilience and reduced total cost of ownership. As a result, new paradigms, beyond the traditional approaches based on best practices, must be in order for future data centers. In this research, we propose and develop a novel Physical AI (PhyAI) framework for advancing DC operations and management. Our system leverages the emerging capabilities of state-of-the-art industrial products and our in-house research and development. Specifically, it presents three core modules, namely: 1) an industry-grade in-house simulation engine to simulate DC operations in a highly accurate manner, 2) an AI engine built upon NVIDIA PhysicsNemo for the training and evaluation of physics-informed machine learning (PIML) models, and 3) a digital twin platform built upon NVIDIA Omniverse for our proposed 5-tier digital twin framework. This system presents a scalable and adaptable solution to digitalize, optimize, and automate future data center operations and management, by enabling real-time digital twins for future data centers. To illustrate its effectiveness, we present a compelling case study on building a surrogate model for predicting the thermal and airflow profiles of a large-scale DC in a real-time manner. Our results demonstrate its superior performance over traditional time-consuming Computational Fluid Dynamics/Heat Transfer (CFD/HT) simulation, with a median absolute temperature prediction error of 0.18 Â°C. This emerging approach would open doors to several potential research directions for advancing Physical AI in future DC operations.

Paperid: 452, https://arxiv.org/pdf/2503.08343.pdf

Abstract:
Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilistic PDE solvers -- Bayesian statistical models mostly based on Gaussian process (GP) priors which seamlessly combine empirical measurements and mechanistic knowledge. As such, they quantify uncertainties arising from e.g. noisy or missing data, unknown PDE parameters or discretization error by design. Prior work has established connections to classical PDE solvers and provided solid theoretical guarantees. However, scaling such methods to large-scale problems remains a fundamental challenge primarily due to dense covariance matrices. Our approach addresses the scalability issues by leveraging the Markov property of many commonly used GP priors. It has been shown that such priors are solutions to stochastic PDEs (SPDEs) which when discretized allow for highly efficient GP regression through sparse linear algebra. In this work, we show how to leverage this prior class to make probabilistic PDE solvers practical, even for large-scale nonlinear PDEs, through greatly accelerated inference mechanisms. Additionally, our approach also allows for flexible and physically meaningful priors beyond what can be modeled with covariance functions. Experiments confirm substantial speedups and accelerated convergence of our physics-informed priors in nonlinear settings.

Paperid: 453, https://arxiv.org/pdf/2502.07230.pdf

Abstract:
As a part of the integrated energy system (IES), gas pipeline networks can provide additional flexibility to power systems through coordinated optimal dispatch. An accurate pipeline network model is critical for the optimal operation and control of IESs. However, inaccuracies or unavailability of accurate pipeline parameters often introduce errors in the state-space models of such networks. This paper proposes a physics-informed recurrent network (PIRN) to identify the state-space model of gas pipelines. It fuses sparse measurement data with fluid-dynamic behavior expressed by partial differential equations. By embedding the physical state-space model within the recurrent network, parameter identification becomes an end-to-end PIRN training task. The model can be realized in PyTorch through modifications to a standard RNN backbone. Case studies demonstrate that our proposed PIRN can accurately estimate gas pipeline models from sparse terminal node measurements, providing robust performance and significantly higher parameter efficiency. Furthermore, the identified state-space model of the pipeline network can be seamlessly integrated into optimization frameworks.

Paperid: 454, https://arxiv.org/pdf/2502.00373.pdf

Abstract:
Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can significantly enhance the training efficiency of PINOs, primarily through techniques like data, architecture, and loss augmentation. In this work, we focus on the latter, highlighting that point symmetries oftentimes result in no training signal, limiting their effectiveness in many problems. To address this, we propose a novel loss augmentation strategy that leverages evolutionary representatives of point symmetries, a specific class of generalized symmetries of the underlying PDE. These generalized symmetries provide a richer set of generators compared to standard symmetries, leading to a more informative training signal. We demonstrate that leveraging evolutionary representatives enhances the performance of neural operators, resulting in improved data efficiency and accuracy during training.

Paperid: 455, https://arxiv.org/pdf/2501.00016.pdf

Abstract:
Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network's loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov-Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately, and the error in the predicted fields is localized near the crack.

Paperid: 456, https://arxiv.org/pdf/2412.05545.pdf

Abstract:
Neural operators are aiming at approximating operators mapping between Banach spaces of functions, achieving much success in the field of scientific computing. Compared to certain deep learning-based solvers, such as Physics-Informed Neural Networks (PINNs), Deep Ritz Method (DRM), neural operators can solve a class of Partial Differential Equations (PDEs). Although much work has been done to analyze the approximation and generalization error of neural operators, there is still a lack of analysis on their training error. In this work, we conduct the convergence analysis of gradient descent for the wide shallow neural operators and physics-informed shallow neural operators within the framework of Neural Tangent Kernel (NTK). The core idea lies on the fact that over-parameterization and random initialization together ensure that each weight vector remains near its initialization throughout all iterations, yielding the linear convergence of gradient descent. In this work, we demonstrate that under the setting of over-parametrization, gradient descent can find the global minimum regardless of whether it is in continuous time or discrete time.

Paperid: 457, https://arxiv.org/pdf/2410.17525.pdf

Abstract:
In cellular mobile networks, wireless channel quality (CQ) is a crucial factor in determining communication performance and user's network experience. Accurately predicting CQ based on real environmental characteristics, specific base station configurations and user trajectories can help network operators optimize base station deployment, improving coverage and capacity. The Received Signal Reference Power (RSRP) and Signal-to-Interference-plus-Noise Ratio (SINR) of user equipment (UE) are key indicators of CQ in wireless communication. However, existing researches have limitations in terms of generation accuracy. Regression methods such as statistical inference and random forests fail to effectively capture the unique characteristics of wireless environments; theoretical derivations relying on specific communication protocols lack generalization capability; data-driven machine learning (ML) methods like Long Short-Term Memory (LSTM) Network often suffer from a lack of interpretability. To overcome these limitations, we propose physics-informed diffusion models, which accurately generate RSRP and SINR at UE based on the wireless environment, base station configurations, and user trajectories. The model adopts a modular and end-to-end design, employing a teacher-student framework to achieve knowledge distillation. This method integrates expert knowledge into the training of diffusion models, enhancing both the interpretability and accuracy, while also facilitating faster convergence of the model parameters. Furthermore, it allows for self-adaptation in various scenarios through few-shot learning. This approach provides valuable guidance for optimizing base station deployment, predicting user network experience, and building real-world simulators.

Paperid: 458, https://arxiv.org/pdf/2410.02698.pdf

Abstract:
The quest for robust and generalizable machine learning models has driven recent interest in exploiting symmetries through equivariant neural networks. In the context of PDE solvers, recent works have shown that Lie point symmetries can be a useful inductive bias for Physics-Informed Neural Networks (PINNs) through data and loss augmentation. Despite this, directly enforcing equivariance within the model architecture for these problems remains elusive. This is because many PDEs admit non-compact symmetry groups, oftentimes not studied beyond their infinitesimal generators, making them incompatible with most existing equivariant architectures. In this work, we propose Lie aLgebrA Canonicalization (LieLAC), a novel approach that exploits only the action of infinitesimal generators of the symmetry group, circumventing the need for knowledge of the full group structure. To achieve this, we address existing theoretical issues in the canonicalization literature, establishing connections with frame averaging in the case of continuous non-compact groups. Operating within the framework of canonicalization, LieLAC can easily be integrated with unconstrained pre-trained models, transforming inputs to a canonical form before feeding them into the existing model, effectively aligning the input for model inference according to allowed symmetries. LieLAC utilizes standard Lie group descent schemes, achieving equivariance in pre-trained models. Finally, we showcase LieLAC's efficacy on tasks of invariant image classification and Lie point symmetry equivariant neural PDE solvers using pre-trained models.

Paperid: 459, https://arxiv.org/pdf/2409.10284.pdf

Abstract:
Learning operators for parametric partial differential equations (PDEs) using neural networks has gained significant attention in recent years. However, standard approaches like Deep Operator Networks (DeepONets) require extensive labeled data, and physics-informed DeepONets encounter training challenges. In this paper, we introduce a novel physics-informed tailored finite point operator network (PI-TFPONet) method to solve parametric interface problems without the need for labeled data. Our method fully leverages the prior physical information of the problem, eliminating the need to include the PDE residual in the loss function, thereby avoiding training challenges. The PI-TFPONet is specifically designed to address certain properties of the problem, allowing us to naturally obtain an approximate solution that closely matches the exact solution. Our method is theoretically proven to converge if the local mesh size is sufficiently small and the training loss is minimized. Notably, our approach is uniformly convergent for singularly perturbed interface problems. Extensive numerical studies show that our unsupervised PI-TFPONet is comparable to or outperforms existing state-of-the-art supervised deep operator networks in terms of accuracy and versatility.

Paperid: 460, https://arxiv.org/pdf/2409.06560.pdf

Abstract:
Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative modelling and inversion tasks due to its built-in Bayesian regularisation and flexibility, essential qualities for physics related problems. For such problems, the underlying physical model determines the dependence between variables of interest, which in turn will require a tailored derivation for the central VI learning objective. Furthermore, in many physical inference applications this structure has rich meaning and is essential for accurately capturing the dynamics of interest. In this paper, we provide an accessible and thorough technical introduction to VI for forward and inverse problems, guiding the reader through standard derivations of the VI framework and how it can best be realized through deep learning. We then review and unify recent literature exemplifying the flexibility allowed by VI. This paper is designed for a general scientific audience looking to solve physics-based problems with an emphasis on uncertainty quantification

Paperid: 461, https://arxiv.org/pdf/2601.20005.pdf

Abstract:
The urgent need for building decarbonization calls for a paradigm shift in future autonomous building energy operation, from human-intensive engineering workflows toward intelligent agents that interact with physics-grounded digital environments. This study proposes an end-to-end agentic AI-enabled Physics-Informed Machine Learning (PIML) environment for scalable building energy modeling, simulation, control, and automation. The framework consists of (1) a modular and physics-consistent PIML digital environment spanning building thermal dynamics, Heating, Ventilation, and Air Conditioning (HVAC), and distributed energy resources (DER) for grid-interactive energy management; and (2) an agentic AI layer with 11 specialist agents and 72 Model Context Protocol (MCP) tools that enable end-to-end execution of multi-step energy analytics. A representative case study demonstrates multi-domain, multi-agent coordination for assessing how system and control upgrades affect energy use, operating cost, thermal comfort, and flexibility. In addition, a large-scale benchmark (about 4000 runs) systematically evaluates workflow performance in terms of accuracy, token consumption, execution time, and inference cost. The results quantify the impacts of intelligence mode design, model size, task complexity, and orchestrator-specialist coordination, and provide key lessons for building future agentic AI systems in real-world building energy applications. This work establishes a scalable, physics-grounded foundation for deploying agentic AI in decarbonized and grid-interactive building operations.

Paperid: 462, https://arxiv.org/pdf/2601.16780.pdf

Abstract:
Live video denoising under realistic, multi-component sensor noise remains challenging for applications such as autofocus, autonomous driving, and surveillance. We propose PocketDVDNet, a lightweight video denoiser developed using our model compression framework that combines sparsity-guided structured pruning, a physics-informed noise model, and knowledge distillation to achieve high-quality restoration with reduced resource demands. Starting from a reference model, we induce sparsity, apply targeted channel pruning, and retrain a teacher on realistic multi-component noise. The student network learns implicit noise handling, eliminating the need for explicit noise-map inputs. PocketDVDNet reduces the original model size by 74% while improving denoising quality and processing 5-frame patches in real-time. These results demonstrate that aggressive compression, combined with domain-adapted distillation, can reconcile performance and efficiency for practical, real-time video denoising.

Paperid: 463, https://arxiv.org/pdf/2601.16283.pdf

Abstract:
Modern buildings are increasingly interconnected with occupancy, heating, ventilation, and air-conditioning (HVAC) systems, distributed energy resources (DERs), and power grids. Modeling, control, and optimization of such multi-domain systems play a critical role in achieving building-sector decarbonization. However, most existing tools lack scalability and physical consistency for addressing these complex, multi-scale ecosystem problems. To bridge this gap, this study presents BESTOpt, a modular, physics-informed machine learning (PIML) framework that unifies building applications, including benchmarking, evaluation, diagnostics, control, optimization, and performance simulation. The framework adopts a cluster-domain-system/building-component hierarchy and a standardized state-action-disturbance-observation data typology. By embedding physics priors into data-driven modules, BESTOpt improves model accuracy and physical consistency under unseen conditions. Case studies on single-building and cluster scenarios demonstrate its capability for multi-level centralized and decentralized control. Looking ahead, BESTOpt lays the foundation for an open, extensible platform that accelerates interdisciplinary research toward smart, resilient, and decarbonized building ecosystems.

Paperid: 464, https://arxiv.org/pdf/2601.12330.pdf

Abstract:
Glacial Lake Outburst Floods (GLOFs) pose a serious threat in high mountain regions. They are hazardous to communities, infrastructure, and ecosystems further downstream. The classical methods of GLOF detection and prediction have so far mainly relied on hydrological modeling, threshold-based lake monitoring, and manual satellite image analysis. These approaches suffer from several drawbacks: slow updates, reliance on manual labor, and losses in accuracy when clouds interfere and/or lack on-site data. To tackle these challenges, we present IceWatch: a novel deep learning framework for GLOF prediction that incorporates both spatial and temporal perspectives. The vision component, RiskFlow, of IceWatch deals with Sentinel-2 multispectral satellite imagery using a CNN-based classifier and predicts GLOF events based on the spatial patterns of snow, ice, and meltwater. Its tabular counterpart confirms this prediction by considering physical dynamics. TerraFlow models glacier velocity from NASA ITS_LIVE time series while TempFlow forecasts near-surface temperature from MODIS LST records; both are trained on long-term observational archives and integrated via harmonized preprocessing and synchronization to enable multimodal, physics-informed GLOF prediction. Both together provide cross-validation, which will improve the reliability and interpretability of GLOF detection. This system ensures strong predictive performance, rapid data processing for real-time use, and robustness to noise and missing information. IceWatch paves the way for automatic, scalable GLOF warning systems. It also holds potential for integration with diverse sensor inputs and global glacier monitoring activities.

Paperid: 465, https://arxiv.org/pdf/2601.08104.pdf

Abstract:
The accurate identification and control of spatiotemporal chaos in reaction-diffusion systems remains a grand challenge in chemical engineering, particularly when the underlying catalytic surface possesses complex, unknown topography. In the \textit{Defect Turbulence} regime, system dynamics are governed by topological phase singularities (spiral waves) whose motion couples to manifold curvature via geometric pinning. Conventional Physics-Informed Neural Networks (PINNs) using ReLU or Tanh activations suffer from fundamental \textit{spectral bias}, failing to resolve high-frequency gradients and causing amplitude collapse or phase drift. We propose a Multi-Scale SIREN-PINN architecture leveraging periodic sinusoidal activations with frequency-diverse initialization, embedding the appropriate inductive bias for wave-like physics directly into the network structure. This enables simultaneous resolution of macroscopic wave envelopes and microscopic defect cores. Validated on the complex Ginzburg-Landau equation evolving on latent Riemannian manifolds, our architecture achieves relative state prediction error $ε_{L_2} \approx 1.92 \times 10^{-2}$, outperforming standard baselines by an order of magnitude while preserving topological invariants ($|ΔN_{defects}| < 1$). We solve the ill-posed \textit{inverse pinning problem}, reconstructing hidden Gaussian curvature fields solely from partial observations of chaotic wave dynamics (Pearson correlation $ρ= 0.965$). Training dynamics reveal a distinctive Spectral Phase Transition at epoch $\sim 2,100$, where cooperative minimization of physics and geometry losses drives the solver to Pareto-optimal solutions. This work establishes a new paradigm for Geometric Catalyst Design, offering a mesh-free, data-driven tool for identifying surface heterogeneity and engineering passive control strategies in turbulent chemical reactors.

Paperid: 466, https://arxiv.org/pdf/2601.06444.pdf

Abstract:
High-dimensional design spaces underpin a wide range of physics-based modeling and computational design tasks in science and engineering. These problems are commonly formulated as constrained black-box searches over rugged objective landscapes, where function evaluations are expensive, and gradients are unavailable or unreliable. Conventional global search engines and optimizers struggle in such settings due to the exponential scaling of design spaces, the presence of multiple local basins, and the absence of physical guidance in sampling. We present a physics-informed Monte Carlo Tree Search (MCTS) framework that extends policy-driven tree-based reinforcement concepts to continuous, high-dimensional scientific optimization. Our method integrates population-level decision trees with surrogate-guided directional sampling, reward shaping, and hierarchical switching between global exploration and local exploitation. These ingredients allow efficient traversal of non-convex, multimodal landscapes where physically meaningful optima are sparse. We benchmark our approach against standard global optimization baselines on a suite of canonical test functions, demonstrating superior or comparable performance in terms of convergence, robustness, and generalization. Beyond synthetic tests, we demonstrate physics-consistent applicability to (i) crystal structure optimization from clusters to bulk, (ii) fitting of classical interatomic potentials, and (iii) constrained engineering design problems. Across all cases, the method converges with high fidelity and evaluation efficiency while preserving physical constraints. Overall, our work establishes physics-informed tree search as a scalable and interpretable paradigm for computational design and high-dimensional scientific optimization, bridging discrete decision-making frameworks with continuous search in scientific design workflows.

Paperid: 467, https://arxiv.org/pdf/2601.00834.pdf

Abstract:
Simulating nonlinear reaction-diffusion dynamics on complex, non-Euclidean manifolds remains a fundamental challenge in computational morphogenesis, constrained by high-fidelity mesh generation costs and symplectic drift in discrete time-stepping schemes. This study introduces the Intrinsic-Metric Physics-Informed Neural Network (IM-PINN), a mesh-free geometric deep learning framework that solves partial differential equations directly in the continuous parametric domain. By embedding the Riemannian metric tensor into the automatic differentiation graph, our architecture analytically reconstructs the Laplace-Beltrami operator, decoupling solution complexity from geometric discretization. We validate the framework on a "Stochastic Cloth" manifold with extreme Gaussian curvature fluctuations ($K \in [-2489, 3580]$), where traditional adaptive refinement fails to resolve anisotropic Turing instabilities. Using a dual-stream architecture with Fourier feature embeddings to mitigate spectral bias, the IM-PINN recovers the "splitting spot" and "labyrinthine" regimes of the Gray-Scott model. Benchmarking against the Surface Finite Element Method (SFEM) reveals superior physical rigor: the IM-PINN achieves global mass conservation error of $\mathcal{E}_{mass} \approx 0.157$ versus SFEM's $0.258$, acting as a thermodynamically consistent global solver that eliminates mass drift inherent in semi-implicit integration. The framework offers a memory-efficient, resolution-independent paradigm for simulating biological pattern formation on evolving surfaces, bridging differential geometry and physics-informed machine learning.

Paperid: 468, https://arxiv.org/pdf/2512.24493.pdf

Abstract:
We study safe control for dynamical systems whose continuous-time dynamics are learned with Gaussian processes (GPs), focusing on mechanical and port-Hamiltonian systems where safety is naturally expressed via energy constraints. The availability of a GP Hamiltonian posterior naturally raises the question of how to systematically exploit this structure to design an energy-aware control barrier function with high-probability safety guarantees. We address this problem by developing a Bayesian-CBF framework and instantiating it with energy-aware Bayesian-CBFs (EB-CBFs) that construct conservative energy-based barriers directly from the Hamiltonian and vector-field posteriors, yielding safety filters that minimally modify a nominal controller while providing probabilistic energy safety guarantees. Numerical simulations on a mass-spring system demonstrate that the proposed EB-CBFs achieve high-probability safety under noisy sampled GP-learned dynamics.

Paperid: 469, https://arxiv.org/pdf/2512.19643.pdf

Abstract:
Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings. Neural operator (NO) surrogates offer fast inference across parametric and functional inputs; however, most autoregressive NO frameworks remain vulnerable to compounding errors, and ensemble-averaged metrics provide limited guarantees for individual inference trajectories. In practice, error accumulation can become unacceptable beyond the training horizon, and existing methods lack mechanisms for online monitoring or correction. To address this gap, we propose ANCHOR (Adaptive Numerical Correction for High-fidelity Operator Rollouts), an online, instance-aware hybrid inference framework for stable long-horizon prediction of nonlinear, time-dependent PDEs. ANCHOR treats a pretrained NO as the primary inference engine and adaptively couples it with a classical numerical solver using a physics-informed, residual-based error estimator. Inspired by adaptive time-stepping in numerical analysis, ANCHOR monitors an exponential moving average (EMA) of the normalized PDE residual to detect accumulating error and trigger corrective solver interventions without requiring access to ground-truth solutions. We show that the EMA-based estimator correlates strongly with the true relative L2 error, enabling data-free, instance-aware error control during inference. Evaluations on four canonical PDEs: 1D and 2D Burgers', 2D Allen-Cahn, and 3D heat conduction, demonstrate that ANCHOR reliably bounds long-horizon error growth, stabilizes extrapolative rollouts, and significantly improves robustness over standalone neural operators, while remaining substantially more efficient than high-fidelity numerical solvers.

Paperid: 470, https://arxiv.org/pdf/2512.03290.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs). However, they notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent spectral bias of standard multilayer perceptron (MLP) architectures, which prevents them from adequately representing high-frequency components. In this work, we introduce the Adaptive Spectral Physics-Enabled Network (ASPEN), a novel architecture designed to overcome this critical limitation. ASPEN integrates an adaptive spectral layer with learnable Fourier features directly into the network's input stage. This mechanism allows the model to dynamically tune its own spectral basis during training, enabling it to efficiently learn and represent the precise frequency content required by the solution. We demonstrate the efficacy of ASPEN by applying it to the complex Ginzburg-Landau equation (CGLE), a canonical and challenging benchmark for nonlinear, stiff spatio-temporal dynamics. Our results show that a standard PINN architecture catastrophically fails on this problem, diverging into non-physical oscillations. In contrast, ASPEN successfully solves the CGLE with exceptional accuracy. The predicted solution is visually indistinguishable from the high-resolution ground truth, achieving a low median physics residual of 5.10 x 10^-3. Furthermore, we validate that ASPEN's solution is not only pointwise accurate but also physically consistent, correctly capturing emergent physical properties, including the rapid free energy relaxation and the long-term stability of the domain wall front. This work demonstrates that by incorporating an adaptive spectral basis, our framework provides a robust and physically-consistent solver for complex dynamical systems where standard PINNs fail, opening new options for machine learning in challenging physical domains.

Paperid: 471, https://arxiv.org/pdf/2512.03055.pdf

Abstract:
Cardiovascular disease is the leading global cause of mortality, with coronary artery disease (CAD) as its most prevalent form, necessitating early risk prediction. While 3D coronary artery digital twins reconstructed from imaging offer detailed anatomy for personalized assessment, their analysis relies on computationally intensive computational fluid dynamics (CFD), limiting scalability. Data-driven approaches are hindered by scarce labeled data and lack of physiological priors. To address this, we present PINS-CAD, a physics-informed self-supervised learning framework. It pre-trains graph neural networks on 200,000 synthetic coronary digital twins to predict pressure and flow, guided by 1D Navier-Stokes equations and pressure-drop laws, eliminating the need for CFD or labeled data. When fine-tuned on clinical data from 635 patients in the multicenter FAME2 study, PINS-CAD predicts future cardiovascular events with an AUC of 0.73, outperforming clinical risk scores and data-driven baselines. This demonstrates that physics-informed pretraining boosts sample efficiency and yields physiologically meaningful representations. Furthermore, PINS-CAD generates spatially resolved pressure and fractional flow reserve curves, providing interpretable biomarkers. By embedding physical priors into geometric deep learning, PINS-CAD transforms routine angiography into a simulation-free, physiology-aware framework for scalable, preventive cardiology.

Paperid: 472, https://arxiv.org/pdf/2511.00338.pdf

Abstract:
This work presents a novel hybrid approach that integrates Deep Operator Networks (DeepONet) with the Neural Tangent Kernel (NTK) to solve complex inverse problem. The method effectively addresses tasks such as source localization governed by the Navier-Stokes equations and image reconstruction, overcoming challenges related to nonlinearity, sparsity, and noisy data. By incorporating physics-informed constraints and task-specific regularization into the loss function, the framework ensures solutions that are both physically consistent and accurate. Validation on diverse synthetic and real datasets demonstrates its robustness, scalability, and precision, showcasing its broad potential applications in computational physics and imaging sciences.

Paperid: 473, https://arxiv.org/pdf/2510.18266.pdf

Abstract:
We introduce the Stable Physics-Informed Kernel Evolution (SPIKE) method for numerical computation of inviscid hyperbolic conservation laws. SPIKE resolves a fundamental paradox: how strong-form residual minimization can capture weak solutions containing discontinuities. SPIKE employs reproducing kernel representations with regularized parameter evolution, where Tikhonov regularization provides a smooth transition mechanism through shock formation, allowing the dynamics to traverse shock singularities. This approach automatically maintains conservation, tracks characteristics, and captures shocks satisfying Rankine-Hugoniot conditions within a unified framework requiring no explicit shock detection or artificial viscosity. Numerical validation across scalar and vector-valued conservation laws confirms the method's effectiveness.

Paperid: 474, https://arxiv.org/pdf/2510.12328.pdf

Abstract:
Accurate rainfall forecasting, particularly for extreme events, remains a significant challenge in climatology and the Earth system. This paper presents novel physics-informed Graph Neural Networks (GNNs) combined with extreme-value analysis techniques to improve gauge-station rainfall predictions across Thailand. The model leverages a graph-structured representation of gauge stations to capture complex spatiotemporal patterns, and it offers explainability through teleconnections. We preprocess relevant climate indices that potentially influence regional rainfall. The proposed Graph Attention Network with Long Short-Term Memory (Attention-LSTM) applies the attention mechanism using initial edge features derived from simple orographic-precipitation physics formulation. The embeddings are subsequently processed by LSTM layers. To address extremes, we perform Peak-Over-Threshold (POT) mapping using the novel Spatial Season-aware Generalized Pareto Distribution (GPD) method, which overcomes limitations of traditional machine-learning models. Experiments demonstrate that our method outperforms well-established baselines across most regions, including areas prone to extremes, and remains strongly competitive with the state of the art. Compared with the operational forecasting system SEAS5, our real-world application improves extreme-event prediction and offers a practical enhancement to produce fine-resolution maps that support decision-making in long-term water management.

Paperid: 475, https://arxiv.org/pdf/2509.14568.pdf

Abstract:
We present the fundamental theory and implementation guidelines underlying Evidential Physics-Informed Neural Network (E-PINN) -- a novel class of uncertainty-aware PINN. It leverages the marginal distribution loss function of evidential deep learning for estimating uncertainty of outputs, and infers unknown parameters of the PDE via a learned posterior distribution. Validating our model on two illustrative case studies -- the 1D Poisson equation with a Gaussian source and the 2D Fisher-KPP equation, we found that E-PINN generated empirical coverage probabilities that were calibrated significantly better than Bayesian PINN and Deep Ensemble methods. To demonstrate real-world applicability, we also present a brief case study on applying E-PINN to analyze clinical glucose-insulin datasets that have featured in medical research on diabetes pathophysiology.

Paperid: 476, https://arxiv.org/pdf/2509.13686.pdf

Abstract:
Accurate localized wireless channel modeling is a cornerstone of cellular network optimization, enabling reliable prediction of network performance during parameter tuning. Localized statistical channel modeling (LSCM) is the state-of-the-art channel modeling framework tailored for cellular network optimization. However, traditional LSCM methods, which infer the channel's Angular Power Spectrum (APS) from Reference Signal Received Power (RSRP) measurements, suffer from critical limitations: they are typically confined to single-cell, single-grid and single-carrier frequency analysis and fail to capture complex cross-domain interactions. To overcome these challenges, we propose RF-LSCM, a novel framework that models the channel APS by jointly representing large-scale signal attenuation and multipath components within a radiance field. RF-LSCM introduces a multi-domain LSCM formulation with a physics-informed frequency-dependent Attenuation Model (FDAM) to facilitate the cross frequency generalization as well as a point-cloud-aided environment enhanced method to enable multi-cell and multi-grid channel modeling. Furthermore, to address the computational inefficiency of typical neural radiance fields, RF-LSCM leverages a low-rank tensor representation, complemented by a novel Hierarchical Tensor Angular Modeling (HiTAM) algorithm. This efficient design significantly reduces GPU memory requirements and training time while preserving fine-grained accuracy. Extensive experiments on real-world multi-cell datasets demonstrate that RF-LSCM significantly outperforms state-of-the-art methods, achieving up to a 30% reduction in mean absolute error (MAE) for coverage prediction and a 22% MAE improvement by effectively fusing multi-frequency data.

Paperid: 477, https://arxiv.org/pdf/2509.13425.pdf

Abstract:
Ecological systems exhibit complex multi-scale dynamics that challenge traditional modeling. New methods must capture temporal oscillations and emergent spatiotemporal patterns while adhering to conservation principles. We present the Unified Spatiotemporal Physics-Informed Learning (USPIL) framework, a deep learning architecture integrating physics-informed neural networks (PINNs) and conservation laws to model predator-prey dynamics across dimensional scales. The framework provides a unified solution for both ordinary (ODE) and partial (PDE) differential equation systems, describing temporal cycles and reaction-diffusion patterns within a single neural network architecture. Our methodology uses automatic differentiation to enforce physics constraints and adaptive loss weighting to balance data fidelity with physical consistency. Applied to the Lotka-Volterra system, USPIL achieves 98.9% correlation for 1D temporal dynamics (loss: 0.0219, MAE: 0.0184) and captures complex spiral waves in 2D systems (loss: 4.7656, pattern correlation: 0.94). Validation confirms conservation law adherence within 0.5% and shows a 10-50x computational speedup for inference compared to numerical solvers. USPIL also enables mechanistic understanding through interpretable physics constraints, facilitating parameter discovery and sensitivity analysis not possible with purely data-driven methods. Its ability to transition between dimensional formulations opens new avenues for multi-scale ecological modeling. These capabilities make USPIL a transformative tool for ecological forecasting, conservation planning, and understanding ecosystem resilience, establishing physics-informed deep learning as a powerful and scientifically rigorous paradigm.

Paperid: 478, https://arxiv.org/pdf/2509.11768.pdf

Abstract:
It was recently shown that the loss function used for training physics-informed neural networks (PINNs) exhibits local minima at solutions corresponding to fixed points of dynamical systems. In the forward setting, where the PINN is trained to solve initial value problems, these local minima can interfere with training and potentially leading to physically incorrect solutions. Building on stability theory, this paper proposes a regularization scheme that penalizes solutions corresponding to unstable fixed points. Experimental results on four dynamical systems, including the Lotka-Volterra model and the van der Pol oscillator, show that our scheme helps avoiding physically incorrect solutions and substantially improves the training success rate of PINNs.

Paperid: 479, https://arxiv.org/pdf/2509.10363.pdf

Abstract:
We present a machine learning framework for adaptive source localization in which agents use a structure-preserving digital twin of a coupled hydrodynamic-transport system for real-time trajectory planning and data assimilation. The twin is constructed with conditional neural Whitney forms (CNWF), coupling the numerical guarantees of finite element exterior calculus (FEEC) with transformer-based operator learning. The resulting model preserves discrete conservation, and adapts in real time to streaming sensor data. It employs a conditional attention mechanism to identify: a reduced Whitney-form basis; reduced integral balance equations; and a source field, each compatible with given sensor measurements. The induced reduced-order environmental model retains the stability and consistency of standard finite-element simulation, yielding a physically realizable, regular mapping from sensor data to the source field. We propose a staggered scheme that alternates between evaluating the digital twin and applying Lloyd's algorithm to guide sensor placement, with analysis providing conditions for monotone improvement of a coverage functional. Using the predicted source field as an importance function within an optimal-recovery scheme, we demonstrate recovery of point sources under continuity assumptions, highlighting the role of regularity as a sufficient condition for localization. Experimental comparisons with physics-agnostic transformer architectures show improved accuracy in complex geometries when physical constraints are enforced, indicating that structure preservation provides an effective inductive bias for source identification.

Paperid: 480, https://arxiv.org/pdf/2509.04966.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful neural framework for solving partial differential equations (PDEs). However, standard MLP-based PINNs often fail to converge when dealing with complex initial-value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classical spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models will be released.

Paperid: 481, https://arxiv.org/pdf/2508.05190.pdf

Abstract:
Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire trajectories in one pass, often fail to capture the causal dependencies and generalize poorly outside the training time horizon. Autoregressive (AR) approaches, evolving the system step by step, suffer from error accumulation, limiting long-term accuracy. These shortcomings limit the long-term accuracy and reliability of both strategies. To address these issues, we introduce the Physics-Informed Time-Integrated Deep Operator Network (PITI-DeepONet), a dual-output architecture trained via fully physics-informed or hybrid physics- and data-driven objectives to ensure stable, accurate long-term evolution well beyond the training horizon. Instead of forecasting future states, the network learns the time-derivative operator from the current state, integrating it using classical time-stepping schemes to advance the solution in time. Additionally, the framework can leverage residual monitoring during inference to estimate prediction quality and detect when the system transitions outside the training domain. Applied to benchmark problems, PITI-DeepONet shows improved accuracy over extended inference time horizons when compared to traditional methods. Mean relative $\mathcal{L}_2$ errors reduced by 84% (vs. FR) and 79% (vs. AR) for the one-dimensional heat equation; by 87% (vs. FR) and 98% (vs. AR) for the one-dimensional Burgers equation; and by 42% (vs. FR) and 89% (vs. AR) for the two-dimensional Allen-Cahn equation. By moving beyond classic FR and AR schemes, PITI-DeepONet paves the way for more reliable, long-term integration of complex, time-dependent PDEs.

Paperid: 482, https://arxiv.org/pdf/2507.09968.pdf

Abstract:
Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic mechanism to control the design complexity. Herein, we address these limitations by proposing a mesh-free and simultaneous framework based on physics-informed Gaussian processes (GPs). In our approach, we parameterize the design and state variables with GP priors which have independent kernels but share a multi-output neural network (NN) as their mean function. The architecture of this NN is based on Parametric Grid Convolutional Attention Networks (PGCANs) which not only mitigate spectral bias issues, but also provide an interpretable mechanism to control design complexity. We estimate all the parameters of our GP-based representations by simultaneously minimizing the compliance, total potential energy, and residual of volume fraction constraint. Importantly, our loss function exclude all data-based residuals as GPs automatically satisfy them. We also develop computational schemes based on curriculum training and numerical integration to increase the efficiency and robustness of our approach which is shown to (1) produce super-resolution topologies with fast convergence, (2) achieve smaller compliance and less gray area fraction compared to traditional numerical methods, (3) provide control over fine-scale features, and (4) outperform competing ML-based methods.

Paperid: 483, https://arxiv.org/pdf/2507.01714.pdf

Abstract:
Training physics-informed neural networks (PINNs) for forward problems often suffers from severe convergence issues, hindering the propagation of information from regions where the desired solution is well-defined. Haitsiukevich and Ilin (2023) proposed an ensemble approach that extends the active training domain of each PINN based on i) ensemble consensus and ii) vicinity to (pseudo-)labeled points, thus ensuring that the information from the initial condition successfully propagates to the interior of the computational domain. In this work, we suggest replacing the ensemble by a Bayesian PINN, and consensus by an evaluation of the PINN's posterior variance. Our experiments show that this mathematically principled approach outperforms the ensemble on a set of benchmark problems and is competitive with PINN ensembles trained with combinations of Adam and LBFGS.

Paperid: 484, https://arxiv.org/pdf/2506.19503.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a promising computational framework for solving differential equations by integrating deep learning with physical constraints. However, their application in gas turbines is still in its early stages, requiring further refinement and standardization for wider adoption. This survey provides a comprehensive review of PINNs in Industrial Gas Turbines (IGTs) research, highlighting their contributions to the analysis of aerodynamic and aeromechanical phenomena, as well as their applications in flow field reconstruction, fatigue evaluation, and flutter prediction, and reviews recent advancements in accuracy, computational efficiency, and hybrid modelling strategies. In addition, it explores key research efforts, implementation challenges, and future directions aimed at improving the robustness and scalability of PINNs.

Paperid: 485, https://arxiv.org/pdf/2506.18357.pdf

Abstract:
Connected automated vehicles (CAVs) cruising control strategies have been extensively studied at the microscopic level. CAV controllers sense and react to traffic both upstream and downstream, yet most macroscopic models still assume locality, where the desired speed only depends on local density. The nonlocal macroscopic traffic flow models that explicitly capture the ``look ahead'' and ``look behind'' nonlocal CAV dynamics remain underexplored. In this paper, we propose a Physics-informed Neural Network framework to directly learn a macroscopic non-local flow model from a generic looking-ahead looking-behind vehicle motion model, which bridges the micro-macro modeling gap. We reconstruct macroscopic traffic states from synthetic CAV trajectories generated by the proposed microscopic control designs, and then learn a non-local traffic flow model that embeds a non-local conservation law to capture the resulting look-ahead look-behind dynamics. To analyze how CAV control parameters affect nonlocal traffic flow, we conduct high-fidelity driving simulator experiments to collect human drivers' trajectory data with varying downstream and upstream visibility, which serves as a baseline for tuning CAV control gains. Our analysis validates that the learned non-local flow model predicts CAV traffic dynamics more accurately than local models, and the fundamental diagram exhibits far less scatter in the speed - density relation. We further show that the looking-ahead/looking-behind control gains mainly reshape the non-local kernels, while the macroscopic speed and non-local density relation mainly depends on the desired speed function choice of the CAV controller. Our results provide a systematic approach for learning non-local macroscopic traffic-flow models directly from generic CAV control designs.

Paperid: 486, https://arxiv.org/pdf/2506.02244.pdf

Abstract:
Recent advances in diffusion-based video generation have yielded unprecedented quality in visual content and semantic coherence. However, current approaches predominantly rely on statistical learning from vast datasets without explicitly modeling the underlying physics of motion, resulting in subtle yet perceptible non-physical artifacts that diminish the realism of generated videos. This paper introduces a physics-informed frequency domain approach to enhance the physical plausibility of generated videos. We first conduct a systematic analysis of the frequency-domain characteristics of diverse physical motions (translation, rotation, scaling), revealing that each motion type exhibits distinctive and identifiable spectral signatures. Building on this theoretical foundation, we propose two complementary components: (1) a physical motion loss function that quantifies and optimizes the conformity of generated videos to ideal frequency-domain motion patterns, and (2) a frequency domain enhancement module that progressively learns to adjust video features to conform to physical motion constraints while preserving original network functionality through a zero-initialization strategy. Experiments across multiple video diffusion architectures demonstrate that our approach significantly enhances motion quality and physical plausibility without compromising visual quality or semantic alignment. Our frequency-domain physical motion framework generalizes effectively across different video generation architectures, offering a principled approach to incorporating physical constraints into deep learning-based video synthesis pipelines. This work seeks to establish connections between data-driven models and physics-based motion models.

Paperid: 487, https://arxiv.org/pdf/2505.18647.pdf

Abstract:
The simulation of N-body systems is a fundamental problem with applications in a wide range of fields, such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based simulators and developing models directly from experimental data. In particular, recent advances based on deep generative modeling and geometric deep learning have enabled probabilistic simulation by modeling complex distributions over trajectories while respecting the permutation symmetry that is fundamental to N-body systems. However, to generate realistic trajectories, existing methods must learn complex transformations starting from uninformed noise and do not allow for the exploitation of domain-informed priors. In this work, we propose STFlow to address this limitation. By leveraging flow matching and data-dependent couplings, STFlow facilitates physics-informed simulation of geometric trajectories without sacrificing model expressivity or scalability. Our evaluation on N-body dynamical systems, molecular dynamics, and pedestrian dynamics benchmarks shows that STFlow produces significantly lower prediction errors while enabling more efficient inference, highlighting the benefits of employing physics-informed prior distributions in probabilistic geometric trajectory modeling.

Paperid: 488, https://arxiv.org/pdf/2505.16035.pdf

Abstract:
We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neural field where a unified shared backbone is conditioned on signal-specific latent variables - represented as point clouds in a Lie group - to model diverse Eikonal solutions. The ENF integration ensures equivariant mapping from these latent representations to the solution field, delivering three key benefits: enhanced representation efficiency through weight-sharing, robust geometric grounding, and solution steerability. This steerability allows transformations applied to the latent point cloud to induce predictable, geometrically meaningful modifications in the resulting Eikonal solution. By coupling these steerable representations with Physics-Informed Neural Networks (PINNs), our framework accurately models Eikonal travel-time solutions while generalizing to arbitrary Riemannian manifolds with regular group actions. This includes homogeneous spaces such as Euclidean, position-orientation, spherical, and hyperbolic manifolds. We validate our approach through applications in seismic travel-time modeling of 2D and 3D benchmark datasets. Experimental results demonstrate superior performance, scalability, adaptability, and user controllability compared to existing Neural Operator-based Eikonal solver methods.

Paperid: 489, https://arxiv.org/pdf/2505.12556.pdf

Abstract:
Real-world systems, from aerospace to railway engineering, are modeled with partial differential equations (PDEs) describing the physics of the system. Estimating robust solutions for such problems is essential. Deep learning-based architectures, such as neural PDE solvers, have recently gained traction as a reliable solution method. The current state of development of these approaches, however, primarily focuses on improving accuracy. The environmental impact of excessive computation, leading to increased carbon emissions, has largely been overlooked. This paper introduces a carbon emission measure for a range of PDE solvers. Our proposed metric, EcoL2, balances model accuracy with emissions across data collection, model training, and deployment. Experiments across both physics-informed machine learning and operator learning architectures demonstrate that the proposed metric presents a holistic assessment of model performance and emission cost. As such solvers grow in scale and deployment, EcoL2 represents a step toward building performant scientific machine learning systems with lower long-term environmental impact.

Paperid: 490, https://arxiv.org/pdf/2505.07090.pdf

Abstract:
Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM level accuracy, modeling dynamic behavior remains more challenging. This work presents a Multiple Input Operator Network (MIONet) that incorporates a second trunk network to explicitly encode temporal dynamics, enabling accurate prediction of structural responses under moving loads. Traditional DeepONet architectures using recurrent neural networks (RNNs) are limited by fixed time discretization and struggle to capture continuous dynamics. In contrast, MIONet predicts responses continuously over both space and time, removing the need for step wise modeling. It maps scalar inputs including load type, velocity, spatial mesh, and time steps to full field structural responses. To improve efficiency and enforce physical consistency, we introduce a physics informed loss based on dynamic equilibrium using precomputed mass, damping, and stiffness matrices, without solving the governing PDEs directly. Further, a Schur complement formulation reduces the training domain, significantly cutting computational costs while preserving global accuracy. The model is validated on both a simple beam and the KW-51 bridge, achieving FEM level accuracy within seconds. Compared to GRU based DeepONet, our model offers comparable accuracy with improved temporal continuity and over 100 times faster inference, making it well suited for real-time structural monitoring and digital twin applications.

Paperid: 491, https://arxiv.org/pdf/2504.21153.pdf

Abstract:
Climate science is the multidisciplinary field that studies the Earth's climate and its evolution. At the very core of climate science are indispensable climate models that predict future climate scenarios, inform policy decisions, and dictate how a country's economy should change in light of the changing climate. Climate models capture a wide range of interacting dynamic processes via extremely complex ordinary and partial differential equations. To model these large-scale complex processes, climate science leverages supercomputers, advanced simulations, and statistical methods to predict future climate. An area of engineering that is rarely studied in climate science is control engineering. Given that climate systems are inherently dynamic, it is intuitive to analyze them within the framework of dynamic system science. This perspective has been underexplored in the literature. In this manuscript, we provide a tutorial that: (i) introduces the control engineering community to climate dynamics and modeling, including spatiotemporal scales and challenges in climate modeling; (ii) offers a fresh perspective on climate models from a control systems viewpoint; and (iii) explores the relevance and applicability of various advanced graph and network control-based approaches in building a physics-informed framework for learning, control and estimation in climate systems. We also present simple and then more complex climate models, depicting fundamental ideas and processes that are instrumental in building climate change projections. This tutorial also builds parallels and observes connections between various contemporary problems at the forefront of climate science and their control theoretic counterparts. We specifically observe that an abundance of climate science problems can be linguistically reworded and mathematically framed as control theoretic ones.

Paperid: 492, https://arxiv.org/pdf/2504.19112.pdf

Abstract:
Marine remote sensing enhances maritime surveillance, environmental monitoring, and naval operations. Vessel length estimation, a key component of this technology, supports effective maritime surveillance by empowering features such as vessel classification. Departing from traditional methods relying on two-dimensional hydrodynamic wakes or computationally intensive satellite imagery, this paper introduces an innovative approach for vessel length estimation that leverages the subtle magnetic wake signatures of vessels, captured through a low-complexity one-dimensional profile from a single airborne magnetic sensor scan. The proposed method centers around our characterized nonlinear integral equations that connect the magnetic wake to the vessel length within a realistic finite-depth marine environment. To solve the derived equations, we initially leverage a deep residual neural network (DRNN). The proposed DRNN-based solution framework is shown to be unable to exactly learn the intricate relationships between parameters when constrained by a limited training-dataset. To overcome this issue, we introduce an innovative approach leveraging a physics-informed residual neural network (PIRNN). This model integrates physical formulations directly into the loss function, leading to improved performance in terms of both accuracy and convergence speed. Considering a sensor scan angle of less than $15^\circ$, which maintains a reasonable margin below Kelvin's limit angle of $19.5^\circ$, we explore the impact of various parameters on the accuracy of the vessel length estimation, including sensor scan angle, vessel speed, and sea depth. Numerical simulations demonstrate the superiority of the proposed PIRNN method, achieving mean length estimation errors consistently below 5\% for vessels longer than 100m. For shorter vessels, the errors generally remain under 10\%.

Paperid: 493, https://arxiv.org/pdf/2504.12952.pdf

Abstract:
This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques enhance the modeling and control of complex dynamical systems, ensuring safety and stability remains a critical challenge, especially in safety-critical applications like autonomous vehicles, robotics, medical decision-making, and energy systems. We explore various approaches for embedding and ensuring safety constraints, including structural priors, Lyapunov and Control Barrier Functions, predictive control, projections, and robust optimization techniques. Additionally, we delve into methods for uncertainty quantification and safety verification, including reachability analysis and neural network verification tools, which help validate that control policies remain within safe operating bounds even in uncertain environments. The paper includes illustrative examples demonstrating the implementation aspects of safe learning frameworks that combine the strengths of data-driven approaches with the rigor of physical principles, offering a path toward the safe control of complex dynamical systems.

Paperid: 494, https://arxiv.org/pdf/2504.06327.pdf

Abstract:
Kolmogorov-Arnold Networks (KANs) have gained attention as an alternative to traditional multilayer perceptrons (MLPs) for deep learning applications in computational physics, particularly for solving inverse problems with sparse data, as exemplified by the physics-informed Kolmogorov-Arnold network (PIKAN). However, the capability of KANs to simultaneously solve inverse problems over multiple irregular geometries within a single training run remains unexplored. To address this gap, we introduce the physics-informed Kolmogorov-Arnold PointNet (PI-KAN-PointNet), in which shared KANs are integrated into the PointNet architecture to capture the geometric features of computational domains. The loss function comprises the squared residuals of the governing equations, computed via automatic differentiation, along with sparse observations and partially known boundary conditions. We construct shared KANs using Jacobi polynomials and investigate their performance by considering Jacobi polynomials of different degrees and types in terms of both computational cost and prediction accuracy. As a benchmark test case, we consider natural convection in a square enclosure with a cylinder, where the cylinder's shape varies across a dataset of 135 geometries. PI-KAN-PointNet offers two main advantages. First, it overcomes the limitation of current PIKANs, which are restricted to solving only a single computational domain per training run, thereby reducing computational costs. Second, when comparing the performance of PI-KAN-PointNet with that of the physics-informed PointNet using MLPs, we observe that, with approximately the same number of trainable parameters and comparable computational cost in terms of the number of epochs, training time per epoch, and memory usage, PI-KAN-PointNet yields more accurate predictions, particularly for values on unknown boundary conditions involving nonsmooth geometries.

Paperid: 495, https://arxiv.org/pdf/2504.05397.pdf

Abstract:
Physics-informed machine learning (PIML) provides a promising solution for building energy modeling and can serve as a virtual environment to enable reinforcement learning (RL) agents to interact and learn. However, challenges remain in efficiently integrating physics priors, evaluating the effectiveness of physics constraints, balancing model accuracy and physics consistency, and enabling real-world implementation. To address these gaps, this study introduces a Physics-Informed Modularized Neural Network (PI-ModNN), which incorporates physics priors through a physics-informed model structure, loss functions, and hard constraints. A new evaluation metric called "temperature response violation" is developed to quantify the physical consistency of data-driven building dynamic models under varying control inputs and training data sizes. Additionally, a physics prior evaluation framework based on rule importance is proposed to assess the contribution of each individual physics prior, offering guidance on selecting appropriate PIML techniques. Results indicate that incorporating physical priors does not always improve model performance; inappropriate priors may decrease model accuracy and consistency. However, hard constraints are effective in enforcing model consistency. Furthermore, we present a general workflow for developing control-oriented PIML models and integrating them with deep reinforcement learning (DRL). Following this framework, a case study implementing DRL in an office space over three months demonstrates potential energy savings of 31.4%. Finally, we provide a general guideline for integrating data-driven models with advanced building control through a four-step evaluation framework, paving the way for reliable and scalable deployment of advanced building controls.

Paperid: 496, https://arxiv.org/pdf/2504.01913.pdf

Abstract:
Accurately reconstructing continuous flow fields from sparse or indirect measurements remains an open challenge, as existing techniques often suffer from oversmoothing artifacts, reliance on heterogeneous architectures, and the computational burden of enforcing physics-informed losses in implicit neural representations (INRs). In this paper, we introduce a novel flow field reconstruction framework based on divergence-free kernels (DFKs), which inherently enforce incompressibility while capturing fine structures without relying on hierarchical or heterogeneous representations. Through qualitative analysis and quantitative ablation studies, we identify the matrix-valued radial basis functions derived from Wendland's $\mathcal{C}^4$ polynomial (DFKs-Wen4) as the optimal form of analytically divergence-free approximation for velocity fields, owing to their favorable numerical properties, including compact support, positive definiteness, and second-order differentiablility. Experiments across various reconstruction tasks, spanning data compression, inpainting, super-resolution, and time-continuous flow inference, has demonstrated that DFKs-Wen4 outperform INRs and other divergence-free representations in both reconstruction accuracy and computational efficiency while requiring the fewest trainable parameters.

Paperid: 497, https://arxiv.org/pdf/2504.00937.pdf

Abstract:
Building performance simulation (BPS) is critical for understanding building dynamics and behavior, analyzing performance of the built environment, optimizing energy efficiency, improving demand flexibility, and enhancing building resilience. However, conducting BPS is not trivial. Traditional BPS relies on an accurate building energy model, mostly physics-based, which depends heavily on detailed building information, expert knowledge, and case-by-case model calibrations, thereby significantly limiting their scalability. With the development of sensing technology and increased data availability, there is a growing attention and interest in data-driven BPS. However, purely data-driven models often suffer from limited generalization ability and a lack of physical consistency, resulting in poor performance in real-world applications. To address these limitations, recent studies have started to incorporate physics priors into data-driven models, a methodology called physics-informed machine learning (PIML). PIML is an emerging field with the definitions, methodologies, evaluation criteria, application scenarios, and future directions that remain open. To bridge those gaps, this study systematically reviews the state-of-art PIML for BPS, offering a comprehensive definition of PIML, and comparing it to traditional BPS approaches regarding data requirements, modeling effort, performance and computation cost. We also summarize the commonly used methodologies, validation approaches, application domains, available data sources, open-source packages and testbeds. In addition, this study provides a general guideline for selecting appropriate PIML models based on BPS applications. Finally, this study identifies key challenges and outlines future research directions, providing a solid foundation and valuable insights to advance R&D of PIML in BPS.

Paperid: 498, https://arxiv.org/pdf/2503.15561.pdf

Abstract:
We introduce a simultaneous and meshfree topology optimization (TO) framework based on physics-informed Gaussian processes (GPs). Our framework endows all design and state variables via GP priors which have a shared, multi-output mean function that is parametrized via a customized deep neural network (DNN). The parameters of this mean function are estimated by minimizing a multi-component loss function that depends on the performance metric, design constraints, and the residuals on the state equations. Our TO approach yields well-defined material interfaces and has a built-in continuation nature that promotes global optimality. Other unique features of our approach include (1) its customized DNN which, unlike fully connected feed-forward DNNs, has a localized learning capacity that enables capturing intricate topologies and reducing residuals in high gradient fields, (2) its loss function that leverages localized weights to promote solution accuracy around interfaces, and (3) its use of curriculum training to avoid local optimality.To demonstrate the power of our framework, we validate it against commercial TO package COMSOL on three problems involving dissipated power minimization in Stokes flow.

Paperid: 499, https://arxiv.org/pdf/2502.08783.pdf

Abstract:
In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such as physics-informed neural networks, depend on automatic differentiation and the sampling of collocation points, which can result in a lack of interpretability and lower accuracy compared to traditional numerical methods. To address this issue, we propose two approaches for learning discontinuous Galerkin solutions to PDEs using small linear convolutional neural networks. Our first approach is supervised and depends on labeled data, while our second approach is unsupervised and does not rely on any training data. In both cases, our methods use substantially fewer parameters than similar numerics-based neural networks while also demonstrating comparable accuracy to the true and DG solutions for elliptic problems.

Paperid: 500, https://arxiv.org/pdf/2501.15908.pdf

Abstract:
We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order distribution. The dependent and trainable variables of the PDE residual loss and data-fitting loss terms are recast as functions of the hyperparameters of an evidential prior distribution. Our model is equipped with an information-theoretic regularizer that contains the Kullback-Leibler divergence between two inverse-gamma distributions characterizing predictive uncertainty. Relative to Bayesian-Physics-Informed-Neural-Networks, our framework appeared to exhibit higher sensitivity to data noise, preserve boundary conditions more faithfully and yield empirical coverage probabilities closer to nominal ones. Toward examining its relevance for data mining in scientific discoveries, we demonstrate how to apply our model to inverse problems involving 1D and 2D nonlinear differential equations.

Paperid: 501, https://arxiv.org/pdf/2501.07700.pdf

Abstract:
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have improved PINN accuracy, the impact of collocation point sampling on their performance remains underexplored. Fixed sampling methods, such as uniform random sampling and equispaced grids, can fail to capture critical regions with high solution gradients, limiting their effectiveness for complex PDEs. Adaptive methods, inspired by adaptive mesh refinement from traditional numerical methods, address this by dynamically updating collocation points during training but may overlook residual dynamics between updates, potentially losing valuable information. To overcome this limitation, we propose two adaptive collocation point selection strategies utilizing the QR Discrete Empirical Interpolation Method (QR-DEIM), a reduced-order modeling technique for efficiently approximating nonlinear functions. Our results on benchmark PDEs demonstrate that our QR-DEIM-based approaches improve PINN accuracy compared to existing methods, offering a promising direction for adaptive collocation point strategies.

Paperid: 502, https://arxiv.org/pdf/2501.06933.pdf

Abstract:
We introduce Neural Discrete Equilibrium (NeurDE), a machine learning framework for stable and accurate long-term forecasting of nonlinear conservation laws. NeurDE leverages a kinetic lifting that decomposes the dynamics into a fixed linear transport component and a local nonlinear relaxation to equilibrium. This structure provides a natural and principled interface between physics, numerical methods, and machine learning methodologies, enabling NeurDE to be viewed as a ``neural twin'' to Boltzmann-BGK. The transport step can be implemented efficiently in solvers such as lattice Boltzmann (LB), while the equilibrium is modeled by a neural network that maps macroscopic observables to a discrete equilibrium distribution. When integrated into a LB solver, the transport step becomes an efficient lattice streaming operation, and NeurDE yields a hybrid algorithm that robustly captures shock propagation and complex compressible dynamics over long time horizons. The NeurDE method is highly data-efficient: a small network trained on limited data generalizes far beyond the training regime, resolving shocks that evolve well outside the initial training distribution. Unlike traditional kinetic solvers, NeurDE achieves this accuracy without costly root-finding procedures or large velocity lattices. These results establish NeurDE as a scalable, efficient, and physics-informed paradigm for learning-based simulation of nonlinear conservation laws

Paperid: 503, https://arxiv.org/pdf/2412.17838.pdf

Abstract:
The Wind Storage Integrated System with Power Smoothing Control (PSC) has emerged as a promising solution to ensure both efficient and reliable wind energy generation. However, existing PSC strategies overlook the intricate interplay and distinct control frequencies between batteries and wind turbines, and lack consideration of wake effect and battery degradation cost. In this paper, a novel coordinated control framework with hierarchical levels is devised to address these challenges effectively, which integrates the wake model and battery degradation model. In addition, after reformulating the problem as a Markov decision process, the multi-agent reinforcement learning method is introduced to overcome the bi-level characteristic of the problem. Moreover, a Physics-informed Neural Network-assisted Multi-agent Deep Deterministic Policy Gradient (PAMA-DDPG) algorithm is proposed to incorporate the power fluctuation differential equation and expedite the learning process. The effectiveness of the proposed methodology is evaluated through simulations conducted in four distinct scenarios using WindFarmSimulator (WFSim). The results demonstrate that the proposed algorithm facilitates approximately an 11% increase in total profit and a 19% decrease in power fluctuation compared to the traditional methods, thereby addressing the dual objectives of economic efficiency and grid-connected energy reliability.

Paperid: 504, https://arxiv.org/pdf/2411.19769.pdf

Abstract:
This study introduces a modified score matching method aimed at generating molecular structures with high energy accuracy. The denoising process of score matching or diffusion models mirrors molecular structure optimization, where scores act like physical force fields that guide particles toward equilibrium states. To achieve energetically accurate structures, it can be advantageous to have the score closely approximate the gradient of the actual potential energy surface. Unlike conventional methods that simply design the target score based on structural differences in Euclidean space, we propose a Riemannian score matching approach. This method represents molecular structures on a manifold defined by physics-informed internal coordinates to efficiently mimic the energy landscape, and performs noising and denoising within this space. Our method has been evaluated by refining several types of starting structures on the QM9 and GEOM datasets, demonstrating that the proposed Riemannian score matching method significantly improves the accuracy of the generated molecular structures, attaining chemical accuracy. The implications of this study extend to various applications in computational chemistry, offering a robust tool for accurate molecular structure prediction.

Paperid: 505, https://arxiv.org/pdf/2411.08702.pdf

Abstract:
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics-informed neural network and deep Ritz methods, we propose the Deep Uzawa algorithm, which incorporates Lagrange multipliers to handle boundary conditions effectively. This modification requires only a minor computational adjustment but ensures enhanced convergence properties and provably accurate enforcement of boundary conditions, even for singularly perturbed problems. We provide a comprehensive mathematical analysis demonstrating the convergence of the scheme and validate the effectiveness of the Deep Uzawa algorithm through numerical experiments, including high-dimensional, singularly perturbed problems and those posed over non-convex domains.

Paperid: 506, https://arxiv.org/pdf/2411.05866.pdf

Abstract:
This paper presents a novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways. The freeway traffic dynamics are described by second-order coupled hyperbolic partial differential equations (PDEs). The proposed framework learns feedback boundary control strategies from the closed-loop PDE solution using backstepping controllers, which are widely employed for boundary stabilization of PDE systems. The PDE backstepping control design is time-consuming and requires intensive depth of expertise, since it involves constructing and solving backstepping control kernels. To address these challenges, we present neural operator (NO) learning schemes for the ARZ traffic system that not only ensure closed-loop stability robust to parameter and initial condition variations but also accelerate boundary controller computation. The stability guarantee of the NO-approximated control laws is obtained using Lyapunov analysis. We further propose the physics-informed neural operator (PINO) to reduce the reliance on extensive training data. The performance of the NO schemes is evaluated by simulated and real traffic data, compared with the benchmark backstepping controller, a Proportional Integral (PI) controller, and a PINN-based controller. The NO-approximated methods achieve a computational speedup of approximately 300 times with only a 1% error trade-off compared to the backstepping controller, while outperforming the other two controllers in both accuracy and computational efficiency. The robustness of the NO schemes is validated using real traffic data, and tested across various initial traffic conditions and demand scenarios. The results show that neural operators can significantly expedite and simplify the process of obtaining controllers for traffic PDE systems with great potential application for traffic management.

Paperid: 507, https://arxiv.org/pdf/2410.21657.pdf

Abstract:
Climate models serve as critical tools for evaluating the effects of climate change and projecting future climate scenarios. However, the reliance on numerical simulations of physical equations renders them computationally intensive and inefficient. While deep learning methodologies have made significant progress in weather forecasting, they are still unstable for climate emulation tasks. Here, we propose PACER, a lightweight 684K parameter Physics Informed Uncertainty Aware Climate Emulator. PACER emulates temperature and precipitation stably for 86 years while only being trained on greenhouse gas emissions data. We incorporate a fundamental physical law of advection-diffusion in PACER accounting for boundary conditions and empirically estimating the diffusion co-efficient and flow velocities from emissions data. PACER has been trained on 15 climate models provided by ClimateSet outperforming baselines across most of the climate models and advancing a new state of the art in a climate diagnostic task.

Paperid: 508, https://arxiv.org/pdf/2410.15089.pdf

Abstract:
Developing efficient methods for solving parametric partial differential equations is crucial for addressing inverse problems. This work introduces a Least-Squares-based Neural Network (LS-Net) method for solving linear parametric PDEs. It utilizes a separated representation form for the parametric PDE solution via a deep neural network and a least-squares solver. In this approach, the output of the deep neural network consists of a vector-valued function, interpreted as basis functions for the parametric solution space, and the least-squares solver determines the optimal solution within the constructed solution space for each given parameter. The LS-Net method requires a quadratic loss function for the least-squares solver to find optimal solutions given the set of basis functions. In this study, we consider loss functions derived from the Deep Fourier Residual and Physics-Informed Neural Networks approaches. We also provide theoretical results similar to the Universal Approximation Theorem, stating that there exists a sufficiently large neural network that can theoretically approximate solutions of parametric PDEs with the desired accuracy. We illustrate the LS-net method by solving one- and two-dimensional problems. Numerical results clearly demonstrate the method's ability to approximate parametric solutions.

Paperid: 509, https://arxiv.org/pdf/2409.00994.pdf

Abstract:
Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by introducing an innovative method for real-time prediction of structural static responses using DeepOnet which relies on a novel approach to physics-informed networks driven by structural balance laws. This approach offers the flexibility to accurately predict responses under various load classes and magnitudes. The trained DeepONet can generate solutions for the entire domain, within a fraction of a second. This capability effectively eliminates the need for extensive remodeling and analysis typically required for each new case in FE modeling. We apply the proposed method to two structures: a simple 2D beam structure and a comprehensive 3D model of a real bridge. To predict multiple variables with DeepONet, we utilize two strategies: a split branch/trunk and multiple DeepONets combined into a single DeepONet. In addition to data-driven training, we introduce a novel physics-informed training approaches. This method leverages structural stiffness matrices to enforce fundamental equilibrium and energy conservation principles, resulting in two novel physics-informed loss functions: energy conservation and static equilibrium using the Schur complement. We use various combinations of loss functions to achieve an error rate of less than 5% with significantly reduced training time. This study shows that DeepONet, enhanced with hybrid loss functions, can accurately and efficiently predict displacements and rotations at each mesh point, with reduced training time.

Paperid: 510, https://arxiv.org/pdf/2601.03673.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ) capabilities. Most existing PINN-based prognostics approaches are deterministic or account only for epistemic uncertainty, limiting their suitability for risk-aware decision-making. This work introduces a heteroscedastic Bayesian Physics-Informed Neural Network (B-PINN) framework that jointly models epistemic and aleatoric uncertainty, yielding full predictive posteriors for spatiotemporal insulation material ageing estimation. The approach integrates Bayesian Neural Networks (BNNs) with physics-based residual enforcement and prior distributions, enabling probabilistic inference within a physics-informed learning architecture. The framework is evaluated on transformer insulation ageing application, validated with a finite-element thermal model and field measurements from a solar power plant, and benchmarked against deterministic PINNs, dropout-based PINNs (d-PINNs), and alternative B-PINN variants. Results show that the proposed B-PINN provides improved predictive accuracy and better-calibrated uncertainty estimates than competing approaches. A systematic sensitivity study further analyzes the impact of boundary-condition, initial-condition, and residual sampling strategies on accuracy, calibration, and generalization. Overall, the findings highlight the potential of Bayesian physics-informed learning to support uncertainty-aware prognostics and informed decision-making in transformer asset management.

Paperid: 511, https://arxiv.org/pdf/2512.10792.pdf

Abstract:
The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a novel deep learning-based reduced-order modeling strategy, leveraging Graph Neural Networks (GNNs) trained on synthetic microvascular graphs to approximate hemodynamic quantities on anatomically realistic domains. Our method combines algorithms for synthetic vascular generation with a physics-informed training procedure that integrates graph topological information and local flow dynamics. To ensure the physical reliability of the learned surrogates, we incorporate a physics-informed loss functional derived from the governing equations, allowing enforcement of mass conservation and rheological constraints. The resulting GNN architecture demonstrates robust generalization capabilities across diverse network configurations. The GNN formulation is validated on benchmark problems with linear and nonlinear rheology, showing accurate pressure and velocity field reconstruction with substantial computational gains over full-order solvers. The methodology showcases significant generalization capabilities with respect to vascular complexity, as highlighted by tests on data from the mouse cerebral cortex. This work establishes a new class of graph-based surrogate models for microvascular flow, grounded in physical laws and equipped with inductive biases that mirror mass conservation and rheological models, opening new directions for real-time inference in vascular modeling and biomedical applications.

Paperid: 512, https://arxiv.org/pdf/2512.09780.pdf

Abstract:
Battery energy storage systems (BESS) have become increasingly vital in three-phase unbalanced distribution grids for maintaining voltage stability and enabling optimal dispatch. However, existing deep learning approaches often lack explicit three-phase representation, making it difficult to accurately model phase-specific dynamics and enforce operational constraints--leading to infeasible dispatch solutions. This paper demonstrates that by embedding detailed three-phase grid information--including phase voltages, unbalanced loads, and BESS states--into heterogeneous graph nodes, diverse GNN architectures (GCN, GAT, GraphSAGE, GPS) can jointly predict network state variables with high accuracy. Moreover, a physics-informed loss function incorporates critical battery constraints--SoC and C-rate limits--via soft penalties during training. Experimental validation on the CIGRE 18-bus distribution system shows that this embedding-loss approach achieves low prediction errors, with bus voltage MSEs of 6.92e-07 (GCN), 1.21e-06 (GAT), 3.29e-05 (GPS), and 9.04e-07 (SAGE). Importantly, the physics-informed method ensures nearly zero SoC and C-rate constraint violations, confirming its effectiveness for reliable, constraint-compliant dispatch.

Paperid: 513, https://arxiv.org/pdf/2512.04100.pdf

Abstract:
Accurately mapping the radio environment (e.g., identifying wireless signal strength at specific frequency bands and geographic locations) is crucial for efficient spectrum sharing, enabling Secondary Users~(SUs) to access underutilized spectrum bands while protecting Primary Users~(PUs). While existing models have made progress, they often degrade in performance when multiple transmitters coexist, due to the compounded effects of shadowing, interference from adjacent transmitters. To address this challenge, we extend our prior work on Physics-Informed Neural Networks~(PINNs) for single-transmitter mapping to derive a new multi-transmitter Partial Differential Equation~(PDE) formulation of the Received Signal Strength Indicator~(RSSI). We then propose \emph{ReVeal-MT} (Re-constructor and Visualizer of Spectrum Landscape for Multiple Transmitters), a novel PINN which integrates the multi-source PDE residual into a neural network loss function, enabling accurate spectrum landscape reconstruction from sparse RF sensor measurements. ReVeal-MT is validated using real-world measurements from the ARA wireless living lab across rural and suburban environments, and benchmarked against 3GPP and ITU-R channel models and a baseline PINN model for a single transmitter use-case. Results show that ReVeal-MT achieves substantial accuracy gains in multi-transmitter scenarios, e.g., achieving an RMSE of only 2.66\,dB with as few as 45 samples over a 370-square-kilometer region, while maintaining low computational complexity. These findings demonstrate that ReVeal-MT significantly advances radio environment mapping under realistic multi-transmitter conditions, with strong potential for enabling fine-grained spectrum management and precise coexistence between PUs and SUs.

Paperid: 514, https://arxiv.org/pdf/2511.16494.pdf

Abstract:
Precise pose estimation of optical microrobots is essential for enabling high-precision object tracking and autonomous biological studies. However, current methods rely heavily on large, high-quality microscope image datasets, which are difficult and costly to acquire due to the complexity of microrobot fabrication and the labour-intensive labelling. Digital twin systems offer a promising path for sim-to-real data augmentation, yet existing techniques struggle to replicate complex optical microscopy phenomena, such as diffraction artifacts and depth-dependent imaging.This work proposes a novel physics-informed deep generative learning framework that, for the first time, integrates wave optics-based physical rendering and depth alignment into a generative adversarial network (GAN), to synthesise high-fidelity microscope images for microrobot pose estimation efficiently. Our method improves the structural similarity index (SSIM) by 35.6% compared to purely AI-driven methods, while maintaining real-time rendering speeds (0.022 s/frame).The pose estimator (CNN backbone) trained on our synthetic data achieves 93.9%/91.9% (pitch/roll) accuracy, just 5.0%/5.4% (pitch/roll) below that of an estimator trained exclusively on real data. Furthermore, our framework generalises to unseen poses, enabling data augmentation and robust pose estimation for novel microrobot configurations without additional training data.

Paperid: 515, https://arxiv.org/pdf/2511.14623.pdf

Abstract:
This paper presents a unified and physics-driven framework of alternating phase-field Fourier neural networks (APF-FNNs) for topology optimization. At its core, an alternating architecture decouples the optimization by parameterizing the state, adjoint and topology fields with three distinct Fourier Neural Networks (FNNs). These networks are trained through a collaborative and stable alternating optimization scheme applicable to both self-adjoint and non-self-adjoint systems. The Ginzburg-Landau energy functional is incorporated into the topology network's loss function, acting as an intrinsic regularizer that promotes well-defined designs with smooth and distinct interfaces. By employing physics-informed losses derived from either variational principles or strong-form PDE residuals, the broad applicability of the APF-FNNs is demonstrated across a spectrum of 2D and 3D multi-physics benchmarks, including compliance minimization, eigenvalue maximization, and Stokes/Navier-Stokes flow optimization. The proposed APF-FNNs consistently yield high-performance and high-resolution topologies, establishing a powerful and versatile foundation for physics-driven computational design.

Paperid: 516, https://arxiv.org/pdf/2511.06802.pdf

Abstract:
We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to approximate the nonlinear parametric solutionof the governing equations. This establishes a continuous mapping between the parameter and solution spaces, which can then be evaluated for a given parameter at any spatial resolution. Second, since the neural approximation may not be exact, it is subsequently refined using a Newton-based correction initialized by the neural output. To evaluate the effectiveness of this hybrid approach, we compare three solution strategies: (i) the standard Newton-Raphson solver used in NFEM, which is robust and accurate but computationally demanding; (ii) physics-informed neural operators, which provide rapid inference but may lose accuracy outside the training distribution and resolution; and (iii) the neural-initialized Newton (NiN) strategy, which combines the efficiency of neural operators with the robustness of NFEM. The results demonstrate that the proposed hybrid approach reduces computational cost while preserving accuracy, highlighting its potential to accelerate large-scale nonlinear simulations.

Paperid: 517, https://arxiv.org/pdf/2511.01592.pdf

Abstract:
Energy estimation is critical to impact identification on aerospace composites, where low-velocity impacts can induce internal damage that is undetectable at the surface. Current methodologies for energy prediction are often constrained by data sparsity, signal noise, complex feature interdependencies, non-linear dynamics, massive design spaces, and the ill-posed nature of the inverse problem. This study introduces a physics-informed framework that embeds domain knowledge into machine learning through a dedicated input space. The approach combines observational biases, which guide the design of physics-motivated features, with targeted feature selection to retain only the most informative indicators. Features are extracted from time, frequency, and time-frequency domains to capture complementary aspects of the structural response. A structured feature selection process integrating statistical significance, correlation filtering, dimensionality reduction, and noise robustness ensures physical relevance and interpretability. Exploratory data analysis further reveals domain-specific trends, yielding a reduced feature set that captures essential dynamic phenomena such as amplitude scaling, spectral redistribution, and transient signal behaviour. Together, these steps produce a compact set of energy-sensitive indicators with both statistical robustness and physical significance, resulting in impact energy predictions that remain interpretable and traceable to measurable structural responses. Using this optimised input space, a fully-connected neural network is trained and validated with experimental data from multiple impact scenarios, including pristine and damaged states. The resulting model demonstrates significantly improved impact energy prediction accuracy, reducing errors by a factor of three compared to conventional time-series techniques and purely data-driven models.

Paperid: 518, https://arxiv.org/pdf/2510.25306.pdf

Abstract:
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first principles, due to their inherent complexity, characterized by high-order derivatives and strong nonlinearities, coupled with incomplete physical knowledge. This has spurred the development of data-driven methods, yet these approaches face limitations: Purely data-driven models are often physically inconsistent and data-intensive, while existing physics-informed methods lack the structural capacity to represent complex operators or systematically integrate partial physical knowledge. Here, we propose a hierarchical physics-embedded learning framework that fundamentally advances both the forward spatiotemporal prediction and inverse discovery of physical laws from sparse and noisy data. The key innovation is a two-level architecture that mirrors the process of scientific discovery: the first level learns fundamental symbolic components of a PDE, while the second learns their governing combinations. This hierarchical decomposition not only reduces learning complexity but, more importantly, enables a structural integration of prior knowledge. Known physical laws are directly embedded into the models computational graph, guaranteeing physical consistency and improving data efficiency. By building the framework upon adaptive Fourier Neural Operators, we can effectively capture the non-local dependencies and high-order operators characteristic of dynamical systems. Additionally, by structurally decoupling known and unknown terms, the framework further enables interpretable discovery of underlying governing equations through symbolic regression, without presupposing functional forms.

Paperid: 519, https://arxiv.org/pdf/2510.24026.pdf

Abstract:
The accuracy of Physics-Informed Neural Networks (PINNs) critically depends on the placement of collocation points, as the PDE loss is approximated through sampling over the solution domain. Global sampling ensures stability by covering the entire domain but requires many samples and is computationally expensive, whereas local sampling improves efficiency by focusing on high-residual regions but may neglect well-learned areas, reducing robustness. We propose a Global-Local Fusion (GLF) Sampling Strategy that combines the strengths of both approaches. Specifically, new collocation points are generated by perturbing training points with Gaussian noise scaled inversely to the residual, thereby concentrating samples in difficult regions while preserving exploration. To further reduce computational overhead, a lightweight linear surrogate is introduced to approximate the global residual-based distribution, achieving similar effectiveness at a fraction of the cost. Together, these components, residual-adaptive sampling and residual-based approximation, preserve the stability of global methods while retaining the efficiency of local refinement. Extensive experiments on benchmark PDEs demonstrate that GLF consistently improves both accuracy and efficiency compared with global and local sampling strategies. This study provides a practical and scalable framework for enhancing the reliability and efficiency of PINNs in solving complex and high-dimensional PDEs.

Paperid: 520, https://arxiv.org/pdf/2510.21160.pdf

Abstract:
How to integrate and verify spatial intelligence in foundation models remains an open challenge. Current practice often proxies Visual-Spatial Intelligence (VSI) with purely textual prompts and VQA-style scoring, which obscures geometry, invites linguistic shortcuts, and weakens attribution to genuinely spatial skills. We introduce Spatial Intelligence Grid (SIG): a structured, grid-based schema that explicitly encodes object layouts, inter-object relations, and physically grounded priors. As a complementary channel to text, SIG provides a faithful, compositional representation of scene structure for foundation-model reasoning. Building on SIG, we derive SIG-informed evaluation metrics that quantify a model's intrinsic VSI, which separates spatial capability from language priors. In few-shot in-context learning with state-of-the-art multimodal LLMs (e.g. GPT- and Gemini-family models), SIG yields consistently larger, more stable, and more comprehensive gains across all VSI metrics compared to VQA-only representations, indicating its promise as a data-labeling and training schema for learning VSI. We also release SIGBench, a benchmark of 1.4K driving frames annotated with ground-truth SIG labels and human gaze traces, supporting both grid-based machine VSI tasks and attention-driven, human-like VSI tasks in autonomous-driving scenarios.

Paperid: 521, https://arxiv.org/pdf/2510.19399.pdf

Abstract:
Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs). To overcome this issue, we propose IFeF-PINN, an algorithm for iterative training of PINNs with Fourier-enhanced features. The key idea is to enrich the latent space using high-frequency components through Random Fourier Features. This creates a two-stage training problem: (i) estimate a basis in the feature space, and (ii) perform regression to determine the coefficients of the enhanced basis functions. For an underlying linear model, it is shown that the latter problem is convex, and we prove that the iterative training scheme converges. Furthermore, we empirically establish that Random Fourier Features enhance the expressive capacity of the network, enabling accurate approximation of high-frequency PDEs. Through extensive numerical evaluation on classical benchmark problems, the superior performance of our method over state-of-the-art algorithms is shown, and the improved approximation across the frequency domain is illustrated.

Paperid: 522, https://arxiv.org/pdf/2510.16064.pdf

Abstract:
Solving the nonlinear AC optimal power flow (AC OPF) problem remains a major computational bottleneck for real-time grid operations. In this paper, we propose a residual learning paradigm that uses fast DC optimal power flow (DC OPF) solutions as a baseline, and learns only the nonlinear corrections required to provide the full AC-OPF solution. The method utilizes a topology-aware Graph Neural Network with local attention and two-level DC feature integration, trained using a physics-informed loss that enforces AC power-flow feasibility and operational limits. Evaluations on OPFData for 57-, 118-, and 2000-bus systems show around 25% lower MSE, up to 3X reduction in feasibility error, and up to 13X runtime speedup compared to conventional AC OPF solvers. The model maintains accuracy under N-1 contingencies and scales efficiently to large networks. These results demonstrate that residual learning is a practical and scalable bridge between linear approximations and AC-feasible OPF, enabling near real-time operational decision making.

Paperid: 523, https://arxiv.org/pdf/2510.12332.pdf

Abstract:
This paper presents a shape-aware whole-body control framework for tendon-driven continuum robots with direct application to endoluminal surgical navigation. Endoluminal procedures, such as bronchoscopy, demand precise and safe navigation through tortuous, patient-specific anatomy where conventional tip-only control often leads to wall contact, tissue trauma, or failure to reach distal targets. To address these challenges, our approach combines a physics-informed backbone model with residual learning through an Augmented Neural ODE, enabling accurate shape estimation and efficient Jacobian computation. A sampling-based Model Predictive Path Integral (MPPI) controller leverages this representation to jointly optimize tip tracking, backbone conformance, and obstacle avoidance under actuation constraints. A task manager further enhances adaptability by allowing real-time adjustment of objectives, such as wall clearance or direct advancement, during tele-operation. Extensive simulation studies demonstrate millimeter-level accuracy across diverse scenarios, including trajectory tracking, dynamic obstacle avoidance, and shape-constrained reaching. Real-robot experiments on a bronchoscopy phantom validate the framework, showing improved lumen-following accuracy, reduced wall contacts, and enhanced adaptability compared to joystick-only navigation and existing baselines. These results highlight the potential of the proposed framework to increase safety, reliability, and operator efficiency in minimally invasive endoluminal surgery, with broader applicability to other confined and safety-critical environments.

Paperid: 524, https://arxiv.org/pdf/2510.07160.pdf

Abstract:
Fixed-wing unmanned aerial vehicles (UAVs) offer endurance and efficiency but lack low-speed agility due to highly coupled dynamics. We present an end-to-end sensing-to-control pipeline that combines bio-inspired hardware, physics-informed dynamics learning, and convex control allocation. Measuring airflow on a small airframe is difficult because near-body aerodynamics, propeller slipstream, control-surface actuation, and ambient gusts distort pressure signals. Inspired by the narwhal's protruding tusk, we mount in-house multi-hole probes far upstream and complement them with sparse, carefully placed wing pressure sensors for local flow measurement. A data-driven calibration maps probe pressures to airspeed and flow angles. We then learn a control-affine dynamics model using the estimated airspeed/angles and sparse sensors. A soft left/right symmetry regularizer improves identifiability under partial observability and limits confounding between wing pressures and flaperon inputs. Desired wrenches (forces and moments) are realized by a regularized least-squares allocator that yields smooth, trimmed actuation. Wind-tunnel studies across a wide operating range show that adding wing pressures reduces force-estimation error by 25-30%, the proposed model degrades less under distribution shift (about 12% versus 44% for an unstructured baseline), and force tracking improves with smoother inputs, including a 27% reduction in normal-force RMSE versus a plain affine model and 34% versus an unstructured baseline.

Paperid: 525, https://arxiv.org/pdf/2510.01039.pdf

Abstract:
Physics-informed neural networks (PINNs) and related methods struggle to resolve sharp gradients in singularly perturbed boundary value problems without resorting to some form of domain decomposition, which often introduce complex interface penalties. While the Extreme Theory of Functional Connections (X-TFC) avoids multi-objective optimization by employing exact boundary condition enforcement, it remains computationally inefficient for boundary layers and incompatible with decomposition. We propose Gated X-TFC, a novel framework for both forward and inverse problems, that overcomes these limitations through a soft, learned domain decomposition. Our method replaces hard interfaces with a differentiable logistic gate that dynamically adapts radial basis function (RBF) kernel widths across the domain, eliminating the need for interface penalties. This approach yields not only superior accuracy but also dramatic improvements in computational efficiency: on a benchmark one dimensional (1D) convection-diffusion, Gated X-TFC achieves an order-of-magnitude lower error than standard X-TFC while using 80 percent fewer collocation points and reducing training time by 66 percent. In addition, we introduce an operator-conditioned meta-learning layer that learns a probabilistic mapping from PDE parameters to optimal gate configurations, enabling fast, uncertainty-aware warm-starting for new problem instances. We further demonstrate scalability to multiple subdomains and higher dimensions by solving a twin boundary-layer equation and a 2D Poisson problem with a sharp Gaussian source. Overall, Gated X-TFC delivers a simple alternative alternative to PINNs that is both accurate and computationally efficient for challenging boundar-layer regimes. Future work will focus on nonlinear problems.

Paperid: 526, https://arxiv.org/pdf/2509.26113.pdf

Abstract:
This paper presents intersection of Physics informed neural networks (PINNs) and Lie symmetry group to enhance the accuracy and efficiency of solving partial differential equation (PDEs). Various methods have been developed to solve these equations. A Lie group is an efficient method that can lead to exact solutions for the PDEs that possessing Lie Symmetry. Leveraging the concept of infinitesimal generators from Lie symmetry group in a novel manner within PINN leads to significant improvements in solution of PDEs. In this study three distinct cases are discussed, each showing progressive improvements achieved through Lie symmetry modifications and adaptive techniques. State-of-the-art numerical methods are adopted for comparing the progressive PINN models. Numerical experiments demonstrate the key role of Lie symmetry in enhancing PINNs performance, emphasizing the importance of integrating abstract mathematical concepts into deep learning for addressing complex scientific problems adequately.

Paperid: 527, https://arxiv.org/pdf/2509.26005.pdf

Abstract:
We introduce a formal active learning methodology for guiding the placement of Lagrangian observers to infer time-dependent vector fields -- a key task in oceanography, marine science, and ocean engineering -- using a physics-informed spatio-temporal Gaussian process surrogate model. The majority of existing placement campaigns either follow standard `space-filling' designs or relatively ad-hoc expert opinions. A key challenge to applying principled active learning in this setting is that Lagrangian observers are continuously advected through the vector field, so they make measurements at different locations and times. It is, therefore, important to consider the likely future trajectories of placed observers to account for the utility of candidate placement locations. To this end, we present BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories. We observe noticeable benefits of BALLAST-aided sequential observer placement strategies on both synthetic and high-fidelity ocean current models.

Paperid: 528, https://arxiv.org/pdf/2509.25311.pdf

Abstract:
We implement physics-informed-neural-networks (PINNs) to compute holographic entanglement entropy and entanglement wedge cross section. This technique allows us to compute these quantities for arbitrary shapes of the subregions in any asymptotically AdS metric. We test our computations against some known results and further demonstrate the utility of PINNs in examples, where it is not straightforward to perform such computations.

Paperid: 529, https://arxiv.org/pdf/2509.25262.pdf

Abstract:
This paper presents adaptive weighted Euler-Lagrange theorem combined physics-informed neural networks (AW-EL-PINNs) for solving Euler-Lagrange systems in optimal control problems. The framework systematically converts optimal control frameworks into two-point boundary value problems (TPBVPs) while establishing a multi-task learning paradigm through innovative integration of the Euler-Lagrange theorem with deep learning architecture. An adaptive loss weighting mechanism dynamically balances loss function components during training, decreasing tedious manual tuning of weighting the loss functions compared to the conventional physics-informed neural networks (PINNs). Based on six numerical examples, it's clear that AW-EL-PINNs achieve enhanced solution accuracy compared to baseline methods while maintaining stability throughout the optimization process. These results highlight the framework's capability to improve precision and ensure stability in solving Euler-Lagrange systems in optimal control problems, offering potential strategies for problems under physical applications.

Paperid: 530, https://arxiv.org/pdf/2509.25104.pdf

Abstract:
X-ray ptychography is a data-intensive imaging technique expected to become ubiquitous at next-generation light sources delivering many-fold increases in coherent flux. The need for real-time feedback under accelerated acquisition rates motivates surrogate reconstruction models like deep neural networks, which offer orders-of-magnitude speedup over conventional methods. However, existing deep learning approaches lack robustness across diverse experimental conditions. We propose an unsupervised training workflow emphasizing probe learning by combining experimentally-measured probes with synthetic, procedurally generated objects. This probe-centric approach enables a single physics-informed neural network to reconstruct unseen experiments across multiple beamlines; among the first demonstrations of multi-probe generalization. We find probe learning is equally important as in-distribution learning; models trained using this synthetic workflow achieve reconstruction fidelity comparable to those trained exclusively on experimental data, even when changing the type of synthetic training object. The proposed approach enables training of experiment-steering models that provide real-time feedback under dynamic experimental conditions.

Paperid: 531, https://arxiv.org/pdf/2509.21393.pdf

Abstract:
Physics Informed Neural Networks offer a mesh free framework for solving PDEs but are highly sensitive to loss weight selection. We propose two dimensional analysis based weighting schemes, one based on quantifiable terms, and another also incorporating unquantifiable terms for more balanced training. Benchmarks on heat conduction, convection diffusion, and lid driven cavity flows show that the second scheme consistently improves stability and accuracy over equal weighting. Notably, in high Peclet number convection diffusion, where traditional solvers fail, PINNs with our scheme achieve stable, accurate predictions, highlighting their robustness and generalizability in CFD problems.

Paperid: 532, https://arxiv.org/pdf/2509.15933.pdf

Abstract:
Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited, partly due to the complexity of incorporating partial differential equations (PDEs) for ageing physics and the scarcity of robust uncertainty quantification methods. This work introduces a Bayesian Physics-Informed Neural Network (B-PINN) framework for probabilistic prognostics estimation. By embedding Bayesian Neural Networks into the PINN architecture, the proposed approach produces principled, uncertainty-aware predictions. The method is applied to a transformer ageing case study, where insulation degradation is primarily driven by thermal stress. The heat diffusion PDE is used as the physical residual, and different prior distributions are investigated to examine their impact on predictive posterior distributions and their ability to encode a priori physical knowledge. The framework is validated against a finite element model developed and tested with real measurements from a solar power plant. Results, benchmarked against a dropout-PINN baseline, show that the proposed B-PINN delivers more reliable prognostic predictions by accurately quantifying predictive uncertainty. This capability is crucial for supporting robust and informed maintenance decision-making in critical power assets.

Paperid: 533, https://arxiv.org/pdf/2509.06257.pdf

Abstract:
Rapid and accurate body weight estimation is critical in emergency medical care, as it directly influences treatment decisions, such as drug dosing, defibrillation energy selection, and fluid resuscitation. Traditional methods such as stand-on scales, length-based tapes, or transfer-based weighing scales are often impractical for immobilized patients, inaccurate, or labor-intensive and time-consuming. This paper introduces MelodyBedScale, a non-intrusive and rapid on-bed weight estimation system that leverages bed vibration induced by music. The core insight is that body weight affects the vibration transfer function of the bed-body system, which is captured using vibration sensors placed on opposite sides of the bed. First, we identify weight-sensitive frequency bands and compose clinically acceptable soft, natural music with high signal energy in these frequency bands. This music is then played through a speaker mounted on the bed to induce bed vibrations. Additionally, to efficiently capture the complex weight-vibration relationship with limited data and enhance generalizability to unseen individuals and weights, we theoretically analyze the weight-vibration relationship and integrate the results into the activation functions of the neural network for physics-informed weight regression. We evaluated MelodyBedScale on both wooden and steel beds across 11 participants, achieving a mean absolute error of up to 1.55 kg.

Paperid: 534, https://arxiv.org/pdf/2509.02366.pdf

Abstract:
Battery management systems (BMSs) are critical to ensuring safety, efficiency, and longevity across electronics, transportation, and energy storage. However, with the rapid growth of lithium-ion batteries, conventional reactive BMS approaches face limitations in health prediction and advanced maintenance management, resulting in increased safety risks and economic costs. To address these challenges, we propose a five-tier digital twin framework for intelligent battery management. The framework spans geometric visualization, predictive modeling, prescriptive optimization, and autonomous operation, enabling full lifecycle optimization. In validation, an electrochemical model calibrated via Bayesian optimization achieved strong alignment with measured voltage and temperature, with Mean Absolute Percentage Errors (MAPE) below 1.57\% and 0.39\%. A Physics-Informed Neural Network (PINN) then combined data and simulations to predict State of Health (SOH), attaining MAPE under 3\% with quantified uncertainty. This framework elevates BMSs into intelligent systems capable of proactive management and autonomous optimization, advancing safety and reliability in critical applications.

Paperid: 535, https://arxiv.org/pdf/2508.14093.pdf

Abstract:
Reward machines (RMs) provide a structured way to specify non-Markovian rewards in reinforcement learning (RL), thereby improving both expressiveness and programmability. Viewed more broadly, they separate what is known about the environment, captured by the reward mechanism, from what remains unknown and must be discovered through sampling. This separation supports techniques such as counterfactual experience generation and reward shaping, which reduce sample complexity and speed up learning. We introduce physics-informed reward machines (pRMs), a symbolic machine designed to express complex learning objectives and reward structures for RL agents, thereby enabling more programmable, expressive, and efficient learning. We present RL algorithms capable of exploiting pRMs via counterfactual experiences and reward shaping. Our experimental results show that these techniques accelerate reward acquisition during the training phases of RL. We demonstrate the expressiveness and effectiveness of pRMs through experiments in both finite and continuous physical environments, illustrating that incorporating pRMs significantly improves learning efficiency across several control tasks.

Paperid: 536, https://arxiv.org/pdf/2508.11216.pdf

Abstract:
Blood flow imaging provides important information for hemodynamic behavior within the vascular system and plays an essential role in medical diagnosis and treatment planning. However, obtaining high-quality flow images remains a significant challenge. In this work, we address the problem of denoising flow images that may suffer from artifacts due to short acquisition times or device-induced errors. We formulate this task as an optimization problem, where the objective is to minimize the discrepancy between the modeled velocity field, constrained to satisfy the Navier-Stokes equations, and the observed noisy velocity data. To solve this problem, we decompose it into two subproblems: a fluid subproblem and a geometry subproblem. The fluid subproblem leverages a Physics-Informed Neural Network to reconstruct the velocity field from noisy observations, assuming a fixed domain. The geometry subproblem aims to infer the underlying flow region by optimizing a quasi-conformal mapping that deforms a reference domain. These two subproblems are solved in an alternating Gauss-Seidel fashion, iteratively refining both the velocity field and the domain. Upon convergence, the framework yields a high-quality reconstruction of the flow image. We validate the proposed method through experiments on synthetic flow data in a converging channel geometry under varying levels of Gaussian noise, and on real-like flow data in an aortic geometry with signal-dependent noise. The results demonstrate the effectiveness and robustness of the approach. Additionally, ablation studies are conducted to assess the influence of key hyperparameters.

Paperid: 537, https://arxiv.org/pdf/2507.19519.pdf

Abstract:
Data used for training structural health monitoring (SHM) systems are expensive and often impractical to obtain, particularly labelled data. Population-based SHM presents a potential solution to this issue by considering the available data across a population of structures. However, differences between structures will mean the training and testing distributions will differ; thus, conventional machine learning methods cannot be expected to generalise between structures. To address this issue, transfer learning (TL), can be used to leverage information across related domains. An important consideration is that the lack of labels in the target domain limits data-based metrics to quantifying the discrepancy between the marginal distributions. Thus, a prerequisite for the application of typical unsupervised TL methods is to identify suitable source structures (domains), and a set of features, for which the conditional distributions are related to the target structure. Generally, the selection of domains and features is reliant on domain expertise; however, for complex mechanisms, such as the influence of damage on the dynamic response of a structure, this task is not trivial. In this paper, knowledge of physics is leveraged to select more similar features, the modal assurance criterion (MAC) is used to quantify the correspondence between the modes of healthy structures. The MAC is shown to have high correspondence with a supervised metric that measures joint-distribution similarity, which is the primary indicator of whether a classifier will generalise between domains. The MAC is proposed as a measure for selecting a set of features that behave consistently across domains when subjected to damage, i.e. features with invariance in the conditional distributions. This approach is demonstrated on numerical and experimental case studies to verify its effectiveness in various applications.

Paperid: 538, https://arxiv.org/pdf/2506.17582.pdf

Abstract:
Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across parameter spaces. However, existing methods either suffer from limited expressiveness due to fixed basis/coefficient designs, or face computational challenges due to the high dimensionality of the parameter-to-weight mapping space. We present LFR-PINO, a novel physics-informed neural operator that introduces two key innovations: (1) a layered hypernetwork architecture that enables specialized parameter generation for each network layer, and (2) a frequency-domain reduction strategy that significantly reduces parameter count while preserving essential spectral features. This design enables efficient learning of a universal PDE solver through pre-training, capable of directly handling new equations while allowing optional fine-tuning for enhanced precision. The effectiveness of this approach is demonstrated through comprehensive experiments on four representative PDE problems, where LFR-PINO achieves 22.8%-68.7% error reduction compared to state-of-the-art baselines. Notably, frequency-domain reduction strategy reduces memory usage by 28.6%-69.3% compared to Hyper-PINNs while maintaining solution accuracy, striking an optimal balance between computational efficiency and solution fidelity.

Paperid: 539, https://arxiv.org/pdf/2506.15687.pdf

Abstract:
We propose S$^2$GPT-PINN, a sparse and small model for solving parametric partial differential equations (PDEs). Similar to Small Language Models (SLMs), S$^2$GPT-PINN is tailored to domain-specific (families of) PDEs and characterized by its compact architecture and minimal computational power. Leveraging a small amount of extremely high quality data via a mathematically rigorous greedy algorithm that is enabled by the large full-order models, S$^2$GPT-PINN relies on orders of magnitude less parameters than PINNs to achieve extremely high efficiency via two levels of customizations. The first is knowledge distillation via task-specific activation functions that are transferred from Pre-Trained PINNs. The second is a judicious down-sampling when calculating the physics-informed loss of the network compressing the number of data sites by orders of magnitude to the size of the small model.

Paperid: 540, https://arxiv.org/pdf/2506.11973.pdf

Abstract:
Free-flow road networks, such as suburban highways, are increasingly experiencing traffic congestion due to growing commuter inflow and limited infrastructure. Traditional control mechanisms, such as traffic signals or local heuristics, are ineffective or infeasible in these high-speed, signal-free environments. We introduce self-regulating cars, a reinforcement learning-based traffic control protocol that dynamically modulates vehicle speeds to optimize throughput and prevent congestion, without requiring new physical infrastructure. Our approach integrates classical traffic flow theory, gap acceptance models, and microscopic simulation into a physics-informed RL framework. By abstracting roads into super-segments, the agent captures emergent flow dynamics and learns robust speed modulation policies from instantaneous traffic observations. Evaluated in the high-fidelity PTV Vissim simulator on a real-world highway network, our method improves total throughput by 5%, reduces average delay by 13%, and decreases total stops by 3% compared to the no-control setting. It also achieves smoother, congestion-resistant flow while generalizing across varied traffic patterns, demonstrating its potential for scalable, ML-driven traffic management.

Paperid: 541, https://arxiv.org/pdf/2506.10243.pdf

Abstract:
In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide range of equations, they often exhibit suboptimal performance when applied to equations with large local gradients, resulting in substantial localized errors. To address this issue, this paper proposes an adaptive PINN algorithm designed to improve accuracy in such cases. The core idea of the algorithm is to adaptively adjust the distribution of collocation points based on the recovery-type a-posterior error of the current numerical solution, enabling a better approximation of the true solution. This approach is inspired by the adaptive finite element method. By combining the recovery-type a-posteriori estimator, a gradient-recovery estimator commonly used in the adaptive finite element method (FEM) with PINNs, we introduce the Recovery-type a-posteriori estimator enhanced adaptive PINN (R-PINN) and compare its performance with a typical adaptive PINN algorithm, FI-PINN. Our results demonstrate that R-PINN achieves faster convergence with fewer adaptive points and significantly outperforms in the cases with multiple regions of large errors than FI-PINN. Notably, our method is a hybrid numerical approach for solving partial differential equations, integrating adaptive FEM with PINNs.

Paperid: 542, https://arxiv.org/pdf/2506.09891.pdf

Abstract:
Traditional models of climate change use complex systems of coupled equations to simulate physical processes across the Earth system. These simulations are highly computationally expensive, limiting our predictions of climate change and analyses of its causes and effects. Machine learning has the potential to quickly emulate data from climate models, but current approaches are not able to incorporate physics-informed causal relationships. Here, we develop an interpretable climate model emulator based on causal representation learning. We derive a physics-informed approach including a Bayesian filter for stable long-term autoregressive emulation. We demonstrate that our emulator learns accurate climate dynamics, and we show the importance of each one of its components on a realistic synthetic dataset and data from two widely deployed climate models.

Paperid: 543, https://arxiv.org/pdf/2506.02489.pdf

Abstract:
We propose a new approach to vision-based dexterous grasp translation, which aims to transfer grasp intent across robotic hands with differing morphologies. Given a visual observation of a source hand grasping an object, our goal is to synthesize a functionally equivalent grasp for a target hand without requiring paired demonstrations or hand-specific simulations. We frame this problem as a stochastic transport between grasp distributions using the SchrÃ¶dinger Bridge formalism. Our method learns to map between source and target latent grasp spaces via score and flow matching, conditioned on visual observations. To guide this translation, we introduce physics-informed cost functions that encode alignment in base pose, contact maps, wrench space, and manipulability. Experiments across diverse hand-object pairs demonstrate our approach generates stable, physically grounded grasps with strong generalization. This work enables semantic grasp transfer for heterogeneous manipulators and bridges vision-based grasping with probabilistic generative modeling.

Paperid: 544, https://arxiv.org/pdf/2505.21404.pdf

Abstract:
Natural-gradient methods markedly accelerate the training of Physics-Informed Neural Networks (PINNs), yet their Gauss--Newton update must be solved in the parameter space, incurring a prohibitive $O(n^3)$ time complexity, where $n$ is the number of network trainable weights. We show that exactly the same step can instead be formulated in a generally smaller residual space of size $m = \sum_Î³ N_Î³ d_Î³$, where each residual class $Î³$ (e.g. PDE interior, boundary, initial data) contributes $N_Î³$ collocation points of output dimension $d_Î³$. Building on this insight, we introduce \textit{Dual Natural Gradient Descent} (D-NGD). D-NGD computes the Gauss--Newton step in residual space, augments it with a geodesic-acceleration correction at negligible extra cost, and provides both a dense direct solver for modest $m$ and a Nystrom-preconditioned conjugate-gradient solver for larger $m$. Experimentally, D-NGD scales second-order PINN optimization to networks with up to 12.8 million parameters, delivers one- to three-order-of-magnitude lower final error $L^2$ than first-order methods (Adam, SGD) and quasi-Newton methods, and -- crucially -- enables natural-gradient training of PINNs at this scale on a single GPU.

Paperid: 545, https://arxiv.org/pdf/2505.19414.pdf

Abstract:
Data centers are the backbone of computing capacity. Operating data centers in the tropical regions faces unique challenges due to consistently high ambient temperature and elevated relative humidity throughout the year. These conditions result in increased cooling costs to maintain the reliability of the computing systems. While existing machine learning-based approaches have demonstrated potential to elevate operations to a more proactive and intelligent level, their deployment remains dubious due to concerns about model extrapolation capabilities and associated system safety issues. To address these concerns, this article proposes incorporating the physical characteristics of data centers into traditional data-driven machine learning solutions. We begin by introducing the data center system, including the relevant multiphysics processes and the data-physics availability. Next, we outline the associated modeling and optimization problems and propose an integrated, physics-informed machine learning system to address them. Using the proposed system, we present relevant applications across varying levels of operational intelligence. A case study on an industry-grade tropical data center is provided to demonstrate the effectiveness of our approach. Finally, we discuss key challenges and highlight potential future directions.

Paperid: 546, https://arxiv.org/pdf/2505.03382.pdf

Abstract:
Active stress models in cardiac biomechanics account for the mechanical deformation caused by muscle activity, thus providing a link between the electrophysiological and mechanical properties of the tissue. The accurate assessment of active stress parameters is fundamental for a precise understanding of myocardial function but remains difficult to achieve in a clinical setting, especially when only displacement and strain data from medical imaging modalities are available. This work investigates, through an in-silico study, the application of physics-informed neural networks (PINNs) for inferring active contractility parameters in time-dependent cardiac biomechanical models from these types of imaging data. In particular, by parametrising the sought state and parameter field with two neural networks, respectively, and formulating an energy minimisation problem to search for the optimal network parameters, we are able to reconstruct in various settings active stress fields in the presence of noise and with a high spatial resolution. To this end, we also advance the vanilla PINN learning algorithm with the use of adaptive weighting schemes, ad-hoc regularisation strategies, Fourier features, and suitable network architectures. In addition, we thoroughly analyse the influence of the loss weights in the reconstruction of active stress parameters. Finally, we apply the method to the characterisation of tissue inhomogeneities and detection of fibrotic scars in myocardial tissue. This approach opens a new pathway to significantly improve the diagnosis, treatment planning, and management of heart conditions associated with cardiac fibrosis.

Paperid: 547, https://arxiv.org/pdf/2504.19564.pdf

Abstract:
Digital twin (DT) techniques have been proposed for the autonomous operation and lifecycle management of next-generation optical networks. To fully utilize potential capacity and accommodate dynamic services, the DT must dynamically update in sync with deployed optical networks throughout their lifecycle, ensuring low-margin operation. This paper proposes a dynamic-updating DT for the lifecycle management of optical networks, employing a hybrid approach that integrates data-driven and physics-informed techniques for fiber channel modeling. This integration ensures both rapid calculation speed and high physics consistency in optical performance prediction while enabling the dynamic updating of critical physical parameters for DT. The lifecycle management of optical networks, covering accurate performance prediction at the network deployment and dynamic updating during network operation, is demonstrated through simulation in a large-scale network. Up to 100 times speedup in prediction is observed compared to classical numerical methods. In addition, the fiber Raman gain strength, amplifier frequency-dependent gain profile, and connector loss between fiber and amplifier on C and L bands can be simultaneously updated. Moreover, the dynamic-updating DT is verified on a field-trial C+L-band transmission link, achieving a maximum accuracy improvement of 1.4 dB for performance estimation post-device replacement. Overall, the dynamic-updating DT holds promise for driving the next-generation optical networks towards lifecycle autonomous management.

Paperid: 548, https://arxiv.org/pdf/2504.12159.pdf

Abstract:
Deep Material Network (DMN) has emerged as a powerful framework for multiscale material modeling, enabling efficient and accurate predictions of material behavior across different length scales. Unlike traditional machine learning approaches, the trainable parameters in DMN have direct physical interpretations, capturing the geometric characteristics of the microstructure rather than serving as purely statistical fitting parameters. Its hierarchical tree structure effectively encodes microstructural interactions and deformation mechanisms, allowing DMN to achieve a balance between accuracy and computational efficiency. This physics-informed architecture significantly reduces computational costs compared to direct numerical simulations while preserving essential microstructural physics. Furthermore, DMN can be trained solely on a linear elastic dataset while effectively extrapolating nonlinear responses during online prediction, making it a highly efficient and scalable approach for multiscale material modeling. This article provides a comprehensive review of DMN, detailing its motivation, underlying methodology, and recent advancements. We discuss key modeling aspects, including its hierarchical structure, training process, and the role of physics-based constraints in enhancing predictive accuracy. Furthermore, we highlight its applications in component-scale multiscale analysis and inverse parameter identification, demonstrating its capability to bridge microscale material behavior with macroscale engineering predictions. Finally, we discuss challenges and future directions in improving DMN's generalization capabilities and its potential extensions for broader applications in multiscale modeling.

Paperid: 549, https://arxiv.org/pdf/2504.11896.pdf

Abstract:
Image decomposition offers deep insights into the imaging factors of visual data and significantly enhances various advanced computer vision tasks. In this work, we introduce a novel approach to low-light image enhancement based on decomposed physics-informed priors. Existing methods that directly map low-light to normal-light images in the sRGB color space suffer from inconsistent color predictions and high sensitivity to spectral power distribution (SPD) variations, resulting in unstable performance under diverse lighting conditions. To address these challenges, we introduce a Physics-informed Color-aware Transform (PiCat), a learning-based framework that converts low-light images from the sRGB color space into deep illumination-invariant descriptors via our proposed Color-aware Transform (CAT). This transformation enables robust handling of complex lighting and SPD variations. Complementing this, we propose the Content-Noise Decomposition Network (CNDN), which refines the descriptor distributions to better align with well-lit conditions by mitigating noise and other distortions, thereby effectively restoring content representations to low-light images. The CAT and the CNDN collectively act as a physical prior, guiding the transformation process from low-light to normal-light domains. Our proposed PiCat framework demonstrates superior performance compared to state-of-the-art methods across five benchmark datasets.

Paperid: 550, https://arxiv.org/pdf/2504.07481.pdf

Abstract:
Land surface temperature (LST) retrieval from remote sensing data is pivotal for analyzing climate processes and surface energy budgets. However, LST retrieval is an ill-posed inverse problem, which becomes particularly severe when only a single band is available. In this paper, we propose a deeply coupled framework integrating mechanistic modeling and machine learning to enhance the accuracy and generalizability of single-channel LST retrieval. Training samples are generated using a physically-based radiative transfer model and a global collection of 5810 atmospheric profiles. A physics-informed machine learning framework is proposed to systematically incorporate the first principles from classical physical inversion models into the learning workflow, with optimization constrained by radiative transfer equations. Global validation demonstrated a 30% reduction in root-mean-square error versus standalone methods. Under extreme humidity, the mean absolute error decreased from 4.87 K to 2.29 K (53% improvement). Continental-scale tests across five continents confirmed the superior generalizability of this model.

Paperid: 551, https://arxiv.org/pdf/2504.03483.pdf

Abstract:
Recent works on the application of Physics-Informed Neural Networks to traffic density estimation have shown to be promising for future developments due to their robustness to model errors and noisy data. In this paper, we introduce a methodology for online approximation of the traffic density using measurements from probe vehicles in two settings: one using the Greenshield model and the other considering a high-fidelity traffic simulation. The proposed method continuously estimates the real-time traffic density in space and performs model identification with each new set of measurements. The density estimate is updated in almost real-time using gradient descent and adaptive weights. In the case of full model knowledge, the resulting algorithm has similar performance to the classical open-loop one. However, in the case of model mismatch, the iterative solution behaves as a closed-loop observer and outperforms the baseline method. Similarly, in the high-fidelity setting, the proposed algorithm correctly reproduces the traffic characteristics.

Paperid: 552, https://arxiv.org/pdf/2504.02459.pdf

Abstract:
In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to establish the mapping between continuous parameter and solution spaces. The decoder constructs the parametric solution field by leveraging an implicit neural field network conditioned on a latent or feature code. Instance-specific codes are derived through a PDE encoding process based on the second-order meta-learning technique. In training and inference, a physics-informed loss function is minimized during the PDE encoding and decoding. iFOL expresses the loss function in an energy or weighted residual form and evaluates it using discrete residuals derived from standard numerical PDE methods. This approach results in the backpropagation of discrete residuals during both training and inference. iFOL features several key properties: (1) its unique loss formulation eliminates the need for the conventional encode-process-decode pipeline previously used in operator learning with conditional neural fields for PDEs; (2) it not only provides accurate parametric and continuous fields but also delivers solution-to-parameter gradients without requiring additional loss terms or sensitivity analysis; (3) it can effectively capture sharp discontinuities in the solution; and (4) it removes constraints on the geometry and mesh, making it applicable to arbitrary geometries and spatial sampling (zero-shot super-resolution capability). We critically assess these features and analyze the network's ability to generalize to unseen samples across both stationary and transient PDEs. The overall performance of the proposed method is promising, demonstrating its applicability to a range of challenging problems in computational mechanics.

Paperid: 553, https://arxiv.org/pdf/2503.06347.pdf

Abstract:
This paper presents two novel, physics-informed extreme learning machine (PIELM)-based algorithms for solving steady and unsteady nonlinear partial differential equations (PDEs) related to fluid flow. Although single-hidden-layer PIELMs outperform deep physics-informed neural networks (PINNs) in speed and accuracy for linear and quasilinear PDEs, their extension to nonlinear problems remains challenging. To address this, we introduce a curriculum learning strategy that reformulates nonlinear PDEs as a sequence of increasingly complex quasilinear PDEs. Additionally, our approach enables a physically interpretable initialization of network parameters by leveraging Radial Basis Functions (RBFs). The performance of the proposed algorithms is validated on two benchmark incompressible flow problems: the viscous Burgers equation and lid-driven cavity flow. To the best of our knowledge, this is the first work to extend PIELM to solving Burgers' shock solution as well as lid-driven cavity flow up to a Reynolds number of 100. As a practical application, we employ PIELM to predict blood flow in a stenotic vessel. The results confirm that PIELM efficiently handles nonlinear PDEs, positioning it as a promising alternative to PINNs for both linear and nonlinear PDEs.

Paperid: 554, https://arxiv.org/pdf/2503.04123.pdf

Abstract:
We propose GAGrasp, a novel framework for dexterous grasp generation that leverages geometric algebra representations to enforce equivariance to SE(3) transformations. By encoding the SE(3) symmetry constraint directly into the architecture, our method improves data and parameter efficiency while enabling robust grasp generation across diverse object poses. Additionally, we incorporate a differentiable physics-informed refinement layer, which ensures that generated grasps are physically plausible and stable. Extensive experiments demonstrate the model's superior performance in generalization, stability, and adaptability compared to existing methods. Additional details at https://gagrasp.github.io/

Paperid: 555, https://arxiv.org/pdf/2502.16444.pdf

Abstract:
Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations as inputs (called "data integration") or variational DA has shown success in improving forecasts. However, it is unclear which methods are performant or optimal for physics-informed machine learning ("differentiable") models, which represent only a small amount of physically-meaningful states while using deep networks to supply parameters or missing processes. Here we developed variational DA methods for differentiable models, including optimizing adjusters for just precipitation data, just model internal hydrological states, or both. Our results demonstrated that differentiable streamflow models using the CAMELS dataset can benefit strongly and equivalently from variational DA as LSTM, with one-day lead time median Nash-Sutcliffe efficiency (NSE) elevated from 0.75 to 0.82. The resulting forecast matched or outperformed LSTM with DA in the eastern, northwestern, and central Great Plains regions of the conterminous United States. Both precipitation and state adjusters were needed to achieve these results, with the latter being substantially more effective on its own, and the former adding moderate benefits for high flows. Our DA framework does not need systematic training data and could serve as a practical DA scheme for whole river networks.

Paperid: 556, https://arxiv.org/pdf/2502.12093.pdf

Abstract:
Weight change estimation is crucial in various applications, particularly for detecting pick-up and put-back actions when people interact with the shelf while shopping in autonomous stores. Moreover, accurate weight change estimation allows autonomous stores to automatically identify items being picked up or put back, ensuring precise cost estimation. However, the conventional approach of estimating weight changes requires specialized weight-sensing shelves, which are densely deployed weight scales, incurring intensive sensor consumption and high costs. Prior works explored the vibration-based weight sensing method, but they failed when the location of weight change varies. In response to these limitations, we made the following contributions: (1) We propose WeVibe, a first item weight change estimation system through active shelf vibration sensing. The main intuition of the system is that the weight placed on the shelf influences the dynamic vibration response of the shelf, thus altering the shelf vibration patterns. (2) We model a physics-informed relationship between the shelf vibration response and item weight across multiple locations on the shelf based on structural dynamics theory. This relationship is linear and allows easy training of a weight estimation model at a new location without heavy data collection. (3) We evaluate our system on a gondola shelf organized as the real-store settings. WeVibe achieved a mean absolute error down to 38.07g and a standard deviation of 31.2g with one sensor and 10% samples from three weight classes on estimating weight change from 0g to 450g, which can be leveraged for differentiating items with more than 100g differences.

Paperid: 557, https://arxiv.org/pdf/2502.11504.pdf

Abstract:
Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive simulations, such as finite element analysis, and the complexity of rigorous optimization algorithms. Data-agnostic AI-based surrogate models, such as Physics-Informed Neural Operators (PINOs), offer a promising alternative to these conventional simulations, providing drastically reduced inference time, unparalleled data efficiency, and zero-shot super-resolution capability. However, the predictive accuracy of these models is often constrained to small, low-dimensional design spaces or systems with relatively simple dynamics. To address this, we introduce a novel Physics-Informed DeepONet (PIDON) architecture, which extends the capabilities of conventional neural operators to effectively model the nonlinear behavior of complex engineering systems across high-dimensional design spaces and a wide range of dynamic design configurations. This new architecture outperforms existing SOTA models, enabling better predictions across broader design spaces. Leveraging PIDON's differentiability, we integrate a gradient-based optimization approach using the Adam optimizer to efficiently determine optimal design variables. This forms an end-to-end gradient-based optimization framework that accelerates the design process while enhancing scalability and efficiency. We demonstrate the effectiveness of this framework in the optimization of aerospace-grade composites curing processes achieving a 3x speedup in obtaining optimal design variables compared to gradient-free methods. Beyond composites processing, the proposed model has the potential to be used as a scalable and efficient optimization tool for broader applications in advanced engineering and digital twin systems.

Paperid: 558, https://arxiv.org/pdf/2502.04917.pdf

Abstract:
We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optimizing the activation parameters, compleX-PINN achieves high accuracy with just a single hidden layer. Empirically, we demonstrate that compleX-PINN solves high-dimensional problems that pose significant challenges for PINNs. Our results show that compleX-PINN consistently achieves substantially greater precision, often improving accuracy by an order of magnitude, on these complex tasks.

Paperid: 559, https://arxiv.org/pdf/2501.18258.pdf

Abstract:
Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce and the dimensionality is high. Although GPs are known for their robust uncertainty quantification in low-dimensional settings, their computational complexity becomes prohibitive as the dimensionality increases. In contrast, while conventional NNs can accommodate high-dimensional input, they often require extensive training data and do not offer uncertainty quantification. To address these challenges, we propose a PDE-constrained Deep Kernel Learning (PDE-DKL) framework that combines DL and GPs under explicit PDE constraints. Specifically, NNs learn a low-dimensional latent representation of the high-dimensional PDE problem, reducing the complexity of the problem. GPs then perform kernel regression subject to the governing PDEs, ensuring accurate solutions and principled uncertainty quantification, even when available data are limited. This synergy unifies the strengths of both NNs and GPs, yielding high accuracy, robust uncertainty estimates, and computational efficiency for high-dimensional PDEs. Numerical experiments demonstrate that PDE-DKL achieves high accuracy with reduced data requirements. They highlight its potential as a practical, reliable, and scalable solver for complex PDE-based applications in science and engineering.

Paperid: 560, https://arxiv.org/pdf/2501.11655.pdf

Abstract:
This paper proposes a novel learning approach for designing Kazantzis-Kravaris/Luenberger (KKL) observers for autonomous nonlinear systems. The design of a KKL observer involves finding an injective map that transforms the system state into a higher-dimensional observer state, whose dynamics is linear and stable. The observer's state is then mapped back to the original system coordinates via the inverse map to obtain the state estimate. However, finding this transformation and its inverse is quite challenging. We propose to sequentially approximate these maps by neural networks that are trained using physics-informed learning. We generate synthetic data for training by numerically solving the system and observer dynamics. Theoretical guarantees for the robustness of state estimation against approximation error and system uncertainties are provided. Additionally, a systematic method for optimizing observer performance through parameter selection is presented. The effectiveness of the proposed approach is demonstrated through numerical simulations on benchmark examples and its application to sensor fault detection and isolation in a network of Kuramoto oscillators using learned KKL observers.

Paperid: 561, https://arxiv.org/pdf/2501.09298.pdf

Abstract:
Accurate forecasting of contagious diseases is critical for public health policymaking and pandemic preparedness. We propose a new infectious disease forecasting model based on physics-informed neural networks (PINNs), an emerging scientific machine learning approach. By embedding a compartmental model into the loss function, our method integrates epidemiological theory with data, helping to prevent model overfitting. We further enhance the model with a sub-network that accounts for covariates such as mobility and cumulative vaccine doses, which influence the transmission rate. Using state-level COVID-19 data from California, we demonstrate that the PINN model accurately predicts cases, deaths, and hospitalizations, aligning well with existing benchmarks. Notably, the PINN model outperforms naive baseline forecasts and several sequence deep learning models, including Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRUs), and Transformers. It also achieves performance comparable to a sophisticated Gaussian infection state forecasting model that combines compartmental dynamics, a data observation model, and parameter regression. However, the PINN model features a simpler structure and is easier to implement. In summary, we systematically evaluate the PINN model's ability to forecast infectious disease dynamics, demonstrating its potential as an efficient computational tool to strengthen forecasting capabilities.

Paperid: 562, https://arxiv.org/pdf/2411.06781.pdf

Abstract:
Forecasting temporal processes such as virus spreading in epidemics often requires more than just observed time-series data, especially at the beginning of a wave when data is limited. Traditional methods employ mechanistic models like the SIR family, which make strong assumptions about the underlying spreading process, often represented as a small set of compact differential equations. Data-driven methods such as deep neural networks make no such assumptions and can capture the generative process in more detail, but fail in long-term forecasting due to data limitations. We propose a new hybrid method called MP-PINN (Multi-Phase Physics-Informed Neural Network) to overcome the limitations of these two major approaches. MP-PINN instils the spreading mechanism into a neural network, enabling the mechanism to update in phases over time, reflecting the dynamics of the epidemics due to policy interventions. Experiments on COVID-19 waves demonstrate that MP-PINN achieves superior performance over pure data-driven or model-driven approaches for both short-term and long-term forecasting.

Paperid: 563, https://arxiv.org/pdf/2411.00143.pdf

Abstract:
Reconstructing brain sources is a fundamental challenge in neuroscience, crucial for understanding brain function and dysfunction. Electroencephalography (EEG) signals have a high temporal resolution. However, identifying the correct spatial location of brain sources from these signals remains difficult due to the ill-posed structure of the problem. Traditional methods predominantly rely on manually crafted priors, missing the flexibility of data-driven learning, while recent deep learning approaches focus on end-to-end learning, typically using the physical information of the forward model only for generating training data. We propose the novel hybrid method 3D-PIUNet for EEG source localization that effectively integrates the strengths of traditional and deep learning techniques. 3D-PIUNet starts from an initial physics-informed estimate by using the pseudo inverse to map from measurements to source space. Secondly, by viewing the brain as a 3D volume, we use a 3D convolutional U-Net to capture spatial dependencies and refine the solution according to the learned data prior. Training the model relies on simulated pseudo-realistic brain source data, covering different source distributions. Trained on this data, our model significantly improves spatial accuracy, demonstrating superior performance over both traditional and end-to-end data-driven methods. Additionally, we validate our findings with real EEG data from a visual task, where 3D-PIUNet successfully identifies the visual cortex and reconstructs the expected temporal behavior, thereby showcasing its practical applicability.

Paperid: 564, https://arxiv.org/pdf/2410.18553.pdf

Abstract:
The Matrix-Element Method (MEM) has long been a cornerstone of data analysis in high-energy physics. It leverages theoretical knowledge of parton-level processes and symmetries to evaluate the likelihood of observed events. In parallel, the advent of geometric deep learning has enabled neural network architectures that incorporate known symmetries directly into their design, leading to more efficient learning. This paper presents a novel approach that combines MEM-inspired symmetry considerations with equivariant neural network design for particle physics analysis. Even though Lorentz invariance and permutation invariance overall reconstructed objects are the largest and most natural symmetry in the input domain, we find that they are sub-optimal in most practical search scenarios. We propose a longitudinal boost-equivariant message-passing neural network architecture that preserves relevant discrete symmetries. We present numerical studies demonstrating MEM-inspired architectures achieve new state-of-the-art performance in distinguishing di-Higgs decays to four bottom quarks from the QCD background, with enhanced sample and parameter efficiencies. This synergy between MEM and equivariant deep learning opens new directions for physics-informed architecture design, promising more powerful tools for probing physics beyond the Standard Model.

Paperid: 565, https://arxiv.org/pdf/2410.15250.pdf

Abstract:
Control in fluid environments is an important research area with numerous applications across various domains, including underwater robotics, aerospace engineering, and biomedical systems. However, in practice, control methods often face challenges due to sparse or missing observations, stemming from sensor limitations and faults. These issues result in observations that are not only sparse but also inconsistent in their number and modalities (e.g., velocity and pressure sensors). In this work, we propose a Physics-Informed Representation (PIR) algorithm for multi-modal policies of control to leverage the sparse and random observations in complex fluid environments. PIR integrates sparse observational data with the Partial Differential Equation (PDE) information to distill a unified representation of fluid systems. The main idea is that PDE solutions are determined by three elements: the equation, initial conditions, and boundary conditions. Given the equation, we only need to learn the representation of the initial and boundary conditions, which define a trajectory of a specific fluid system. Specifically, it leverages PDE loss to fit the neural network and data loss calculated on the observations with random quantities and multi-modalities to propagate the information with initial and boundary conditions into the representations. The representations are the learnable parameters or the output of the encoder. In the experiments, the PIR illustrates the superior consistency with the features of the ground truth compared with baselines, even when there are missing modalities. Furthermore, PIR combined with Reinforcement Learning has been successfully applied in control tasks where the robot leverages the learned state by PIR faster and more accurately, passing through the complex vortex street from a random starting location to reach a random target.

Paperid: 566, https://arxiv.org/pdf/2410.04743.pdf

Abstract:
Integrated energy systems (IESs) are complex systems consisting of diverse operating units spanning multiple domains. To address its operational challenges, we propose a physics-informed hybrid time-series neural network (NN) surrogate to predict the dynamic performance of IESs across multiple time scales. This neural network-based modeling approach develops time-series multi-layer perceptrons (MLPs) for the operating units and integrates them with prior process knowledge about system structure and fundamental dynamics. This integration forms three hybrid NNs (long-term, slow, and fast MLPs) that predict the entire system dynamics across multiple time scales. Leveraging these MLPs, we design an NN-based scheduler and an NN-based economic model predictive control (NEMPC) framework to meet global operational requirements: rapid electrical power responsiveness to operators requests, adequate cooling supply to customers, and increased system profitability, while addressing the dynamic time-scale multiplicity present in IESs. The proposed day-ahead scheduler is formulated using the ReLU network-based MLP, which effectively represents IES performance under a broad range of conditions from a long-term perspective. The scheduler is then exactly recast into a mixed-integer linear programming problem for efficient evaluation. The real-time NEMPC, based on slow and fast MLPs, comprises two sequential distributed control agents: a slow NEMPC for the cooling-dominant subsystem with slower transient responses and a fast NEMPC for the power-dominant subsystem with faster responses. Extensive simulations demonstrate that the developed scheduler and NEMPC schemes outperform their respective benchmark scheduler and controller by about 25% and 40%. Together, they enhance overall system performance by over 70% compared to benchmark approaches.

Paperid: 567, https://arxiv.org/pdf/2409.19221.pdf

Abstract:
We have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex analysis and is specifically tailored for problems requiring high precision. This innovation has led to the creation of a new class of neural networks, which we call (Comple)XNet, or simply XNet. We will demonstrate that XNet is particularly effective for high-dimensional challenges such as image classification and solving Partial Differential Equations (PDEs). Our evaluations show that XNet significantly outperforms established benchmarks like MNIST and CIFAR-10 in computer vision, and offers substantial advantages over Physics-Informed Neural Networks (PINNs) in both low-dimensional and high-dimensional PDE scenarios.

Paperid: 568, https://arxiv.org/pdf/2409.18426.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their remarkable empirical performance in various scientific computing tasks, PINNs often fail to generate reasonable solutions, and such pathological behaviors remain difficult to explain and resolve. In this paper, we identify that PINNs can be adversely trained when gradients of each loss function exhibit a significant imbalance in their magnitudes and present a negative inner product value. To address these issues, we propose a novel optimization framework, Dual Cone Gradient Descent (DCGD), which adjusts the direction of the updated gradient to ensure it falls within a dual cone region. This region is defined as a set of vectors where the inner products with both the gradients of the PDE residual loss and the boundary loss are non-negative. Theoretically, we analyze the convergence properties of DCGD algorithms in a non-convex setting. On a variety of benchmark equations, we demonstrate that DCGD outperforms other optimization algorithms in terms of various evaluation metrics. In particular, DCGD achieves superior predictive accuracy and enhances the stability of training for failure modes of PINNs and complex PDEs, compared to existing optimally tuned models. Moreover, DCGD can be further improved by combining it with popular strategies for PINNs, including learning rate annealing and the Neural Tangent Kernel (NTK).

Paperid: 569, https://arxiv.org/pdf/2409.09207.pdf

Abstract:
Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large datasets for effective training. While physics-informed operators offer a data-agnostic learning approach, they introduce additional training complexities and convergence issues, especially in highly nonlinear systems. To overcome these challenges, we introduce Finite Basis Physics-Informed HyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic domain decomposition. By leveraging hypernetworks and finite basis functions, FB-HyDON effectively mitigates the training limitations associated with existing physics-informed operator learning methods. We validated our approach on the high-frequency harmonic oscillator, Burgers' equation at different viscosity levels, and Allen-Cahn equation demonstrating substantial improvements over other operator learning models.

Paperid: 570, https://arxiv.org/pdf/2601.17192.pdf

Abstract:
Coronary microvascular dysfunction (CMD) affects millions worldwide yet remains underdiagnosed because gold-standard physiological measurements are invasive and variably reproducible. We introduce a non-invasive, uncertainty-aware framework for estimating coronary flow reserve (CFR) directly from standard angiography. The system integrates physics-informed neural networks with variational inference to infer coronary blood flow from first-principles models of contrast transport, without requiring ground-truth flow measurements. The pipeline runs in approximately three minutes per patient on a single GPU, with no population-level training. Using 1{,}000 synthetic spatiotemporal intensity maps (kymographs) with controlled noise and artifacts, the framework reliably identifies degraded data and outputs appropriately inflated uncertainty estimates, showing strong correspondence between predictive uncertainty and error (Pearson $r = 0.997$, Spearman $ρ= 0.998$). Clinical validation in 12 patients shows strong agreement between PUNCH-derived CFR and invasive bolus thermodilution (Pearson $r = 0.90$, $p = 6.3 \times 10^{-5}$). We focus on the LAD, the artery most commonly assessed in routine CMD testing. Probabilistic CFR estimates have confidence intervals narrower than the variability of repeated invasive measurements. By transforming routine angiography into quantitative, uncertainty-aware assessment, this approach enables scalable, safer, and more reproducible evaluation of coronary microvascular function. Because standard angiography is widely available globally, the framework could expand access to CMD diagnosis and establish a new paradigm for physics-informed, patient-specific inference from clinical imaging.

Paperid: 571, https://arxiv.org/pdf/2601.03367.pdf

Abstract:
Understanding and modeling the constitutive behavior of concrete is crucial for civil and defense applications, yet widely used phenomenological models such as Karagozian \& Case concrete (KCC) model depend on empirically calibrated failure surfaces that lack flexibility in model form and associated uncertainty quantification. This work develops a physics-informed framework that retains the modular elastoplastic structure of KCC model while replacing its empirical failure surface with a constrained Gaussian Process Regression (GPR) surrogate that can be learned directly from experimentally accessible observables. Triaxial compression data under varying confinement levels are used for training, and the surrogate is then evaluated at confinement levels not included in the training set to assess its generalization capability. Results show that an unconstrained GPR interpolates well near training conditions but deteriorates and violates essential physical constraints under extrapolation, even when augmented with simulated data. In contrast, a physics-informed GPR that incorporates derivative-based constraints aligned with known material behavior yields markedly better accuracy and reliability, including at higher confinement levels beyond the training range. Probabilistic enforcement of these constraints also reduces predictive variance, producing tighter confidence intervals in data-scarce regimes. Overall, the proposed approach delivers a robust, uncertainty-aware surrogate that improves generalization and streamlines calibration without sacrificing the interpretability and numerical efficiency of the KCC model, offering a practical path toward an improved constitutive models for concrete.

Paperid: 572, https://arxiv.org/pdf/2601.02706.pdf

Abstract:
Optimal power flow (OPF) is one of the fundamental tasks for power system operations. While machine learning (ML) approaches such as deep neural networks (DNNs) have been widely studied to enhance OPF solution speed and performance, their practical deployment faces two critical scaling questions: What is the minimum training data volume required for reliable results? How should ML models' complexity balance accuracy with real-time computational limits? Existing studies evaluate discrete scenarios without quantifying these scaling relationships, leading to trial-and-error-based ML development in real-world applications. This work presents the first systematic scaling study for ML-based OPF across two dimensions: data scale (0.1K-40K training samples) and compute scale (multiple NN architectures with varying FLOPs). Our results reveal consistent power-law relationships on both DNNs and physics-informed NNs (PINNs) between each resource dimension and three core performance metrics: prediction error (MAE), constraint violations and speed. We find that for ACOPF, the accuracy metric scales with dataset size and training compute. These scaling laws enable predictable and principled ML pipeline design for OPF. We further identify the divergence between prediction accuracy and constraint feasibility and characterize the compute-optimal frontier. This work provides quantitative guidance for ML-OPF design and deployments.

Paperid: 573, https://arxiv.org/pdf/2512.24075.pdf

Abstract:
Lane-change intention prediction is safety-critical for autonomous driving and ADAS, but remains difficult in naturalistic traffic due to noisy kinematics, severe class imbalance, and limited generalization across heterogeneous highway scenarios. We propose Temporal Physics-Informed AI (TPI-AI), a hybrid framework that fuses deep temporal representations with physics-inspired interaction cues. A two-layer bidirectional LSTM (Bi-LSTM) encoder learns compact embeddings from multi-step trajectory histories; we concatenate these embeddings with kinematics-, safety-, and interaction-aware features (e.g., headway, TTC, and safe-gap indicators) and train a LightGBM classifier for three-class intention recognition (No-LC, Left-LC, Right-LC). To improve minority-class reliability, we apply imbalance-aware optimization including resampling/weighting and fold-wise threshold calibration. Experiments on two large-scale drone-based datasets, highD (straight highways) and exiD (ramp-rich environments), use location-based splits and evaluate prediction horizons T = 1, 2, 3 s. TPI-AI outperforms standalone LightGBM and Bi-LSTM baselines, achieving macro-F1 of 0.9562, 0.9124, 0.8345 on highD and 0.9247, 0.8197, 0.7605 on exiD at T = 1, 2, 3 s, respectively. These results show that combining physics-informed interaction features with learned temporal embeddings yields robust multi-scenario lane-change intention prediction.

Paperid: 574, https://arxiv.org/pdf/2512.22425.pdf

Abstract:
Fluence map prediction is central to automated radiotherapy planning but remains an ill-posed inverse problem due to the complex relationship between volumetric anatomy and beam-intensity modulation. Convolutional methods in prior work often struggle to capture long-range dependencies, which can lead to structurally inconsistent or physically unrealizable plans. We introduce \textbf{FluenceFormer}, a backbone-agnostic transformer framework for direct, geometry-aware fluence regression. The model uses a unified two-stage design: Stage~1 predicts a global dose prior from anatomical inputs, and Stage~2 conditions this prior on explicit beam geometry to regress physically calibrated fluence maps. Central to the approach is the \textbf{Fluence-Aware Regression (FAR)} loss, a physics-informed objective that integrates voxel-level fidelity, gradient smoothness, structural consistency, and beam-wise energy conservation. We evaluate the generality of the framework across multiple transformer backbones, including Swin UNETR, UNETR, nnFormer, and MedFormer, using a prostate IMRT dataset. FluenceFormer with Swin UNETR achieves the strongest performance among the evaluated models and improves over existing benchmark CNN and single-stage methods, reducing Energy Error to $\mathbf{4.5\%}$ and yielding statistically significant gains in structural fidelity ($p < 0.05$).

Paperid: 575, https://arxiv.org/pdf/2512.12026.pdf

Abstract:
Model Predictive Control (MPC) is a powerful control strategy for power electronics, but it highly relies on manually-derived and topology-specific analytical models, which is labor-intensive and time-consuming in practical designs. To overcome this bottleneck, this paper introduces a Digital-Twin-based MPC (DT-MPC) framework for generic power converters that can systematically translate a high-level circuit into an objective-aware control policy by leveraging a DT as a high-fidelity system model. Furthermore, a physics-informed neural surrogate predictor is proposed to accelerate predictions by DT and enable real-time operation. A gradient-free simplex search optimizer is also introduced to efficiently handle complex multi-objective optimization. The efficacy of the framework has been validated through a cloud-to-edge deployment on a 1500 W dual active bridge converter. Experimental results show that the synthesized predictive model achieves an inference speed over 7 times faster than real time, the DT-MPC controller outperforms several human-designed counterparts, and the overall framework reduces engineering design time by over 95\%, verifying the superiority of DT-MPC on generalized power converters.

Paperid: 576, https://arxiv.org/pdf/2512.11339.pdf

Abstract:
This paper introduces a projected Sobolev natural gradient descent (NGD) method for computing ground states of the Gross-Pitaevskii equation. By projecting a continuous Riemannian Sobolev gradient flow onto the normalized neural network tangent space, we derive a discrete NGD algorithm that preserves the normalization constraint. The numerical implementation employs variational Monte Carlo with a hybrid sampling strategy to accurately account for the normalization constant arising from nonlinear interaction terms. To enhance computational efficiency, a matrix-free Nyström-preconditioned conjugate gradient solver is adopted to approximate the NGD operator without explicit matrix assembly. Numerical experiments demonstrate that the proposed method converges significantly faster than physics-informed neural network approaches and exhibits linear scalability with respect to spatial dimensions. Moreover, the resulting neural-network solutions provide high-quality initial guesses that substantially accelerate subsequent refinement by traditional high-precision solvers.

Paperid: 577, https://arxiv.org/pdf/2512.10873.pdf

Abstract:
Physics-informed polynomial chaos expansions (PC$^2$) provide an efficient physically constrained surrogate modeling framework by embedding governing equations and other physical constraints into the standard data-driven polynomial chaos expansions (PCE) and solving via the Karush-Kuhn-Tucker (KKT) conditions. This approach improves the physical interpretability of surrogate models while achieving high computational efficiency and accuracy. However, the performance and efficiency of PC$^2$ can still be degraded with high-dimensional parameter spaces, limited data availability, or unrepresentative training data. To address this problem, this study explores two complementary enhancements to the PC$^2$ framework. First, a numerically efficient constrained optimization solver, straightforward updating of Lagrange multipliers (SULM), is adopted as an alternative to the conventional KKT solver. The SULM method significantly reduces computational cost when solving physically constrained problems with high-dimensionality and derivative boundary conditions that require a large number of virtual points. Second, a D-optimal sampling strategy is utilized to select informative virtual points to improve the stability and achieve the balance of accuracy and efficiency of the PC$^2$. The proposed methods are integrated into the PC$^2$ framework and evaluated through numerical examples of representative physical systems governed by ordinary or partial differential equations. The results demonstrate that the enhanced PC$^2$ has better comprehensive capability than standard PC$^2$, and is well-suited for high-dimensional uncertainty quantification tasks.

Paperid: 578, https://arxiv.org/pdf/2512.01163.pdf

Abstract:
Thermal analysis is increasingly critical in modern integrated circuits, where non-uniform power dissipation and high transistor densities can cause rapid temperature spikes and reliability concerns. Traditional methods, such as FEM-based simulations offer high accuracy but computationally prohibitive for early-stage design, often requiring multiple iterative redesign cycles to resolve late-stage thermal failures. To address these challenges, we propose 'ThermAl', a physics-informed generative AI framework which effectively identifies heat sources and estimates full-chip transient and steady-state thermal distributions directly from input activity profiles. ThermAl employs a hybrid U-Net architecture enhanced with positional encoding and a Boltzmann regularizer to maintain physical fidelity. Our model is trained on an extensive dataset of heat dissipation maps, ranging from simple logic gates (e.g., inverters, NAND, XOR) to complex designs, generated via COMSOL. Experimental results demonstrate that ThermAl delivers precise temperature mappings for large circuits, with a root mean squared error (RMSE) of only 0.71°C, and outperforms conventional FEM tools by running up to ~200 times faster. We analyze performance across diverse layouts and workloads, and discuss its applicability to large-scale EDA workflows. While thermal reliability assessments often extend beyond 85°C for post-layout signoff, our focus here is on early-stage hotspot detection and thermal pattern learning. To ensure generalization beyond the nominal operating range 25-55°C, we additionally performed cross-validation on an extended dataset spanning 25-95°C maintaining a high accuracy (<2.2% full-scale RMSE) even under elevated temperature conditions representative of peak power and stress scenarios.

Paperid: 579, https://arxiv.org/pdf/2511.21861.pdf

Abstract:
We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral tokenization, physics-aware conditioning, and a Mamba-based state-space backbone with an operator-theoretic decoder, enabling scalable and data-efficient modeling of complex physical dynamics. In contrast to task-specific neural operators, PDE-FM is pretrained once on diverse PDE datasets and can be transferred to new physical regimes without architectural or data-specific modifications. Evaluated on twelve 2D and 3D datasets from The Well benchmark - spanning hydrodynamic, radiative, elastic, and astrophysical phenomena - PDE-FM achieves state-of-the-art accuracy in six domains, reducing mean VRMSE by 46% relative to prior operator-learning baselines. The model demonstrates robust cross-physics generalization, excelling in turbulent and radiative systems while maintaining strong performance in linear and steady-state regimes. These results suggest that large-scale pretraining across diverse physical processes can yield transferable representations of dynamics, marking a step toward unified, foundation-level surrogates for multi-physics simulation and scientific discovery.

Paperid: 580, https://arxiv.org/pdf/2511.10387.pdf

Abstract:
Accurate retrieval of vegetation biophysical variables from satellite imagery is crucial for ecosystem monitoring and agricultural management. In this work, we propose a physics-informed Transformer-VAE architecture to invert the PROSAIL radiative transfer model for simultaneous estimation of key canopy parameters from Sentinel-2 data. Unlike previous hybrid approaches that require real satellite images for self-supevised training. Our model is trained exclusively on simulated data, yet achieves performance on par with state-of-the-art methods that utilize real imagery. The Transformer-VAE incorporates the PROSAIL model as a differentiable physical decoder, ensuring that inferred latent variables correspond to physically plausible leaf and canopy properties. We demonstrate retrieval of leaf area index (LAI) and canopy chlorophyll content (CCC) on real-world field datasets (FRM4Veg and BelSAR) with accuracy comparable to models trained with real Sentinel-2 data. Our method requires no in-situ labels or calibration on real images, offering a cost-effective and self-supervised solution for global vegetation monitoring. The proposed approach illustrates how integrating physical models with advanced deep networks can improve the inversion of RTMs, opening new prospects for large-scale, physically-constrained remote sensing of vegetation traits.

Paperid: 581, https://arxiv.org/pdf/2511.08655.pdf

Abstract:
The Method of Moments (MoM) is constrained by the usage of static, geometry-defined basis functions, such as the Rao-Wilton-Glisson (RWG) basis. This letter reframes electromagnetic modeling around a learnable basis representation rather than solving for the coefficients over a fixed basis. We first show that the RWG basis is essentially a static and piecewise-linear realization of the Kolmogorov-Arnold representation theorem. Inspired by this insight, we propose PhyKAN, a physics-informed Kolmogorov-Arnold Network (KAN) that generalizes RWG into a learnable and adaptive basis family. Derived from the EFIE, PhyKAN integrates a local KAN branch with a global branch embedded with Green's function priors to preserve physical consistency. It is demonstrated that, across canonical geometries, PhyKAN achieves sub-0.01 reconstruction errors as well as accurate, unsupervised radar cross section predictions, offering an interpretable, physics-consistent bridge between classical solvers and modern neural network models for electromagnetic modeling.

Paperid: 582, https://arxiv.org/pdf/2511.06083.pdf

Abstract:
Reliability analysis of engineering systems under uncertainty poses significant computational challenges, particularly for problems involving high-dimensional stochastic inputs, nonlinear system responses, and multiphysics couplings. Traditional surrogate modeling approaches often incur high energy consumption, which severely limits their scalability and deployability in resource-constrained environments. We introduce NeuroPOL, \textit{the first neuroscience-inspired physics-informed operator learning framework} for reliability analysis. NeuroPOL incorporates Variable Spiking Neurons into a physics-informed operator architecture, replacing continuous activations with event-driven spiking dynamics. This innovation promotes sparse communication, significantly reduces computational load, and enables an energy-efficient surrogate model. The proposed framework lowers both computational and power demands, supporting real-time reliability assessment and deployment on edge devices and digital twins. By embedding governing physical laws into operator learning, NeuroPOL builds physics-consistent surrogates capable of accurate uncertainty propagation and efficient failure probability estimation, even for high-dimensional problems. We evaluate NeuroPOL on five canonical benchmarks, the Burgers equation, Nagumo equation, two-dimensional Poisson equation, two-dimensional Darcy equation, and incompressible Navier-Stokes equation with energy coupling. Results show that NeuroPOL achieves reliability measures comparable to standard physics-informed operators, while introducing significant communication sparsity, enabling scalable, distributed, and energy-efficient deployment.

Paperid: 583, https://arxiv.org/pdf/2511.04751.pdf

Abstract:
Human-in-the-loop calibration is often addressed via preference-based optimization, where algorithms learn from pairwise comparisons rather than explicit cost evaluations. While effective, methods such as Preferential Bayesian Optimization or Global optimization based on active preference learning with radial basis functions (GLISp) treat the system as a black box and ignore informative sensor measurements. In this work, we introduce a sensor-guided regularized extension of GLISp that integrates measurable descriptors into the preference-learning loop through a physics-informed hypothesis function and a least-squares regularization term. This injects grey-box structure, combining subjective feedback with quantitative sensor information while preserving the flexibility of preference-based search. Numerical evaluations on an analytical benchmark and on a human-in-the-loop vehicle suspension tuning task show faster convergence and superior final solutions compared to baseline GLISp.

Paperid: 584, https://arxiv.org/pdf/2510.25752.pdf

Abstract:
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral bases on arbitrary spatiotemporal domains, whereby the basis is defined on a hyperrectangle containing the true domain. We find the coefficients of the basis expansion by solving an optimization problem whereby both the equations, the boundary conditions and any optimization targets are enforced by a loss function, building on a key idea from Physics-Informed Neural Networks (PINNs). Since the representation of the function natively has exponential convergence, so does the solution of the optimization problem, as long as it can be solved efficiently. We find empirically that the optimization protocols developed for machine learning find solutions with exponential convergence on a wide range of equations. The method naturally allows for the incorporation of data assimilation by including additional terms in the loss function, and for the efficient solution of optimization problems over the PDE solutions.

Paperid: 585, https://arxiv.org/pdf/2510.21281.pdf

Abstract:
Kinetic modeling enables \textit{in vivo} quantification of tracer uptake and glucose metabolism in [${}^{18}$F]Fluorodeoxyglucose ([${}^{18}$F]FDG) dynamic positron emission tomography (dPET) imaging of mice. However, kinetic modeling requires the accurate determination of the arterial input function (AIF) during imaging, which is time-consuming and invasive. Recent studies have shown the efficacy of using deep learning to directly predict the input function, surpassing established methods such as the image-derived input function (IDIF). In this work, we trained a physics-informed deep learning-based input function prediction model (PIDLIF) to estimate the AIF directly from the PET images, incorporating a kinetic modeling loss during training. The proposed method uses a two-tissue compartment model over two regions, the myocardium and brain of the mice, and is trained on a dataset of 70 [${}^{18}$F]FDG dPET images of mice accompanied by the measured AIF during imaging. The proposed method had comparable performance to the network without a physics-informed loss, and when sudden movement causing blurring in the images was simulated, the PIDLIF model maintained high performance in severe cases of image degradation. The proposed physics-informed method exhibits an improved robustness that is promoted by physically constraining the problem, enforcing consistency for out-of-distribution samples. In conclusion, the PIDLIF model offers insight into the effects of leveraging physiological distribution mechanics in mice to guide a deep learning-based AIF prediction network in images with severe degradation as a result of blurring due to movement during imaging.

Paperid: 586, https://arxiv.org/pdf/2510.17756.pdf

Abstract:
As an increasing amount of remote sensing data becomes available in the Arctic Ocean, data-driven machine learning (ML) techniques are becoming widely used to predict sea ice velocity (SIV) and sea ice concentration (SIC). However, fully data-driven ML models have limitations in generalizability and physical consistency due to their excessive reliance on the quantity and quality of training data. In particular, as Arctic sea ice entered a new phase with thinner ice and accelerated melting, there is a possibility that an ML model trained with historical sea ice data cannot fully represent the dynamically changing sea ice conditions in the future. In this study, we develop physics-informed neural network (PINN) strategies to integrate physical knowledge of sea ice into the ML model. Based on the Hierarchical Information-sharing U-net (HIS-Unet) architecture, we incorporate the physics loss function and the activation function to produce physically plausible SIV and SIC outputs. Our PINN model outperforms the fully data-driven model in the daily predictions of SIV and SIC, even when trained with a small number of samples. The PINN approach particularly improves SIC predictions in melting and early freezing seasons and near fast-moving ice regions.

Paperid: 587, https://arxiv.org/pdf/2510.14656.pdf

Abstract:
Inverse problems involving partial differential equations (PDEs) with discontinuous coefficients are fundamental challenges in modeling complex spatiotemporal systems with heterogeneous structures and uncertain dynamics. Traditional numerical and machine learning approaches often face limitations in addressing these problems due to high dimensionality, inherent nonlinearity, and discontinuous parameter spaces. In this work, we propose a novel computational framework that synergistically integrates physics-informed deep learning with Bayesian inference for accurate parameter identification in PDEs with jump discontinuities in coefficients. The core innovation of our framework lies in a dual-network architecture employing a gradient-adaptive weighting strategy: a main network approximates PDE solutions while a sub network samples its coefficients. To effectively identify mixture structures in parameter spaces, we employ Markovian dynamics methods to capture hidden state transitions of complex spatiotemporal systems. The framework has applications in reconstruction of solutions and identification of parameter-varying regions. Comprehensive numerical experiments on various PDEs with jump-varying coefficients demonstrate the framework's exceptional adaptability, accuracy, and robustness compared to existing methods. This study provides a generalizable computational approach of parameter identification for PDEs with discontinuous parameter structures, particularly in non-stationary or heterogeneous systems.

Paperid: 588, https://arxiv.org/pdf/2510.13886.pdf

Abstract:
DSC-MRI perfusion is a medical imaging technique for diagnosing and prognosing brain tumors and strokes. Its analysis relies on mathematical deconvolution, but noise or motion artifacts in a clinical environment can disrupt this process, leading to incorrect estimate of perfusion parameters. Although deep learning approaches have shown promising results, their calibration typically rely on third-party deconvolution algorithms to generate reference outputs and are bound to reproduce their limitations. To adress this problem, we propose a physics-informed autoencoder that leverages an analytical model to decode the perfusion parameters and guide the learning of the encoding network. This autoencoder is trained in a self-supervised fashion without any third-party software and its performance is evaluated on a database with glioma patients. Our method shows reliable results for glioma grading in accordance with other well-known deconvolution algorithms despite a lower computation time. It also achieved competitive performance even in the presence of high noise which is critical in a medical environment.

Paperid: 589, https://arxiv.org/pdf/2510.06684.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) provide a powerful and general framework for solving Partial Differential Equations (PDEs) by embedding physical laws into loss functions. However, training PINNs is notoriously difficult due to the need to balance multiple loss terms, such as PDE residuals and boundary conditions, which often have conflicting objectives and vastly different curvatures. Existing methods address this issue by manipulating gradients before optimization (a "pre-combine" strategy). We argue that this approach is fundamentally limited, as forcing a single optimizer to process gradients from spectrally heterogeneous loss landscapes disrupts its internal preconditioning. In this work, we introduce AutoBalance, a novel "post-combine" training paradigm. AutoBalance assigns an independent adaptive optimizer to each loss component and aggregates the resulting preconditioned updates afterwards. Extensive experiments on challenging PDE benchmarks show that AutoBalance consistently outperforms existing frameworks, achieving significant reductions in solution error, as measured by both the MSE and $L^{\infty}$ norms. Moreover, AutoBalance is orthogonal to and complementary with other popular PINN methodologies, amplifying their effectiveness on demanding benchmarks.

Paperid: 590, https://arxiv.org/pdf/2510.03589.pdf

Abstract:
Spatio-temporal sensor data is often sparse, noisy, and irregular, and existing interpolation or learning methods struggle here because they either ignore governing PDEs or do not scale. We introduce FieldFormer, a transformer-based framework for mesh-free spatio-temporal field reconstruction that combines data-driven flexibility with physics-based structure. For each query, FieldFormer gathers a local neighborhood using a learnable velocity-scaled distance metric, enabling anisotropic adaptation to different propagation regimes. Neighborhoods are built efficiently via per-batch offset recomputation, and refined in an expectation-maximization style as the velocity scales evolve. Predictions are made by a local transformer encoder, and physics consistency is enforced through autograd-based PDE residuals and boundary-specific penalties. Across three benchmarks--a scalar anisotropic heat equation, a vector-valued shallow-water system, and a realistic advection-diffusion pollution simulation--FieldFormer consistently outperforms strong baselines by more than 40%. Our results demonstrate that FieldFormer enables accurate (RMSE$<10^{-2}$), efficient, and physically consistent field reconstruction from sparse (0.4%-2%) and noisy(10%) data.

Paperid: 591, https://arxiv.org/pdf/2509.25097.pdf

Abstract:
Learning control policies for multi-robot systems (MRS) remains a major challenge due to long-term coordination and the difficulty of obtaining realistic training data. In this work, we address both limitations within an imitation learning framework. First, we shift the typical role of Curriculum Learning in MRS, from scalability with the number of robots, to focus on improving long-term coordination. We propose a curriculum strategy that gradually increases the length of expert trajectories during training, stabilizing learning and enhancing the accuracy of long-term behaviors. Second, we introduce a method to approximate the egocentric perception of each robot using only third-person global state demonstrations. Our approach transforms idealized trajectories into locally available observations by filtering neighbors, converting reference frames, and simulating onboard sensor variability. Both contributions are integrated into a physics-informed technique to produce scalable, distributed policies from observations. We conduct experiments across two tasks with varying team sizes and noise levels. Results show that our curriculum improves long-term accuracy, while our perceptual estimation method yields policies that are robust to realistic uncertainty. Together, these strategies enable the learning of robust, distributed controllers from global demonstrations, even in the absence of expert actions or onboard measurements.

Paperid: 592, https://arxiv.org/pdf/2509.23085.pdf

Abstract:
Activation functions critically influence trainability and expressivity, and recent work has therefore explored a broad range of nonlinearities. However, widely used Gaussian i.i.d. initializations are designed to preserve activation variance under wide or infinite width assumptions. In deep and relatively narrow networks with sigmoidal nonlinearities, these schemes often drive preactivations into saturation, and collapse gradients. To address this, we introduce an odd-sigmoid activations and propose an activation aware initialization tailored to any function in this class. Our method remains robust over a wide band of variance scales, preserving both forward signal variance and backpropagated gradient norms even in very deep and narrow networks. Empirically, across standard image benchmarks we find that the proposed initialization is substantially less sensitive to depth, width, and activation scale than Gaussian initializations. In physics informed neural networks (PINNs), scaled odd-sigmoid activations combined with our initialization achieve lower losses than Gaussian based setups, suggesting that diagonal-plus-noise weights provide a practical alternative when Gaussian initialization breaks down.

Paperid: 593, https://arxiv.org/pdf/2509.19588.pdf

Abstract:
Most refrigerants currently used in air-conditioning systems, such as hydrofluorocarbons, are potent greenhouse gases and are being phased down. Large-scale molecular screening has been applied to the search for alternatives, but in practice only about 300 refrigerants are known, and only a few additional candidates have been suggested without experimental validation. This scarcity of reliable data limits the effectiveness of purely data-driven methods. We present Refgen, a generative pipeline that integrates machine learning with physics-grounded inductive biases. Alongside fine-tuning for valid molecular generation, Refgen incorporates predictive models for critical properties, equations of state, thermochemical polynomials, and full vapor compression cycle simulations. These models enable reinforcement learning fine-tuning under thermodynamic constraints, enforcing consistency and guiding discovery toward molecules that balance efficiency, safety, and environmental impact. By embedding physics into the learning process, Refgen leverages scarce data effectively and enables de novo refrigerant discovery beyond the known set of compounds.

Paperid: 594, https://arxiv.org/pdf/2509.18483.pdf

Abstract:
The prediction of quantum dynamical responses lies at the heart of modern physics. Yet, modeling these time-dependent behaviors remains a formidable challenge because quantum systems evolve in high-dimensional Hilbert spaces, often rendering traditional numerical methods computationally prohibitive. While large language models have achieved remarkable success in sequential prediction, quantum dynamics presents a fundamentally different challenge: forecasting the entire temporal evolution of quantum systems rather than merely the next element in a sequence. Existing neural architectures such as recurrent and convolutional networks often require vast training datasets and suffer from spurious oscillations that compromise physical interpretability. In this work, we introduce a fundamentally new approach: Kolmogorov Arnold Networks (KANs) augmented with physics-informed loss functions that enforce the Ehrenfest theorems. Our method achieves superior accuracy with significantly less training data: it requires only 5.4 percent of the samples (200) compared to Temporal Convolution Networks (3,700). We further introduce the Chain of KANs, a novel architecture that embeds temporal causality directly into the model design, making it particularly well-suited for time series modeling. Our results demonstrate that physics-informed KANs offer a compelling advantage over conventional black-box models, maintaining both mathematical rigor and physical consistency while dramatically reducing data requirements.

Paperid: 595, https://arxiv.org/pdf/2509.17621.pdf

Abstract:
Accurate battery modeling is essential for reliable state estimation in modern applications, such as predicting the remaining discharge time and remaining discharge energy in battery management systems. Existing approaches face several limitations: model-based methods require a large number of parameters; data-driven methods rely heavily on labeled datasets; and current physics-informed neural networks (PINNs) often lack aging adaptation, or still depend on many parameters, or continuously regenerate states. In this work, we propose SeqBattNet, a discrete-state PINN with built-in aging adaptation for battery modeling, to predict terminal voltage during the discharge process. SeqBattNet consists of two components: (i) an encoder, implemented as the proposed HRM-GRU deep learning module, which generates cycle-specific aging adaptation parameters; and (ii) a decoder, based on the equivalent circuit model (ECM) combined with deep learning, which uses these parameters together with the input current to predict voltage. The model requires only three basic battery parameters and, when trained on data from a single cell, still achieves robust performance. Extensive evaluations across three benchmark datasets (TRI, RT-Batt, and NASA) demonstrate that SeqBattNet significantly outperforms classical sequence models and PINN baselines, achieving consistently lower RMSE while maintaining computational efficiency.

Paperid: 596, https://arxiv.org/pdf/2509.16114.pdf

Abstract:
Laser Powder Bed Fusion (L-PBF) is a widely adopted additive manufacturing process for fabricating complex metallic parts layer by layer. Effective thermal management is essential to ensure part quality and structural integrity, as thermal gradients and residual stresses can lead to defects such as warping and cracking. However, existing experimental or computational techniques lack the ability to forecast future temperature distributions in real time, an essential capability for proactive process control. This paper presents a real-time thermal state forecasting framework for L-PBF, based on a physics-informed reduced-order thermal model integrated with a Kalman filtering scheme. The proposed approach efficiently captures inter-layer heat transfer dynamics and enables accurate tracking and forecasting of spatial and temporal temperature evolution. Validation across multiple part geometries using measured data demonstrates that the method reliably estimates and forecasts peak temperatures and cooling trends. By enabling predictive thermal control, this framework offers a practical and computationally efficient solution for thermal management in L-PBF, paving the way toward closed-loop control in L-PBF.

Paperid: 597, https://arxiv.org/pdf/2509.15124.pdf

Abstract:
Modelling the underlying mechanisms of neurodegenerative diseases demands methods that capture heterogeneous and spatially varying dynamics from sparse, high-dimensional neuroimaging data. Integrating partial differential equation (PDE) based physics knowledge with machine learning provides enhanced interpretability and utility over classic numerical methods. However, current physics-integrated machine learning methods are limited to considering a single PDE, severely limiting their application to diseases where multiple mechanisms are responsible for different groups (i.e., subtypes) and aggravating problems with model misspecification and degeneracy. Here, we present a deep generative model for learning mixtures of latent dynamic models governed by physics-based PDEs, going beyond traditional approaches that assume a single PDE structure. Our method integrates reaction-diffusion PDEs within a variational autoencoder (VAE) mixture model framework, supporting inference of subtypes of interpretable latent variables (e.g. diffusivity and reaction rates) from neuroimaging data. We evaluate our method on synthetic benchmarks and demonstrate its potential for uncovering mechanistic subtypes of Alzheimer's disease progression from positron emission tomography (PET) data.

Paperid: 598, https://arxiv.org/pdf/2509.00663.pdf

Abstract:
In this paper, we propose an evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Operator learning Network, which is a novel operator learning network to efficiently solve parametric partial differential equations. In forward and inverse settings, this operator learning network only admits minimum requirement of noisy observational data. While physics-informed neural networks and operator learning approaches such as Deep Operator Networks and Fourier Neural Operators offer promising alternatives to traditional numerical solvers, they struggle with balancing operator and physics losses, maintaining robustness under noisy or sparse data, and providing uncertainty quantification. The proposed framework addresses these limitations by integrating: (i) evolutionary multi-objective optimization to adaptively balance operator and physics-based losses in the Pareto front; (ii) replica exchange stochastic gradient Langevin dynamics to improve global parameter-space exploration and accelerate convergence; and (iii) built-in Bayesian uncertainty quantification from stochastic sampling. The proposed operator learning method is tested numerically on several different problems including one-dimensional Burgers equation and the time-fractional mixed diffusion-wave equation. The results indicate that our framework consistently outperforms the general operator learning methods in accuracy, noise robustness, and the ability to quantify uncertainty.

Paperid: 599, https://arxiv.org/pdf/2508.20886.pdf

Abstract:
Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of partial differential equations (PDEs). While much of the progress in this area has been driven by deep neural network-based approaches such as Deep Operator Networks (DeepONet) and Fourier Neural Operator (FNO), recent work has begun to explore traditional machine learning methods for OL. In this work, we introduce polynomial chaos expansion (PCE) as an OL method. PCE has been widely used for uncertainty quantification (UQ) and has recently gained attention in the context of SciML. For OL, we establish a mathematical framework that enables PCE to approximate operators in both purely data-driven and physics-informed settings. The proposed framework reduces the task of learning the operator to solving a system of equations for the PCE coefficients. Moreover, the framework provides UQ by simply post-processing the PCE coefficients, without any additional computational cost. We apply the proposed method to a diverse set of PDE problems to demonstrate its capabilities. Numerical results demonstrate the strong performance of the proposed method in both OL and UQ tasks, achieving excellent numerical accuracy and computational efficiency.

Paperid: 600, https://arxiv.org/pdf/2508.19031.pdf

Abstract:
Ground motion models (GMMs) predict how strongly the ground will shake during an earthquake. They are essential for structural analysis, seismic design, and seismic risk assessment studies. Traditional machine learning (ML) approaches are popular to develop GMMs, due to large earthquake databases worldwide. However, they operate as "black boxes," which are hard to interpret and trust, limiting their use in high-stake decisions. Additionally, these databases suffer from significant data imbalances: fewer large, critically damaging records near the fault compared to abundant, less severely damaging distant records. These two limitations are addressed in this work by developing a transparent ML architecture using the HazBinLoss function. Each input (e.g., magnitude, distance, their interaction term, etc.) is processed separately and added linearly to obtain the output, resulting in exact contribution of each term. The HazBinLoss function assigns higher weights to critical near-field large magnitude records and lower weights to less-critical far-field smaller magnitude records, during training to prevent underprediction of the most damaging scenarios. Our model captures known seismological principles and achieves comparable performance with established GMMs while maintaining transparency. This framework enables broader adoption of ML-based approaches for risk assessment studies and disaster planning.

Paperid: 601, https://arxiv.org/pdf/2508.16554.pdf

Abstract:
Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under external time-dependent perturbations such as laser fields. In this work, we present a machine learning approach to accelerate electron dynamics simulations based on real time TDDFT using autoregressive neural operators as time-propagators for the electron density. By leveraging physics-informed constraints and featurization, and high-resolution training data, our model achieves superior accuracy and computational speed compared to traditional numerical solvers. We demonstrate the effectiveness of our model on a class of one-dimensional diatomic molecules under the influence of a range of laser parameters. This method has potential in enabling on-the-fly modeling of laser-irradiated molecules and materials by utilizing fast machine learning predictions in a large space of varying experimental parameters of the laser.

Paperid: 602, https://arxiv.org/pdf/2508.03774.pdf

Abstract:
Electromagnetic (EM) scattering modeling is critical for radar remote sensing, however, its inherent complexity introduces significant computational challenges. Traditional numerical solvers offer high accuracy, but suffer from scalability issues and substantial computational costs. Pure data-driven deep learning approaches, while efficient, lack physical constraints embedding during training and require extensive labeled data, limiting their applicability and generalization. To overcome these limitations, we propose a U-shaped Physics-Informed Network (U-PINet), the first fully deep-learning-based, physics-informed hierarchical framework for computational EM designed to ensure physical consistency while maximizing computational efficiency. Motivated by the hierarchical decomposition strategy in EM solvers and the inherent sparsity of local EM coupling, the U-PINet models the decomposition and coupling of near- and far-field interactions through a multiscale processing neural network architecture, while employing a physics-inspired sparse graph representation to efficiently model both self- and mutual- coupling among mesh elements of complex $3$-Dimensional (3D) objects. This principled approach enables end-to-end multiscale EM scattering modeling with improved efficiency, generalization, and physical consistency. Experimental results showcase that the U-PINet accurately predicts surface current distributions, achieving close agreement with traditional solver, while significantly reducing computational time and outperforming conventional deep learning baselines in both accuracy and robustness. Furthermore, our evaluations on radar cross section prediction tasks confirm the feasibility of the U-PINet for downstream EM scattering applications.

Paperid: 603, https://arxiv.org/pdf/2508.01720.pdf

Abstract:
We propose a mesh-free policy iteration framework based on physics-informed neural networks (PINNs) for solving entropy-regularized stochastic control problems. The method iteratively alternates between soft policy evaluation and improvement using automatic differentiation and neural approximation, without relying on spatial discretization. We present a detailed $L^2$ error analysis that decomposes the total approximation error into three sources: iteration error, policy network error, and PDE residual error. The proposed algorithm is validated with a range of challenging control tasks, including high-dimensional linear-quadratic regulation in 5D and 10D, as well as nonlinear systems such as pendulum and cartpole problems. Numerical results confirm the scalability, accuracy, and robustness of our approach across both linear and nonlinear benchmarks.

Paperid: 604, https://arxiv.org/pdf/2508.01718.pdf

Abstract:
We propose a physics-informed neural network policy iteration (PINN-PI) framework for solving stochastic optimal control problems governed by second-order Hamilton--Jacobi--Bellman (HJB) equations. At each iteration, a neural network is trained to approximate the value function by minimizing the residual of a linear PDE induced by a fixed policy. This linear structure enables systematic $L^2$ error control at each policy evaluation step, and allows us to derive explicit Lipschitz-type bounds that quantify how value gradient errors propagate to the policy updates. This interpretability provides a theoretical basis for evaluating policy quality during training. Our method extends recent deterministic PINN-based approaches to stochastic settings, inheriting the global exponential convergence guarantees of classical policy iteration under mild conditions. We demonstrate the effectiveness of our method on several benchmark problems, including stochastic cartpole, pendulum problems and high-dimensional linear quadratic regulation (LQR) problems in up to 10D.

Paperid: 605, https://arxiv.org/pdf/2507.08121.pdf

Abstract:
Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on the impressive performance of quasi Monte-Carlo methods in high dimensional problems, this paper proposes Quasi-Random Physics-Informed Neural Networks (QRPINNs), which use low-discrepancy sequences for sampling instead of random points directly from the domain. Theoretically, QRPINNs have been proven to have a better convergence rate than PINNs. Empirically, experiments demonstrate that QRPINNs significantly outperform PINNs and some representative adaptive sampling methods, especially in high-dimensional PDEs. Furthermore, combining QRPINNs with adaptive sampling can further improve the performance.

Paperid: 606, https://arxiv.org/pdf/2506.22365.pdf

Abstract:
When using reinforcement learning (RL) to tackle physical control tasks, inductive biases that encode physics priors can help improve sample efficiency during training and enhance generalization in testing. However, the current practice of incorporating these helpful physics-informed inductive biases inevitably runs into significant manual labor and domain expertise, making them prohibitive for general users. This work explores a symbolic approach to distill physics-informed inductive biases into RL agents, where the physics priors are expressed in a domain-specific language (DSL) that is human-readable and naturally explainable. Yet, the DSL priors do not translate directly into an implementable policy due to partial and noisy observations and additional physical constraints in navigation tasks. To address this gap, we develop a physics-informed program-guided RL (PiPRL) framework with applications to indoor navigation. PiPRL adopts a hierarchical and modularized neuro-symbolic integration, where a meta symbolic program receives semantically meaningful features from a neural perception module, which form the bases for symbolic programming that encodes physics priors and guides the RL process of a low-level neural controller. Extensive experiments demonstrate that PiPRL consistently outperforms purely symbolic or neural policies and reduces training time by over 26% with the help of the program-based inductive biases.

Paperid: 607, https://arxiv.org/pdf/2506.19805.pdf

Abstract:
Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by computational limitations, PINNs are typically optimized using a finite set of points, which poses significant challenges in guaranteeing their convergence and accuracy. In this study, we proposed a new weighting scheme that will adaptively change the weights to the loss functions from isolated points to their continuous neighborhood regions. The empirical results show that our weighting scheme can reduce the relative $L^2$ errors to a lower value.

Paperid: 608, https://arxiv.org/pdf/2506.17755.pdf

Abstract:
Retired electric vehicle batteries offer immense potential to support low-carbon energy systems, but uncertainties in their degradation behavior and data inaccessibilities under second-life use pose major barriers to safe and scalable deployment. This work proposes a Physics-Informed Mixture of Experts (PIMOE) network that computes battery degradation trajectories using partial, field-accessible signals in a single cycle. PIMOE leverages an adaptive multi-degradation prediction module to classify degradation modes using expert weight synthesis underpinned by capacity-voltage and relaxation data, producing latent degradation trend embeddings. These are input to a use-dependent recurrent network for long-term trajectory prediction. Validated on 207 batteries across 77 use conditions and 67,902 cycles, PIMOE achieves an average mean absolute percentage (MAPE) errors of 0.88% with a 0.43 ms inference time. Compared to the state-of-the-art Informer and PatchTST, it reduces computational time and MAPE by 50%, respectively. Compatible with random state of charge region sampling, PIMOE supports 150-cycle forecasts with 1.50% average and 6.26% maximum MAPE, and operates effectively even with pruned 5MB training data. Broadly, PIMOE framework offers a deployable, history-free solution for battery degradation trajectory computation, redefining how second-life energy storage systems are assessed, optimized, and integrated into the sustainable energy landscape.

Paperid: 609, https://arxiv.org/pdf/2506.17626.pdf

Abstract:
Random Feature Methods (RFMs) and their variants such as extreme learning machine finite-basis physics-informed neural networks (ELM-FBPINNs) offer a scalable approach for solving partial differential equations (PDEs) by using localized, overlapping and randomly initialized neural network basis functions to approximate the PDE solution and training them to minimize PDE residuals through solving structured least-squares problems. This combination leverages the approximation power of randomized neural networks and the parallelism of domain decomposition. However, the resulting least-squares systems are often severely ill-conditioned, due to local redundancy among random basis functions, which significantly affects the convergence of standard solvers. In this work, we introduce a block rank-revealing QR (RRQR) filtering and preconditioning strategy that operates directly on the structured least-squares problem. First, local RRQR factorizations identify and remove redundant basis functions while preserving numerically informative ones, reducing problem size, and improving conditioning. Second, we use these factorizations to construct a right preconditioner for the global problem which preserves block-sparsity and numerical stability. Third, we derive deterministic bounds of the condition number of the preconditioned system, with probabilistic refinements for small overlaps. We validate our approach on challenging, multi-scale PDE problems in 1D, 2D, and (2+1)D, demonstrating reductions in condition numbers by up to eleven orders of magnitude, LSQR convergence speedups by factors of 10-1000, and higher accuracy than both unpreconditioned and additive Schwarz-preconditioned baselines, all at significantly lower memory and computational cost. These results establish RRQR-based preconditioning as a scalable, accurate, and efficient enhancement for RFM-based PDE solvers.

Paperid: 610, https://arxiv.org/pdf/2506.15960.pdf

Abstract:
This study presents a physics-informed neural network (PINN) framework for reactive transport modeling for simulating fast bimolecular reactions in porous media. Accurate characterization of chemical interactions and product formation in surface and subsurface environments is essential for advancing critical mineral extraction and related geoscience applications.

Paperid: 611, https://arxiv.org/pdf/2506.08563.pdf

Abstract:
Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed Neural Networks (PINNs) have recently been proposed to solve complex differential equations and have demonstrated superior performance in many applications. While the L2 loss function is usually a default choice in PINNs, it has been shown that the corresponding numerical solution is incorrect and unstable for some complex equations. In this work, we propose a new PINNs framework named Kernel Packet accelerated PINNs (KP-PINNs), which gives a new expression of the loss function using the reproducing kernel Hilbert space (RKHS) norm and uses the Kernel Packet (KP) method to accelerate the computation. Theoretical results show that KP-PINNs can be stable across various differential equations. Numerical experiments illustrate that KP-PINNs can solve differential equations effectively and efficiently. This framework provides a promising direction for improving the stability and accuracy of PINNs-based solvers in scientific computing.

Paperid: 612, https://arxiv.org/pdf/2506.00731.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving forward and inverse problems involving partial differential equations (PDEs) by incorporating physical laws into the training process. However, the performance of PINNs is often hindered in real-world scenarios involving noisy observational data and missing physics, particularly in inverse problems. In this work, we propose an iterative multi-objective PINN ensemble Kalman filter (MoPINNEnKF) framework that improves the robustness and accuracy of PINNs in both forward and inverse problems by using the \textit{ensemble Kalman filter} and the \textit{non-dominated sorting genetic algorithm} III (NSGA-III). Specifically, NSGA-III is used as a multi-objective optimizer that can generate various ensemble members of PINNs along the optimal Pareto front, while accounting the model uncertainty in the solution space. These ensemble members are then utilized within the EnKF to assimilate noisy observational data. The EnKF's analysis is subsequently used to refine the data loss component for retraining the PINNs, thereby iteratively updating their parameters. The iterative procedure generates improved solutions to the PDEs. The proposed method is tested on two benchmark problems: the one-dimensional viscous Burgers equation and the time-fractional mixed diffusion-wave equation (TFMDWE). The numerical results show it outperforms standard PINNs in handling noisy data and missing physics.

Paperid: 613, https://arxiv.org/pdf/2505.23002.pdf

Abstract:
Physics-informed neural network (PINN) has shown great potential in solving partial differential equations. However, it faces challenges when dealing with problems involving steep gradients. The solutions to singularly perturbed time-dependent reaction-advection-diffusion equations exhibit internal moving transition layers with sharp gradients, and thus the standard PINN becomes ineffective. In this work, we propose a deep asymptotic expansion (DAE) method, which is inspired by asymptotic analysis and leverages deep learning to approximate the smooth part of the expansion. We first derive the governing equations for transition layers, which are then solved using PINN. Numerical experiments show that the DAE outperforms the standard PINN, gPINN, and PINN with adaptive sampling. We also show its robustness with respect to training point distributions, network architectures, and random seeds.

Paperid: 614, https://arxiv.org/pdf/2505.22391.pdf

Abstract:
Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems. Recently, diffusion models have gained increasing attention in the modeling of physical systems, particularly those governed by partial differential equations (PDEs). However, diffusion models only access noisy data $\boldsymbol{x}_t$ at intermediate steps, making it infeasible to directly enforce constraints on the clean sample $\boldsymbol{x}_0$ at each noisy level. As a workaround, constraints are typically applied to the expectation of clean samples $\mathbb{E}[\boldsymbol{x}_0|\boldsymbol{x}_t]$, which is estimated using the learned score network. However, imposing PDE constraints on the expectation does not strictly represent the one on the true clean data, known as Jensen's Gap. This gap creates a trade-off: enforcing PDE constraints may come at the cost of reduced accuracy in generative modeling. To address this, we propose a simple yet effective post-hoc distillation approach, where PDE constraints are not injected directly into the diffusion process, but instead enforced during a post-hoc distillation stage. We term our method as Physics-Informed Distillation of Diffusion Models (PIDDM). This distillation not only facilitates single-step generation with improved PDE satisfaction, but also support both forward and inverse problem solving and reconstruction from randomly partial observation. Extensive experiments across various PDE benchmarks demonstrate that PIDDM significantly improves PDE satisfaction over several recent and competitive baselines, such as PIDM, DiffusionPDE, and ECI-sampling, with less computation overhead. Our approach can shed light on more efficient and effective strategies for incorporating physical constraints into diffusion models.

Paperid: 615, https://arxiv.org/pdf/2505.11755.pdf

Abstract:
Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending safety guarantees to a general control framework, but they are notoriously difficult to generate beyond low dimensions. Existing methods often yield non-differentiable or inaccurate approximations that lack integrity, and thus fail to ensure safety. In this work, we use physics-informed neural networks (PINNs) to generate smooth approximations of CBFs by computing Hamilton-Jacobi (HJ) optimal control solutions. These reachability barrier networks (RBNs) avoid traditional dimensionality constraints and support the tuning of their conservativeness post-training through a parameterized discount term. To ensure robustness of the discounted solutions, we leverage conformal prediction methods to derive probabilistic safety guarantees for RBNs. We demonstrate that RBNs are highly accurate in low dimensions, and safer than the standard neural CBF approach in high dimensions. Namely, we showcase the RBNs in a 9D multi-vehicle collision avoidance problem where it empirically proves to be 5.5x safer and 1.9x less conservative than the neural CBFs, offering a promising method to synthesize CBFs for general nonlinear autonomous systems.

Paperid: 616, https://arxiv.org/pdf/2505.06331.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws directly into the loss function. However, as a fundamental optimization issue, internal covariate shift (ICS) hinders the stable and effective training of PINNs by disrupting feature distributions and limiting model expressiveness. Unlike standard deep learning tasks, conventional remedies for ICS -- such as Batch Normalization and Layer Normalization -- are not directly applicable to PINNs, as they distort the physical consistency required for reliable PDE solutions. To address this issue, we propose Mask-PINNs, a novel architecture that introduces a learnable mask function to regulate feature distributions while preserving the underlying physical constraints of PINNs. We provide a theoretical analysis showing that the mask suppresses the expansion of feature representations through a carefully designed modulation mechanism. Empirically, we validate the method on multiple PDE benchmarks -- including convection, wave propagation, and Helmholtz equations -- across diverse activation functions. Our results show consistent improvements in prediction accuracy, convergence stability, and robustness. Furthermore, we demonstrate that Mask-PINNs enable the effective use of wider networks, overcoming a key limitation in existing PINN frameworks.

Paperid: 617, https://arxiv.org/pdf/2505.05625.pdf

Abstract:
Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability and poor convergence, which hinder effective rate coefficient estimation using learning-based approaches. To address this, we propose a Stiff Physics-Informed Neural ODE framework (SPIN-ODE) for chemical reaction modelling. Our method introduces a three-stage optimisation process: first, a black-box neural ODE is trained to fit concentration trajectories; second, a Chemical Reaction Neural Network (CRNN) is pre-trained to learn the mapping between concentrations and their time derivatives; and third, the rate coefficients are fine-tuned by integrating with the pre-trained CRNN. Extensive experiments on both synthetic and newly proposed real-world datasets validate the effectiveness and robustness of our approach. As the first work addressing stiff neural ODE for chemical rate coefficient discovery, our study opens promising directions for integrating neural networks with detailed chemistry.

Paperid: 618, https://arxiv.org/pdf/2505.03590.pdf

Abstract:
Magnetic resonance spectroscopy (MRS) is a non-invasive technique to measure the metabolic composition of tissues, offering valuable insights into neurological disorders, tumor detection, and other metabolic dysfunctions. However, accurate metabolite quantification is hindered by challenges such as spectral overlap, low signal-to-noise ratio, and various artifacts. Traditional methods like linear-combination modeling are susceptible to ambiguities and commonly only provide a theoretical lower bound on estimation accuracy in the form of the CramÃ©r-Rao bound. This work introduces a Bayesian inference framework using Sylvester normalizing flows (SNFs) to approximate posterior distributions over metabolite concentrations, enhancing quantification reliability. A physics-based decoder incorporates prior knowledge of MRS signal formation, ensuring realistic distribution representations. We validate the method on simulated 7T proton MRS data, demonstrating accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.

Paperid: 619, https://arxiv.org/pdf/2505.01047.pdf

Abstract:
Physics-Informed Machine Learning (PIML) offers a powerful paradigm of integrating data with physical laws to address important scientific problems, such as parameter estimation, inferring hidden physics, equation discovery, and state prediction, etc. However, PIML still faces many serious optimization challenges that significantly restrict its applications. In this study, we propose a comprehensive framework that transforms PIML to convex optimization to overcome all these limitations, referred to as Convex-PIML. The linear combination of B-splines is utilized to approximate the data, promoting the convexity of the loss function. By replacing the non-convex components of the loss function with convex approximations, the problem is further converted into a sequence of successively refined approximated convex optimization problems. This conversion allows the use of well-established convex optimization algorithms, obtaining solutions effectively and efficiently. Furthermore, an adaptive knot optimization method based on error estimate is introduced to mitigate the spectral bias issue of PIML, further improving the performance. The proposed theoretically guaranteed framework is tested in scenarios with distinct types of physical prior. The results indicate that optimization problems are effectively solved in these scenarios, highlighting the potential of the framework for broad applications.

Paperid: 620, https://arxiv.org/pdf/2503.16455.pdf

Abstract:
Quantitative estimation of human joint motion in daily living spaces is essential for early detection and rehabilitation tracking of neuromusculoskeletal disorders (e.g., Parkinson's) and mitigating trip and fall risks for older adults. Existing approaches involve monitoring devices such as cameras, wearables, and pressure mats, but have operational constraints such as direct line-of-sight, carrying devices, and dense deployment. To overcome these limitations, we leverage gait-induced floor vibration to estimate lower-limb joint motion (e.g., ankle, knee, and hip flexion angles), allowing non-intrusive and contactless gait health monitoring in people's living spaces. To overcome the high uncertainty in lower-limb movement given the limited information provided by the gait-induced floor vibrations, we formulate a physics-informed graph to integrate domain knowledge of gait biomechanics and structural dynamics into the model. Specifically, different types of nodes represent heterogeneous information from joint motions and floor vibrations; Their connecting edges represent the physiological relationships between joints and forces governed by gait biomechanics, as well as the relationships between forces and floor responses governed by the structural dynamics. As a result, our model poses physical constraints to reduce uncertainty while allowing information sharing between the body and the floor to make more accurate predictions. We evaluate our approach with 20 participants through a real-world walking experiment. We achieved an average of 3.7 degrees of mean absolute error in estimating 12 joint flexion angles (38% error reduction from baseline), which is comparable to the performance of cameras and wearables in current medical practices.

Paperid: 621, https://arxiv.org/pdf/2503.15168.pdf

Abstract:
World Models help Artificial Intelligence (AI) predict outcomes, reason about its environment, and guide decision-making. While widely used in reinforcement learning, they lack the structured, adaptive representations that even young children intuitively develop. Advancing beyond pattern recognition requires dynamic, interpretable frameworks inspired by Piaget's cognitive development theory. We highlight six key research areas -- physics-informed learning, neurosymbolic learning, continual learning, causal inference, human-in-the-loop AI, and responsible AI -- as essential for enabling true reasoning in AI. By integrating statistical learning with advances in these areas, AI can evolve from pattern recognition to genuine understanding, adaptation and reasoning capabilities.

Paperid: 622, https://arxiv.org/pdf/2502.19890.pdf

Abstract:
This work focuses on understanding the minimum eradication time for the controlled Susceptible-Infectious-Recovered (SIR) model in the time-homogeneous setting, where the infection and recovery rates are constant. The eradication time is defined as the earliest time the infectious population drops below a given threshold and remains below it. For time-homogeneous models, the eradication time is well-defined due to the predictable dynamics of the infectious population, and optimal control strategies can be systematically studied. We utilize Physics-Informed Neural Networks (PINNs) to solve the partial differential equation (PDE) governing the eradication time and derive the corresponding optimal vaccination control. The PINN framework enables a mesh-free solution to the PDE by embedding the dynamics directly into the loss function of a deep neural network. We use a variable scaling method to ensure stable training of PINN and mathematically analyze that this method is effective in our setting. This approach provides an efficient computational alternative to traditional numerical methods, allowing for an approximation of the eradication time and the optimal control strategy. Through numerical experiments, we validate the effectiveness of the proposed method in computing the minimum eradication time and achieving optimal control. This work offers a novel application of PINNs to epidemic modeling, bridging mathematical theory and computational practice for time-homogeneous SIR models.

Paperid: 623, https://arxiv.org/pdf/2502.19543.pdf

Abstract:
Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional numerical solvers due to high computational cost, making them impractical for large-scale applications. Neural operators' reliance on data-driven training limits their applicability in real-world scenarios, as data is often scarce or expensive to obtain. Here, we propose a novel paradigm, physics-informed parallel neural operator (PIPNO), a scalable and unsupervised learning framework that enables data-free PDE modelling by leveraging only governing physical laws. The parallel kernel integration design, incorporating ensemble learning, significantly enhances both compatibility and computational efficiency, enabling scalable operator learning for nonlinear and strongly coupled PDEs. PIPNO efficiently captures nonlinear operator mappings across diverse physics, including geotechnical engineering, material science, electromagnetism, quantum mechanics, and fluid dynamics. The proposed method achieves high-fidelity and rapid predictions, outperforming existing operator learning approaches in modelling nonlinear and strongly coupled multiphysics systems. Therefore, PIPNO offers a powerful alternative to conventional solvers, broadening the applicability of neural operators for multiphysics modelling while ensuring efficiency, robustness, and scalability.

Paperid: 624, https://arxiv.org/pdf/2502.04799.pdf

Abstract:
Finding an $ε$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face a trade-off between global and local convergence. Whether a parameter-free algorithm of this type can simultaneously achieve optimal global complexity and quadratic local convergence remains an open question. To bridge this long-standing gap, we propose a new class of regularizers constructed from the current and previous gradients, and leverage the conjugate gradient approach with a negative curvature monitor to solve the regularized Newton equation. The proposed algorithm is adaptive, requiring no prior knowledge of the Hessian Lipschitz constant, and achieves a global complexity of $O(ε^{-3/2})$ in terms of the second-order oracle calls, and $\tilde{O}(ε^{-7/4})$ for Hessian-vector products, respectively. When the iterates converge to a point where the Hessian is positive definite, the method exhibits quadratic local convergence. Preliminary numerical results, including training the physics-informed neural networks, illustrate the competitiveness of our algorithm.

Paperid: 625, https://arxiv.org/pdf/2501.15085.pdf

Abstract:
The recent advances in information technology and artificial intelligence have fueled a rapid expansion of the data center (DC) industry worldwide, accompanied by an immense appetite for electricity to power the DCs. In a typical DC, around 30~40% of the energy is spent on the cooling system rather than on computer servers, posing a pressing need for developing new energy-saving optimization technologies for DC cooling systems. However, optimizing such real-world industrial systems faces numerous challenges, including but not limited to a lack of reliable simulation environments, limited historical data, and stringent safety and control robustness requirements. In this work, we present a novel physics-informed offline reinforcement learning (RL) framework for energy efficiency optimization of DC cooling systems. The proposed framework models the complex dynamical patterns and physical dependencies inside a server room using a purposely designed graph neural network architecture that is compliant with the fundamental time-reversal symmetry. Because of its well-behaved and generalizable state-action representations, the model enables sample-efficient and robust latent space offline policy learning using limited real-world operational data. Our framework has been successfully deployed and verified in a large-scale production DC for closed-loop control of its air-cooling units (ACUs). We conducted a total of 2000 hours of short and long-term experiments in the production DC environment. The results show that our method achieves 14~21% energy savings in the DC cooling system, without any violation of the safety or operational constraints. Our results have demonstrated the significant potential of offline RL in solving a broad range of data-limited, safety-critical real-world industrial control problems.

Paperid: 626, https://arxiv.org/pdf/2412.05133.pdf

Abstract:
Big data is transforming scientific progress by enabling the discovery of novel models, enhancing existing frameworks, and facilitating precise uncertainty quantification, while advancements in scientific machine learning complement this by providing powerful tools to solve inverse problems to identify the complex systems where traditional methods falter due to sparse or noisy data. We introduce two innovative neural operator frameworks tailored for discovering hidden physics and identifying unknown system parameters from sparse measurements. The first framework integrates a popular neural operator, DeepONet, and a physics-informed neural network to capture the relationship between sparse data and the underlying physics, enabling the accurate discovery of a family of governing equations. The second framework focuses on system parameter identification, leveraging a DeepONet pre-trained on sparse sensor measurements to initialize a physics-constrained inverse model. Both frameworks excel in handling limited data and preserving physical consistency. Benchmarking on the Burgers' equation and reaction-diffusion system demonstrates state-of-the-art performance, achieving average $L_2$ errors of $\mathcal{O}(10^{-2})$ for hidden physics discovery and absolute errors of $\mathcal{O}(10^{-3})$ for parameter identification. These results underscore the frameworks' robustness, efficiency, and potential for solving complex scientific problems with minimal observational data.

Paperid: 627, https://arxiv.org/pdf/2411.11467.pdf

Abstract:
Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for adaptable learning-based methods capable of capturing complex interactions beyond explicit physical models and simulations. While graph neural networks can handle simple scenarios, they struggle with complex scenes and long-term predictions. We introduce a novel framework for modeling rigid body dynamics and learning collision interactions, addressing key limitations of existing graph-based methods. Our approach extends the traditional representation of meshes by incorporating higher-order topology complexes, offering a physically consistent representation. Additionally, we propose a physics-informed message-passing neural architecture, embedding physical laws directly in the model. Our method demonstrates superior accuracy, even during long rollouts, and exhibits strong generalization to unseen scenarios. Importantly, this work addresses the challenge of multi-entity dynamic interactions, with applications spanning diverse scientific and engineering domains.

Paperid: 628, https://arxiv.org/pdf/2411.00989.pdf

Abstract:
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical modeling, nonlinearity, and high dimensionality. In this work, we introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems directly from raw experimental data. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our approach employs time-delay embedding, physics-informed deep autoencoders, and annealing-based regularization to identify novel low-dimensional coordinate representations, unlocking insights across a variety of simulated and previously unstudied experimental dynamical systems. These new coordinate representations enable accurate long-horizon predictions and automatic identification of intricate invariant sets while providing empirical stability guarantees. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering, with broad implications for understanding nonlinear systems in the real world.

Paperid: 629, https://arxiv.org/pdf/2410.19492.pdf

Abstract:
Modeling distributions that depend on external control parameters is a common scenario in diverse applications like molecular simulations, where system properties like temperature affect molecular configurations. Despite the relevance of these applications, existing solutions are unsatisfactory as they require severely restricted model architectures or rely on energy-based training, which is prone to instability. We introduce TRADE, which overcomes these limitations by formulating the learning process as a boundary value problem. By initially training the model for a specific condition using either i.i.d.~samples or backward KL training, we establish a boundary distribution. We then propagate this information across other conditions using the gradient of the unnormalized density with respect to the external parameter. This formulation, akin to the principles of physics-informed neural networks, allows us to efficiently learn parameter-dependent distributions without restrictive assumptions. Experimentally, we demonstrate that TRADE achieves excellent results in a wide range of applications, ranging from Bayesian inference and molecular simulations to physical lattice models.

Paperid: 630, https://arxiv.org/pdf/2410.04096.pdf

Abstract:
In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attention as alternatives to multilayer perceptron. Many different function representations have already been tried, but we show that Sinc interpolation proposes a viable alternative, since it is known in numerical analysis to represent well both smooth functions and functions with singularities. This is important not only for function approximation but also for the solutions of partial differential equations with physics-informed neural networks. Through a series of experiments, we show that SincKANs provide better results in almost all of the examples we have considered.

Paperid: 631, https://arxiv.org/pdf/2409.20383.pdf

Abstract:
Physics-informed neural networks (PINNs) have recently emerged as effective methods for solving partial differential equations (PDEs) in various problems. Substantial research focuses on the failure modes of PINNs due to their frequent inaccuracies in predictions. However, most are based on the premise that minimizing the loss function to zero causes the network to converge to a solution of the governing PDE. In this study, we prove that PINNs encounter a fundamental issue that the premise is invalid. We also reveal that this issue stems from the inability to regulate the behavior of the derivatives of the predicted solution. Inspired by the \textit{derivative pathology} of PINNs, we propose a \textit{variable splitting} strategy that addresses this issue by parameterizing the gradient of the solution as an auxiliary variable. We demonstrate that using the auxiliary variable eludes derivative pathology by enabling direct monitoring and regulation of the gradient of the predicted solution. Moreover, we prove that the proposed method guarantees convergence to a generalized solution for second-order linear PDEs, indicating its applicability to various problems.

Paperid: 632, https://arxiv.org/pdf/2409.01949.pdf

Abstract:
Physics Informed Neural Networks (PINNs) offer several advantages when compared to traditional numerical methods for solving PDEs, such as being a mesh-free approach and being easily extendable to solving inverse problems. One promising approach for allowing PINNs to scale to multi-scale problems is to combine them with domain decomposition; for example, finite basis physics-informed neural networks (FBPINNs) replace the global PINN network with many localised networks which are summed together to approximate the solution. In this work, we significantly accelerate the training of FBPINNs by linearising their underlying optimisation problem. We achieve this by employing extreme learning machines (ELMs) as their subdomain networks and showing that this turns the FBPINN optimisation problem into one of solving a linear system or least-squares problem. We test our workflow in a preliminary fashion by using it to solve an illustrative 1D problem.

Paperid: 633, https://arxiv.org/pdf/2409.01410.pdf

Abstract:
Dataset distillation (DD) is an increasingly important technique that focuses on constructing a synthetic dataset capable of capturing the core information in training data to achieve comparable performance in models trained on the latter. While DD has a wide range of applications, the theory supporting it is less well evolved. New methods of DD are compared on a common set of benchmarks, rather than oriented towards any particular learning task. In this work, we present a formal model of DD, arguing that a precise characterization of the underlying optimization problem must specify the inference task associated with the application of interest. Without this task-specific focus, the DD problem is under-specified, and the selection of a DD algorithm for a particular task is merely heuristic. Our formalization reveals novel applications of DD across different modeling environments. We analyze existing DD methods through this broader lens, highlighting their strengths and limitations in terms of accuracy and faithfulness to optimal DD operation. Finally, we present numerical results for two case studies important in contemporary settings. Firstly, we address a critical challenge in medical data analysis: merging the knowledge from different datasets composed of intersecting, but not identical, sets of features, in order to construct a larger dataset in what is usually a small sample setting. Secondly, we consider out-of-distribution error across boundary conditions for physics-informed neural networks (PINNs), showing the potential for DD to provide more physically faithful data. By establishing this general formulation of DD, we aim to establish a new research paradigm by which DD can be understood and from which new DD techniques can arise.

Paperid: 634, https://arxiv.org/pdf/2601.12143.pdf

Abstract:
Attention-based neural architectures have become central to state-of-the-art methods in real-time nonlinear control. As these data-driven models continue to be integrated into increasingly safety-critical domains, ensuring statistically grounded and provably safe decision-making becomes essential. This paper introduces a novel reactive control framework for gap-based navigation using the Attentive Neural Process (AttNP) and a physics-informed extension, the PI-AttNP. Both models are evaluated in a simulated F1TENTH-style Ackermann steering racecar environment, chosen as a fast-paced proxy for safety-critical autonomous driving scenarios. The PI-AttNP augments the AttNP architecture with approximate model-based priors to inject physical inductive bias, enabling faster convergence and improved prediction accuracy suited for real-time control. To further ensure safety, we derive and implement a control barrier function (CBF)-based filtering mechanism that analytically enforces collision avoidance constraints. This CBF formulation is fully compatible with the learned AttNP controller and generalizes across a wide range of racing scenarios, providing a lightweight and certifiable safety layer. Our results demonstrate competitive closed-loop performance while ensuring real-time constraint satisfaction.

Paperid: 635, https://arxiv.org/pdf/2601.02007.pdf

Abstract:
Accurate and efficient modeling of radio wave propagation in railway tunnels is is critical for ensuring reliable communication-based train control (CBTC) systems. Fine-grid parabolic wave equation (PWE) solvers provide high-fidelity field predictions but are computationally expensive for large-scale tunnels, whereas coarse-grid models lose essential modal and geometric details. To address this challenge, we propose a physics-informed recurrent back-projection propagation network (PRBPN) that reconstructs fine-resolution received-signal-strength (RSS) fields from coarse PWE slices. The network integrates multi-slice temporal fusion with an iterative projection/back-projection mechanism that enforces physical consistency and avoids any pre-upsampling stage, resulting in strong data efficiency and improved generalization. Simulations across four tunnel cross-section geometries and four frequencies show that the proposed PRBPN closely tracks fine-mesh PWE references. Engineering-level validation on the Massif Central tunnel in France further confirms robustness in data-scarce scenarios, trained with only a few paired coarse/fine RSS. These results indicate that the proposed PRBPN can substantially reduce reliance on computationally intensive fine-grid solvers while maintaining high-fidelity tunnel propagation predictions.

Paperid: 636, https://arxiv.org/pdf/2512.14610.pdf

Abstract:
We develop a self-adaptive physics-informed neural network (PINN) framework that reliably solves forward Darcy flow and performs accurate permeability inversion in heterogeneous porous media. In the forward setting, the PINN predicts velocity and pressure for discontinuous, piecewise-constant permeability; in the inverse setting, it identifies spatially varying permeability directly from indirect flow observations. Both models use a region-aware permeability parameterization with binary spatial masks, which preserves sharp permeability jumps and avoids the smoothing artifacts common in standard PINNs. To stabilize training, we introduce self-learned loss weights that automatically balance PDE residuals, boundary constraints, and data mismatch, eliminating manual tuning and improving robustness, particularly for inverse problems. An interleaved AdamW-L-BFGS optimization strategy further accelerates and stabilizes convergence. Numerical results demonstrate accurate forward surrogates and reliable inverse permeability recovery, establishing the method as an effective mesh-free solver and data-driven inversion tool for porous-media systems governed by partial differential equations.

Paperid: 637, https://arxiv.org/pdf/2512.08948.pdf

Abstract:
We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation, physics-informed models, safe reinforcement learning, and algorithmic fairness. We develop a stochastic sequential quadratic programming (SSQP) method to solve these problems, where the step direction is computed by sequentially performing a quadratic approximation of the objective and a linear approximation of the constraints. Despite having access to unbiased estimates of population gradients, a key challenge in constrained stochastic problems lies in dealing with the bias in the step direction. As such, we apply a momentum-style gradient moving-average technique within SSQP to debias the step. We show that our method achieves global almost-sure convergence and exhibits local asymptotic normality with an optimal primal-dual limiting covariance matrix in the sense of Hájek and Le Cam. In addition, we provide a plug-in covariance matrix estimator for practical inference. To our knowledge, the proposed SSQP method is the first fully online method that attains primal-dual asymptotic minimax optimality without relying on projection operators onto the constraint set, which are generally intractable for nonlinear problems. Through extensive experiments on benchmark nonlinear problems, as well as on constrained generalized linear models and portfolio allocation problems using both synthetic and real data, we demonstrate superior performance of our method, showing that the method and its asymptotic behavior not only solve constrained stochastic problems efficiently but also provide valid and practical online inference in real-world applications.

Paperid: 638, https://arxiv.org/pdf/2512.01897.pdf

Abstract:
Autonomous ground vehicles (AGVs) must navigate safely in cluttered environments while accounting for complex dynamics and environmental uncertainty. Hamilton-Jacobi Reachability (HJR) offers formal safety guarantees through the computation of forward and backward reachable sets, but its application is hindered by poor scalability in environments with numerous obstacles. In this paper, we present a novel framework called NeuroHJR that leverages Physics-Informed Neural Networks (PINNs) to approximate the HJR solution for real-time obstacle avoidance. By embedding system dynamics and safety constraints directly into the neural network loss function, our method bypasses the need for grid-based discretization and enables efficient estimation of reachable sets in continuous state spaces. We demonstrate the effectiveness of our approach through simulation results in densely cluttered scenarios, showing that it achieves safety performance comparable to that of classical HJR solvers while significantly reducing the computational cost. This work provides a new step toward real-time, scalable deployment of reachability-based obstacle avoidance in robotics.

Paperid: 639, https://arxiv.org/pdf/2511.13595.pdf

Abstract:
This work addresses the full-information output regulation problem for nonlinear systems, assuming the states of both the plant and the exosystem are known. In this setting, perfect tracking or rejection is achieved by constructing a zero-regulation-error manifold $π(w)$ and a feedforward input $c(w)$ that render such manifold invariant. The pair $(π(w), c(w))$ is characterized by the regulator equations, i.e., a system of PDEs with an algebraic constraint. We focus on accurately solving the regulator equations introducing a physics-informed neural network (PINN) approach that directly approximates $π(w)$ and $c(w)$ by minimizing the residuals under boundary and feasibility conditions, without requiring precomputed trajectories or labeled data. The learned operator maps exosystem states to steady state plant states and inputs, enables real-time inference and, critically, generalizes across families of the exosystem with varying initial conditions and parameters. The framework is validated on a regulation task that synchronizes a helicopter's vertical dynamics with a harmonically oscillating platform. The resulting PINN-based solver reconstructs the zero-error manifold with high fidelity and sustains regulation performance under exosystem variations, highlighting the potential of learning-enabled solvers for nonlinear output regulation. The proposed approach is broadly applicable to nonlinear systems that admit a solution to the output regulation problem.

Paperid: 640, https://arxiv.org/pdf/2511.08231.pdf

Abstract:
Various neural network architectures are used in many of the state-of-the-art approaches for real-time nonlinear state estimation. With the ever-increasing incorporation of these data-driven models into the estimation domain, model predictions with reliable margins of error are a requirement -- especially for safety-critical applications. This paper discusses the application of a novel real-time, data-driven estimation approach based on the multi-fidelity residual physics-informed neural process (MFR-PINP) toward the real-time state estimation of a robotic system. Specifically, we address the model-mismatch issue of selecting an accurate kinematic model by tasking the MFR-PINP to also learn the residuals between simple, low-fidelity predictions and complex, high-fidelity ground-truth dynamics. To account for model uncertainty present in a physical implementation, robust uncertainty guarantees from the split conformal (SC) prediction framework are modeled in the training and inference paradigms. We provide implementation details of our MFR-PINP-based estimator for a hybrid online learning setting to validate our model's usage in real-time applications. Experimental results of our approach's performance in comparison to the state-of-the-art variants of the Kalman filter (i.e. unscented Kalman filter and deep Kalman filter) in estimation scenarios showed promising results for the MFR-PINP model as a viable option in real-time estimation tasks.

Paperid: 641, https://arxiv.org/pdf/2511.06583.pdf

Abstract:
Traditional statistical optimization-based state estimation (DSSE) algorithms rely on detailed grid parameters and mathematical assumptions of all possible uncertainties. Furthermore, random data missing due to communication failures, congestion, and cyberattacks, makes these methods easily infeasible. Inspired by recent advances in digital twins (DTs), this paper proposes an interactive attention-based DSSE model for robust grid monitoring by integrating three core components: physical entities, virtual modeling, and data fusion. To enable robustness against various data missing in heterogeneous measurements, we first propose physics-informed data augmentation and transfer. Moreover, a state-of-the-art attention-based spatiotemporal feature learning is proposed, followed by a novel cross-interaction feature fusion for robust voltage estimation. A case study in a real-world unbalanced 84-bus distribution system with raw data validates the accuracy and robustness of the proposed DT model in estimating voltage states, with random locational, arbitrary ratios (up to 40% of total measurements) of data missing.

Paperid: 642, https://arxiv.org/pdf/2511.04665.pdf

Abstract:
Robotic manipulation policies are advancing rapidly, but their direct evaluation in the real world remains costly, time-consuming, and difficult to reproduce, particularly for tasks involving deformable objects. Simulation provides a scalable and systematic alternative, yet existing simulators often fail to capture the coupled visual and physical complexity of soft-body interactions. We present a real-to-sim policy evaluation framework that constructs soft-body digital twins from real-world videos and renders robots, objects, and environments with photorealistic fidelity using 3D Gaussian Splatting. We validate our approach on representative deformable manipulation tasks, including plush toy packing, rope routing, and T-block pushing, demonstrating that simulated rollouts correlate strongly with real-world execution performance and reveal key behavioral patterns of learned policies. Our results suggest that combining physics-informed reconstruction with high-quality rendering enables reproducible, scalable, and accurate evaluation of robotic manipulation policies. Website: https://real2sim-eval.github.io/

Paperid: 643, https://arxiv.org/pdf/2511.02694.pdf

Abstract:
We present DropleX, the first system that enables liquid sensing using the capacitive touchscreen of commodity tablets. DropleX detects microliter-scale liquid samples, and performs non-invasive, through-container measurements to detect whether a drink has been spiked or if a sealed liquid has been contaminated. These capabilities are made possible by a physics-informed mechanism that disables the touchscreen's built-in adaptive filters, originally designed to reject the effects of liquid drops such as rain, without any hardware modifications. We model the touchscreen's sensing capabilities, limits, and non-idealities to inform the design of a signal processing and learning-based pipeline for liquid sensing. Our system achieves 96-99% accuracy in detecting microliter-scale adulteration in soda, wine, and milk, 93-96% accuracy in threshold detection of trace chemical concentrations, and 86-96% accuracy in through-container adulterant detection. Given the predominance of touchscreens, these exploratory results can open new opportunities for liquid sensing on everyday devices.

Paperid: 644, https://arxiv.org/pdf/2510.24557.pdf

Abstract:
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be enforced either weakly by penalizing deviations in the loss function or strongly by training a solution structure that inherently matches the prescribed values and derivatives. The former approach is easy to implement but the latter can provide benefits with respect to accuracy and training times. However, previous approaches to strongly enforcing Neumann or Robin boundary conditions require a domain with a fully $C^1$ boundary and, as we demonstrate, can lead to instability if those boundary conditions are posed on a segment of the boundary that is piecewise $C^1$ but only $C^0$ globally. We introduce a generalization of the approach by Sukumar \& Srivastava (doi: 10.1016/j.cma.2021.114333), and a new approach based on orthogonal projections that overcome this limitation. The performance of these new techniques is compared against weakly and semi-weakly enforced boundary conditions for the scalar Darcy flow equation and the stationary Navier-Stokes equations.

Paperid: 645, https://arxiv.org/pdf/2510.23810.pdf

Abstract:
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to obtain in some real-world engineering applications. These datasets may be unevenly discretized from one realization to another, with the grid resolution varying across samples. In this study, we introduce a physics-informed operator learning approach by extending the Resolution Independent Neural Operator (RINO) framework to a fully data-free setup, addressing both challenges simultaneously. Here, the arbitrarily (but sufficiently finely) discretized input functions are projected onto a latent embedding space (i.e., a vector space of finite dimensions), using pre-trained basis functions. The operator associated with the underlying partial differential equations (PDEs) is then approximated by a simple multi-layer perceptron (MLP), which takes as input a latent code along with spatiotemporal coordinates to produce the solution in the physical space. The PDEs are enforced via a finite difference solver in the physical space. The validation and performance of the proposed method are benchmarked on several numerical examples with multi-resolution data, where input functions are sampled at varying resolutions, including both coarse and fine discretizations.

Paperid: 646, https://arxiv.org/pdf/2510.23181.pdf

Abstract:
Discovering materials with previously unreported crystal frameworks is key to achieving transformative functionality. Generative artificial intelligence offers a scalable means to propose candidate crystal structures, however existing approaches mainly reproduce decorated variants of established motifs rather than uncover new configurations. Here we develop a physics-informed diffusion method, supported by chemically grounded validation protocol, which embeds descriptors of compactness and local environment diversity to balance physical plausibility with structural novelty. Conditioning on these metrics improves generative performance across architectures, increasing the fraction of structures outside 100 most common prototypes up to 67%. When crystal structure prediction (CSP) is seeded with generative structures, most candidates (97%) are reconstructed by CSP, yielding 145 (66%) low-energy frameworks not matching any known prototypes. These results show that while generative models are not substitutes for CSP, their chemically informed, diversity-guided outputs can enhance CSP efficiency, establishing a practical generative-CSP synergy for discovery-oriented exploration of chemical space.

Paperid: 647, https://arxiv.org/pdf/2510.21238.pdf

Abstract:
As communication networks evolve towards greater complexity (e.g., 6G and beyond), a deep understanding of the wireless environment becomes increasingly crucial. When explicit knowledge of the environment is unavailable, geometry-aware feature extraction from channel state information (CSI) emerges as a pivotal methodology to bridge physical-layer measurements with network intelligence. This paper proposes to explore the received signal strength (RSS) data, without explicit 3D environment knowledge, to jointly construct the radio beam map and environmental geometry for a multiple-input multiple-output (MIMO) system. Unlike existing methods that only learn blockage structures, we propose an oriented virtual obstacle model that captures the geometric features of both blockage and reflection. Reflective zones are formulated to identify relevant reflected paths according to the geometry relation of the environment. We derive an analytical expression for the reflective zone and further analyze its geometric characteristics to develop a reformulation that is more compatible with deep learning representations. A physics-informed deep learning framework that incorporates the reflective-zone-based geometry model is proposed to learn the blockage, reflection, and scattering components, along with the beam pattern, which leverages physics prior knowledge to enhance network transferability. Numerical experiments demonstrate that, in addition to reconstructing the blockage and reflection geometry, the proposed model can construct a more accurate MIMO beam map with a 32%-48% accuracy improvement.

Paperid: 648, https://arxiv.org/pdf/2510.17762.pdf

Abstract:
We apply a physics-informed neural network (PINN) to solve the two-point boundary value problem (BVP) arising from the necessary conditions postulated by Pontryagin's Minimum Principle for optimal control. Such BVPs are known to be numerically difficult to solve by traditional shooting methods due to extremely high sensitivity to initial guesses. In the light of recent successes in applying PINNs for solving high-dimensional differential equations, we develop a PINN to solve the problem of finding trajectories with minimum exposure to a spatiotemporal threat for a vehicle kinematic model. First, we implement PINNs that are trained to solve the BVP for a given pair of initial and final states for a given threat field. Next, we implement a PINN conditioned on the initial state for a given threat field, which eliminates the need for retraining for each initial state. We demonstrate that the PINN outputs satisfy the necessary conditions with low numerical error.

Paperid: 649, https://arxiv.org/pdf/2510.15075.pdf

Abstract:
Two-photon lithography (TPL) is a sophisticated additive manufacturing technology for creating three-dimensional (3D) micro- and nano-structures. Maintaining the health of TPL systems is critical for ensuring consistent fabrication quality. Current maintenance practices often rely on experience rather than informed monitoring of machine health, resulting in either untimely maintenance that causes machine downtime and poor-quality fabrication, or unnecessary maintenance that leads to inefficiencies and avoidable downtime. To address this gap, this paper presents three methods for accurate and timely monitoring of TPL machine health. Through integrating physics-informed data-driven predictive models for structure dimensions with statistical approaches, the proposed methods are able to handle increasingly complex scenarios featuring different levels of generalizability. A comprehensive experimental dataset that encompasses six process parameter combinations and six structure dimensions under two machine health conditions was collected to evaluate the effectiveness of the proposed approaches. Across all test scenarios, the approaches are shown to achieve high accuracies, demonstrating excellent effectiveness, robustness, and generalizability. These results represent a significant step toward condition-based maintenance for TPL systems.

Paperid: 650, https://arxiv.org/pdf/2510.09082.pdf

Abstract:
Learning complex network dynamics is fundamental to understanding, modelling and controlling real-world complex systems. There are two main problems in the task of predicting the dynamic evolution of complex networks: on the one hand, existing methods usually use simple graphs to describe the relationships in complex networks; however, this approach can only capture pairwise relationships, while there may be rich non-pairwise structured relationships in the network. First-order GNNs have difficulty in capturing dynamic non-pairwise relationships. On the other hand, theoretical prediction models lack accuracy and data-driven prediction models lack interpretability. To address the above problems, this paper proposes a higher-order network dynamics identification method for long-term dynamic prediction of complex networks. Firstly, to address the problem that traditional graph machine learning can only deal with pairwise relations, dynamic hypergraph learning is introduced to capture the higher-order non-pairwise relations among complex networks and improve the accuracy of complex network modelling. Then, a dual-driven dynamic prediction module for physical data is proposed. The Koopman operator theory is introduced to transform the nonlinear dynamical differential equations for the dynamic evolution of complex networks into linear systems for solving. Meanwhile, the physical information neural differential equation method is utilised to ensure that the dynamic evolution conforms to the physical laws. The dual-drive dynamic prediction module ensures both accuracy and interpretability of the prediction. Validated on public datasets and self-built industrial chain network datasets, the experimental results show that the method in this paper has good prediction accuracy and long-term prediction performance.

Paperid: 651, https://arxiv.org/pdf/2510.01519.pdf

Abstract:
Robot navigation in large, complex, and unknown indoor environments is a challenging problem. The existing approaches, such as traditional sampling-based methods, struggle with resolution control and scalability, while imitation learning-based methods require a large amount of demonstration data. Active Neural Time Fields (ANTFields) have recently emerged as a promising solution by using local observations to learn cost-to-go functions without relying on demonstrations. Despite their potential, these methods are hampered by challenges such as spectral bias and catastrophic forgetting, which diminish their effectiveness in complex scenarios. To address these issues, our approach decomposes the planning problem into a hierarchical structure. At the high level, a sparse graph captures the environment's global connectivity, while at the low level, a planner based on neural fields navigates local obstacles by solving the Eikonal PDE. This physics-informed strategy overcomes common pitfalls like spectral bias and neural field fitting difficulties, resulting in a smooth and precise representation of the cost landscape. We validate our framework in large-scale environments, demonstrating its enhanced adaptability and precision compared to previous methods, and highlighting its potential for online exploration, mapping, and real-world navigation.

Paperid: 652, https://arxiv.org/pdf/2509.26358.pdf

Abstract:
Solving nonlinear algebraic equations is a fundamental but challenging problem in scientific computations and also has many applications in system engineering. Though traditional iterative methods and modern optimization algorithms have exerted effective roles in addressing certain specific problems, there still exist certain weaknesses such as the initial value sensitivity, limited accuracy and slow convergence rate, particulary without flexible input for the neural network methods. In this paper, we propose a homotopy auxiliary neural network (HANN) for solving nonlinear algebraic equations which integrates the classical homotopy continuation method and popular physics-informed neural network. Consequently, the HANN-1 has strong learning ability and can rapidly give an acceptable solution for the problem which outperforms some known methods, while the HANN-2 can further improve its accuracy. Numerical results on the benchmark problems confirm that the HANN method can effectively solve the problems of determining the total number of solutions of a single equation, finding solutions of transcendental systems involving the absolute value function or trigonometric function, ill-conditioned and normal high-dimensional nonlinear systems and time-varying nonlinear problems, for which the Python's built-in Fsolve function exhibits significant limitations, even fails to work.

Paperid: 653, https://arxiv.org/pdf/2509.20733.pdf

Abstract:
Variational quantum algorithms (VQAs) are leading strategies to reach practical utilities of near-term quantum devices. However, the no-cloning theorem in quantum mechanics precludes standard backpropagation, leading to prohibitive quantum resource costs when applying VQAs to large-scale tasks. To address this challenge, we reformulate the training dynamics of VQAs as a nonlinear partial differential equation and propose a novel protocol that leverages physics-informed neural networks (PINNs) to model this dynamical system efficiently. Given a small amount of training trajectory data collected from quantum devices, our protocol predicts the parameter updates of VQAs over multiple iterations on the classical side, dramatically reducing quantum resource costs. Through systematic numerical experiments, we demonstrate that our method achieves up to a 30x speedup compared to conventional methods and reduces quantum resource costs by as much as 90\% for tasks involving up to 40 qubits, including ground state preparation of different quantum systems, while maintaining competitive accuracy. Our approach complements existing techniques aimed at improving the efficiency of VQAs and further strengthens their potential for practical applications.

Paperid: 654, https://arxiv.org/pdf/2509.12522.pdf

Abstract:
Various neural network architectures are used in many of the state-of-the-art approaches for real-time nonlinear state estimation in dynamical systems. With the ever-increasing incorporation of these data-driven models into the estimation domain, models with reliable margins of error are required -- especially for safety-critical applications. This paper discusses a novel hybrid, data-driven state estimation approach based on the physics-informed attentive neural process (PI-AttNP), a model-informed extension of the attentive neural process (AttNP). We augment this estimation approach with the regression-based split conformal prediction (CP) framework to obtain quantified model uncertainty with probabilistic guarantees. After presenting the algorithm in a generic form, we validate its performance in the task of grey-box state estimation of a simulated under-actuated six-degree-of-freedom quadrotor with multimodal Gaussian sensor noise and several external perturbations typical to quadrotors. Further, we compare outcomes with state-of-the-art data-driven methods, which provide significant evidence of the physics-informed neural process as a viable novel approach for model-driven estimation.

Paperid: 655, https://arxiv.org/pdf/2509.10866.pdf

Abstract:
We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By encoding the underlying physical laws into the loss function and designing network architectures that incorporate the singular behavior and dynamic boundaries, our approach enables robust and accurate solutions to both ordinary and partial differential equations with complex boundary conditions. We demonstrate the versatility of this framework through applications to minimal surface problems in anti-de Sitter (AdS) spacetime, including examples relevant to the AdS/CFT correspondence (e.g. Wilson loops and gluon scattering amplitudes) popularly used in the context of string theory in theoretical physics. Our methods efficiently handle singularities at boundaries, and also support both "soft" (loss-based) and "hard" (formulation-based) imposition of boundary conditions, including cases where the position of a boundary is promoted to a trainable parameter. The techniques developed here are not limited to high-energy theoretical physics but are broadly applicable to boundary value problems encountered in mathematics, engineering, and the natural sciences, wherever singularities and moving boundaries play a critical role.

Paperid: 656, https://arxiv.org/pdf/2509.00203.pdf

Abstract:
Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is to accurately infer the parameters, particularly when the parameters exhibit non-linear and spatiotemporal variations. Existing parameter estimation methods, such as sparse identification and physics-informed neural networks (PINNs), struggle in such cases, especially with nonlinear dynamics, multiphysics interactions, or limited observations of the system response. To address these challenges, we introduce Neptune, a general-purpose method capable of inferring parameter fields from sparse measurements of system responses. Neptune employs independent coordinate neural networks to continuously represent each parameter field in physical space or in state variables. Across various physical and biomedical problems, where direct parameter measurements are prohibitively expensive or unattainable, Neptune significantly outperforms existing methods, achieving robust parameter estimation from as few as 50 observations, reducing parameter estimation errors by two orders of magnitude and dynamic response prediction errors by a factor of ten compared to PINNs. Furthermore, Neptune exhibits superior extrapolation capabilities, enabling accurate predictions in regimes beyond training data where PINN fail. By facilitating reliable and data-efficient parameter inference, Neptune promises broad transformative impacts in engineering, healthcare, and beyond.

Paperid: 657, https://arxiv.org/pdf/2508.21022.pdf

Abstract:
Subsampled natural gradient descent (SNGD) has shown impressive results for parametric optimization tasks in scientific machine learning, such as neural network wavefunctions and physics-informed neural networks, but it has lacked a theoretical explanation. We address this gap by analyzing the convergence of SNGD and its accelerated variant, SPRING, for idealized parametric optimization problems where the model is linear and the loss function is strongly convex and quadratic. In the special case of a least-squares loss, namely the standard linear least-squares problem, we prove that SNGD is equivalent to a regularized Kaczmarz method while SPRING is equivalent to an accelerated regularized Kaczmarz method. As a result, by leveraging existing analyses we obtain under mild conditions (i) the first fast convergence rate for SNGD, (ii) the first convergence guarantee for SPRING in any setting, and (iii) the first proof that SPRING can accelerate SNGD. In the case of a general strongly convex quadratic loss, we extend the analysis of the regularized Kaczmarz method to obtain a fast convergence rate for SNGD under stronger conditions, providing the first explanation for the effectiveness of SNGD outside of the least-squares setting. Overall, our results illustrate how tools from randomized linear algebra can shed new light on the interplay between subsampling and curvature-aware optimization strategies.

Paperid: 658, https://arxiv.org/pdf/2508.15695.pdf

Abstract:
We present several advances to the physics and equality constrained artificial neural networks (PECANN) framework that substantially improve its capability to learn solutions of canonical partial differential equations (PDEs). First, we generalize the augmented Lagrangian method (ALM) to support multiple independent penalty parameters, enabling simultaneous enforcement of heterogeneous constraints. Second, we reformulate pointwise constraint enforcement and Lagrange multipliers as expectations over constraint terms, reducing memory overhead and permitting efficient mini-batch training. Third, to address PDEs with oscillatory, multi-scale features, we incorporate Fourier feature mappings and show that a single mapping suffices where multiple mappings or more costly architectures were required in related methods. Fourth, we introduce a time-windowing strategy for long-time evolution in which the terminal state of each window is enforced as an initial-condition constraint for the next, ensuring continuity without discrete time models. Crucially, we propose a conditionally adaptive penalty update (CAPU) strategy for ALM, which preserves the principle that larger constraint violations incur stronger penalties. CAPU accelerates the growth of Lagrange multipliers for selectively challenging constraints, enhancing constraint enforcement during training. We demonstrate the effectiveness of PECANN-CAPU on problems including the transonic rarefaction problem, reversible advection of a passive by a vortex, high-wavenumber Helmholtz and Poisson equations, and inverse identification of spatially varying heat sources. Comparisons with established methods and recent Kolmogorov-Arnold network approaches show that PECANN-CAPU achieves competitive accuracy across all cases. Collectively, these advances improve PECANN's robustness, efficiency, and applicability to demanding problems in scientific computing.

Paperid: 659, https://arxiv.org/pdf/2507.12941.pdf

Abstract:
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally expensive. While deep-learning-based approaches, such as Physics-Informed Neural Networks (PINNs) and the Random Feature Method (RFM), offer mesh-free alternatives, they often lack adaptive resolution in critical regions, limiting their accuracy for solutions with steep gradients or singularities. In this work, we propose the Adaptive Feature Capture Method (AFCM), a novel machine learning framework that adaptively redistributes neurons and collocation points in high-gradient regions to enhance local expressive power. Inspired by adaptive moving mesh techniques, AFCM employs the gradient norm of an approximate solution as a monitor function to guide the reinitialization of feature function parameters. This ensures that partition hyperplanes and collocation points cluster where they are most needed, achieving higher resolution without increasing computational overhead. The AFCM extends the capabilities of RFM to handle PDEs with near-singular solutions while preserving its mesh-free efficiency. Numerical experiments demonstrate the method's effectiveness in accurately resolving near-singular problems, even in complex geometries. By bridging the gap between adaptive mesh refinement and randomized neural networks, AFCM offers a robust and scalable approach for solving challenging PDEs in scientific and engineering applications.

Paperid: 660, https://arxiv.org/pdf/2506.18565.pdf

Abstract:
Modeling viscoelastic behavior is crucial in engineering and biomechanics, where materials undergo time-dependent deformations, including stress relaxation, creep buckling and biological tissue development. Traditional numerical methods, like the finite element method, often require explicit meshing, artificial perturbations or embedding customised programs to capture these phenomena, adding computational complexity. In this study, we develop an energy-based physics-informed neural network (PINN) framework using an incremental approach to model viscoelastic creep, stress relaxation, buckling, and growth-induced morphogenesis. Physics consistency is ensured by training neural networks to minimize the systems potential energy functional, implicitly satisfying equilibrium and constitutive laws. We demonstrate that this framework can naturally capture creep buckling without pre-imposed imperfections, leveraging inherent training dynamics to trigger instabilities. Furthermore, we extend our framework to biological tissue growth and morphogenesis, predicting both uniform expansion and differential growth-induced buckling in cylindrical structures. Results show that the energy-based PINN effectively predicts viscoelastic instabilities, post-buckling evolution and tissue morphological evolution, offering a promising alternative to traditional methods. This study demonstrates that PINN can be a flexible robust tool for modeling complex, time-dependent material behavior, opening possible applications in structural engineering, soft materials, and tissue development.

Paperid: 661, https://arxiv.org/pdf/2506.12902.pdf

Abstract:
In the modern context of power systems, rapid, scalable, and physically plausible power flow predictions are essential for ensuring the grid's safe and efficient operation. While traditional numerical methods have proven robust, they require extensive computation to maintain physical fidelity under dynamic or contingency conditions. In contrast, recent advancements in artificial intelligence (AI) have significantly improved computational speed; however, they often fail to enforce fundamental physical laws during real-world contingencies, resulting in physically implausible predictions. In this work, we introduce KCLNet, a physics-informed graph neural network that incorporates Kirchhoff's Current Law as a hard constraint via hyperplane projections. KCLNet attains competitive prediction accuracy while ensuring zero KCL violations, thereby delivering reliable and physically consistent power flow predictions critical to secure the operation of modern smart grids.

Paperid: 662, https://arxiv.org/pdf/2506.08475.pdf

Abstract:
We propose an efficient thermodynamics-informed latent space dynamics identification (tLaSDI) framework for the reduced-order modeling of parametric nonlinear dynamical systems. This framework integrates autoencoders for dimensionality reduction with newly developed parametric GENERIC formalism-informed neural networks (pGFINNs), which enable efficient learning of parametric latent dynamics while preserving key thermodynamic principles such as free energy conservation and entropy generation across the parameter space. To further enhance model performance, a physics-informed active learning strategy is incorporated, leveraging a greedy, residual-based error indicator to adaptively sample informative training data, outperforming uniform sampling at equivalent computational cost. Numerical experiments on the Burgers' equation and the 1D/1V Vlasov-Poisson equation demonstrate that the proposed method achieves up to 3,528x speed-up with 1-3% relative errors, and significant reduction in training (50-90%) and inference (57-61%) cost. Moreover, the learned latent space dynamics reveal the underlying thermodynamic behavior of the system, offering valuable insights into the physical-space dynamics.

Paperid: 663, https://arxiv.org/pdf/2505.19136.pdf

Abstract:
Uncertainty quantification (UQ) in scientific machine learning is increasingly critical as neural networks are widely adopted to tackle complex problems across diverse scientific disciplines. For physics-informed neural networks (PINNs), a prominent model in scientific machine learning, uncertainty is typically quantified using Bayesian or dropout methods. However, both approaches suffer from a fundamental limitation: the prior distribution or dropout rate required to construct honest confidence sets cannot be determined without additional information. In this paper, we propose a novel method within the framework of extended fiducial inference (EFI) to provide rigorous uncertainty quantification for PINNs. The proposed method leverages a narrow-neck hyper-network to learn the parameters of the PINN and quantify their uncertainty based on imputed random errors in the observations. This approach overcomes the limitations of Bayesian and dropout methods, enabling the construction of honest confidence sets based solely on observed data. This advancement represents a significant breakthrough for PINNs, greatly enhancing their reliability, interpretability, and applicability to real-world scientific and engineering challenges. Moreover, it establishes a new theoretical framework for EFI, extending its application to large-scale models, eliminating the need for sparse hyper-networks, and significantly improving the automaticity and robustness of statistical inference.

Paperid: 664, https://arxiv.org/pdf/2505.12149.pdf

Abstract:
Natural gradient methods significantly accelerate the training of Physics-Informed Neural Networks (PINNs), but are often prohibitively costly. We introduce a suite of techniques to improve the accuracy and efficiency of energy natural gradient descent (ENGD) for PINNs. First, we leverage the Woodbury formula to dramatically reduce the computational complexity of ENGD. Second, we adapt the Subsampled Projected-Increment Natural Gradient Descent algorithm from the variational Monte Carlo literature to accelerate the convergence. Third, we explore the use of randomized algorithms to further reduce the computational cost in the case of large batch sizes. We find that randomization accelerates progress in the early stages of training for low-dimensional problems, and we identify key barriers to attaining acceleration in other scenarios. Our numerical experiments demonstrate that our methods outperform previous approaches, achieving the same $L^2$ error as the original ENGD up to $75\times$ faster.

Paperid: 665, https://arxiv.org/pdf/2505.07855.pdf

Abstract:
Accurate and interpretable motion planning is essential for autonomous vehicles (AVs) navigating complex and uncertain environments. While recent end-to-end occupancy prediction methods have improved environmental understanding, they typically lack explicit physical constraints, limiting safety and generalization. In this paper, we propose a unified end-to-end framework that integrates verifiable physical rules into the occupancy learning process. Specifically, we embed artificial potential fields (APF) as physics-informed guidance during network training to ensure that predicted occupancy maps are both data-efficient and physically plausible. Our architecture combines convolutional and recurrent neural networks to capture spatial and temporal dependencies while preserving model flexibility. Experimental results demonstrate that our method improves task completion rate, safety margins, and planning efficiency across diverse driving scenarios, confirming its potential for reliable deployment in real-world AV systems.

Paperid: 666, https://arxiv.org/pdf/2505.04627.pdf

Abstract:
The rise of deep learning challenges the longstanding scientific ideal of insight - the human capacity to understand phenomena by uncovering underlying mechanisms. In many modern applications, accurate predictions no longer require interpretable models, prompting debate about whether explainability is a realistic or even meaningful goal. From our perspective in physics, we examine this tension through a concrete case study: a physics-informed neural network (PINN) trained on a rarefied gas dynamics problem governed by the Boltzmann equation. Despite the system's clear structure and well-understood governing laws, the trained network's weights resemble Gaussian-distributed random matrices, with no evident trace of the physical principles involved. This suggests that deep learning and traditional simulation may follow distinct cognitive paths to the same outcome - one grounded in mechanistic insight, the other in statistical interpolation. Our findings raise critical questions about the limits of explainable AI and whether interpretability can - or should-remain a universal standard in artificial reasoning.

Paperid: 667, https://arxiv.org/pdf/2505.04263.pdf

Abstract:
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport in biological cells to the motion of human crowds. While traditional numerical schemes require a large amount of tailoring, especially in the case of model design or parameter identification problems, physics informed deep operator networks (DeepONet) have emerged as a versatile tool for the solution of partial differential equations with the particular advantage that they easily incorporate parameter identification questions. We here present an approach where we first learn three DeepONet models for representative inflow, inner and outflow edges, resp., and then subsequently couple these models for the solution of the drift-diffusion metric graph problem by relying on an edge-based domain decomposition approach. We illustrate that our framework is applicable for the accurate evaluation of graph-coupled physics models and is well suited for solving optimization or inverse problems on these coupled networks.

Paperid: 668, https://arxiv.org/pdf/2504.19372.pdf

Abstract:
An adaptive physics-informed model design strategy for machine-learning interatomic potentials (MLIPs) is proposed. This strategy follows an iterative reconfiguration of composite models from single-term models, followed by a unified training procedure. A model evaluation method based on the Fisher information matrix (FIM) and multiple-property error metrics is proposed to guide model reconfiguration and hyperparameter optimization. Combining the model reconfiguration and the model evaluation subroutines, we provide an adaptive MLIP design strategy that balances flexibility and extensibility. In a case study of designing models against a structurally diverse niobium dataset, we managed to obtain an optimal configuration with 75 parameters generated by our framework that achieved a force RMSE of 0.172 eV/Ã and an energy RMSE of 0.013 eV/atom.

Paperid: 669, https://arxiv.org/pdf/2504.17966.pdf

Abstract:
The ability to predict trajectories of surrounding agents and obstacles is a crucial component in many robotic applications. Data-driven approaches are commonly adopted for state prediction in scenarios where the underlying dynamics are unknown. However, the performance, reliability, and uncertainty of data-driven predictors become compromised when encountering out-of-distribution observations relative to the training data. In this paper, we introduce a Plug-and-Play Physics-Informed Machine Learning (PnP-PIML) framework to address this challenge. Our method employs conformal prediction to identify outlier dynamics and, in that case, switches from a nominal predictor to a physics-consistent model, namely distributed Port-Hamiltonian systems (dPHS). We leverage Gaussian processes to model the energy function of the dPHS, enabling not only the learning of system dynamics but also the quantification of predictive uncertainty through its Bayesian nature. In this way, the proposed framework produces reliable physics-informed predictions even for the out-of-distribution scenarios.

Paperid: 670, https://arxiv.org/pdf/2504.13875.pdf

Abstract:
This paper presents a physics-informed training framework for projection-based Reduced Order Models (ROMs). We extend the PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual loss, bridging the gap between traditional projection-based ROMs and physics-informed neural networks (PINNs). Unlike conventional PINNs that rely on analytical PDEs, our approach leverages FEM residuals to guide the learning of the ROM approximation manifold. Key contributions include: (1) a parameter-agnostic, discrete residual loss applicable to non-linear problems, (2) an architectural modification to PROM-ANN improving accuracy for fast-decaying singular values, and (3) an empirical study on the proposed physics informed training process for ROMs. The method is demonstrated on a non-linear hyperelasticity problem, simulating a rubber cantilever under multi-axial loads. The main accomplishment in regards to the proposed residual-based loss is its applicability on non-linear problems by interfacing with FEM software while maintaining reasonable training times. The modified PROM-ANN outperforms POD by orders of magnitude in snapshot reconstruction accuracy, while the original formulation is not able to learn a proper mapping for this use-case. Finally, the application of physics informed training in ANN-PROM modestly narrows the gap between data reconstruction and ROM accuracy, however it highlights the untapped potential of the proposed residual-driven optimization for future ROM development. This work underscores the critical role of FEM residuals in ROM construction and calls for further exploration on architectures beyond PROM-ANN.

Paperid: 671, https://arxiv.org/pdf/2504.02918.pdf

Abstract:
Recent advances in image and video generation raise hopes that these models possess world modeling capabilities, the ability to generate realistic, physically plausible videos. This could revolutionize applications in robotics, autonomous driving, and scientific simulation. However, before treating these models as world models, we must ask: Do they adhere to physical conservation laws? To answer this, we introduce Morpheus, a benchmark for evaluating video generation models on physical reasoning. It features 80 real-world videos capturing physical phenomena, guided by conservation laws. Since artificial generations lack ground truth, we assess physical plausibility using physics-informed metrics evaluated with respect to infallible conservation laws known per physical setting, leveraging advances in physics-informed neural networks and vision-language foundation models. Our findings reveal that even with advanced prompting and video conditioning, current models struggle to encode physical principles despite generating aesthetically pleasing videos. All data, leaderboard, and code are open-sourced at our project page.

Paperid: 672, https://arxiv.org/pdf/2504.00746.pdf

Abstract:
Data-enabled predictive control (DeePC) has emerged as a powerful technique to control complex systems without the need for extensive modeling efforts. However, relying solely on offline collected data trajectories to represent the system dynamics introduces certain drawbacks. Therefore, we present a novel semi-data-driven model predictive control (SD-MPC) framework that combines (limited) model information with DeePC to address a range of these drawbacks, including sensitivity to noisy data and a lack of robustness. In this work, we focus on the performance of DeePC in operating regimes not captured by the offline collected data trajectories and demonstrate how incorporating an underlying parametric model can counteract this issue. SD-MPC exhibits equivalent closed-loop performance as DeePC for deterministic linear time-invariant systems. Simulations demonstrate the general control performance of the proposed SD-MPC for both a linear time-invariant system and a nonlinear system modeled as a linear parameter-varying system. These results provide numerical evidence of the enhanced robustness of SD-MPC over classical DeePC.

Paperid: 673, https://arxiv.org/pdf/2503.19158.pdf

Abstract:
Type 1 Diabetes (T1D) management is a complex task due to many variability factors. Artificial Pancreas (AP) systems have alleviated patient burden by automating insulin delivery through advanced control algorithms. However, the effectiveness of these systems depends on accurate modeling of glucose-insulin dynamics, which traditional mathematical models often fail to capture due to their inability to adapt to patient-specific variations. This study introduces a Biological-Informed Recurrent Neural Network (BIRNN) framework to address these limitations. The BIRNN leverages a Gated Recurrent Units (GRU) architecture augmented with physics-informed loss functions that embed physiological constraints, ensuring a balance between predictive accuracy and consistency with biological principles. The framework is validated using the commercial UVA/Padova simulator, outperforming traditional linear models in glucose prediction accuracy and reconstruction of unmeasured states, even under circadian variations in insulin sensitivity. The results demonstrate the potential of BIRNN for personalized glucose regulation and future adaptive control strategies in AP systems.

Paperid: 674, https://arxiv.org/pdf/2503.17393.pdf

Abstract:
In contrast to the assumptions of most existing Electromigration (EM) analysis tools, the evolution of EM-induced stress is inherently non-deterministic, influenced by factors such as input current fluctuations and manufacturing non-idealities. Traditional approaches for estimating stress variations typically involve computationally expensive and inefficient Monte Carlo simulations with industrial solvers, which quantify variations using mean and variance metrics. In this work, we introduce a novel machine learning-based framework, termed BPINNEM- Post, for efficient stochastic analysis of EM-induced postvoiding aging processes. This new approach integrates closedform analytical solutions with a Bayesian Physics-Informed Neural Network (BPINN) framework to accelerate the analysis for the first time. The closed-form solutions enforce physical laws at the individual wire segment level, while the BPINN ensures that physics constraints at inter-segment junctions are satisfied and stochastic behaviors are accurately modeled. By reducing the number of variables in the loss functions through the use of analytical solutions, our method significantly improves training efficiency without accuracy loss and naturally incorporates variational effects. Additionally, the analytical solutions effectively address the challenge of incorporating initial stress distributions in interconnect structures during post-void stress calculations. Numerical results demonstrate that BPINN-EM-Post achieves over 240x speedup compared to Monte Carlo simulations using the FEM-based COMSOL solver and more than 65x speedup compared to Monte Carlo simulations using the FDM-based EMSpice method.

Paperid: 675, https://arxiv.org/pdf/2503.11124.pdf

Abstract:
While magnetic micro-robots have demonstrated significant potential across various applications, including drug delivery and microsurgery, the open issue of precise navigation and control in complex fluid environments is crucial for in vivo implementation. This paper introduces a novel flow-aware navigation and control strategy for magnetic micro-robots that explicitly accounts for the impact of fluid flow on their movement. First, the proposed method employs a Physics-Informed U-Net (PI-UNet) to refine the numerically predicted fluid velocity using local observations. Then, the predicted velocity is incorporated in a flow-aware A* path planning algorithm, ensuring efficient navigation while mitigating flow-induced disturbances. Finally, a control scheme is developed to compensate for the predicted fluid velocity, thereby optimizing the micro-robot's performance. A series of simulation studies and real-world experiments are conducted to validate the efficacy of the proposed approach. This method enhances both planning accuracy and control precision, expanding the potential applications of magnetic micro-robots in fluid-affected environments typical of many medical scenarios.

Paperid: 676, https://arxiv.org/pdf/2503.04579.pdf

Abstract:
Geodesic distances play a fundamental role in robotics, as they efficiently encode global geometric information of the domain. Recent methods use neural networks to approximate geodesic distances by solving the Eikonal equation through physics-informed approaches. While effective, these approaches often suffer from unstable convergence during training in complex environments. We propose a framework to learn geodesic distances in irregular domains by using the Soner boundary condition, and systematically evaluate the impact of data losses on training stability and solution accuracy. Our experiments demonstrate that incorporating data losses significantly improves convergence robustness, reducing training instabilities and sensitivity to initialization. These findings suggest that hybrid data-physics approaches can effectively enhance the reliability of learning-based geodesic distance solvers with sparse data.

Paperid: 677, https://arxiv.org/pdf/2502.16373.pdf

Abstract:
The optimal power flow (OPF) problem can be rapidly and reliably solved by employing responsive online solvers based on neural networks. The dynamic nature of renewable energy generation and the variability of power grid conditions necessitate frequent neural network updates with new data instances. To address this need and reduce the time required for data preparation time, we propose a semi-supervised learning framework aided by data augmentation. In this context, ridge regression replaces the traditional solver, facilitating swift prediction of optimal solutions for the given input load demands. Additionally, to accelerate the backpropagation during training, we develop novel batch-mean gradient estimation approaches along with a reduced branch set to alleviate the complexity of gradient computation. Numerical simulations demonstrate that our neural network, equipped with the proposed gradient estimators, consistently achieves feasible and near-optimal solutions. These results underline the effectiveness of our approach for practical implementation in real-time OPF applications.

Paperid: 678, https://arxiv.org/pdf/2502.11369.pdf

Abstract:
Alloy design can be framed as a constraint-satisfaction problem. Building on previous methodologies, we propose equipping Gaussian Process Classifiers (GPCs) with physics-informed prior mean functions to model the boundaries of feasible design spaces. Through three case studies, we highlight the utility of informative priors for handling constraints on continuous and categorical properties. (1) Phase Stability: By incorporating CALPHAD predictions as priors for solid-solution phase stability, we enhance model validation using a publicly available XRD dataset. (2) Phase Stability Prediction Refinement: We demonstrate an in silico active learning approach to efficiently correct phase diagrams. (3) Continuous Property Thresholds: By embedding priors into continuous property models, we accelerate the discovery of alloys meeting specific property thresholds via active learning. In each case, integrating physics-based insights into the classification framework substantially improved model performance, demonstrating an efficient strategy for constraint-aware alloy design.

Paperid: 679, https://arxiv.org/pdf/2501.18879.pdf

Abstract:
Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior knowledge in non-hybrid settings, overlooking the crucial integration of observational data, and are frequently limited to linear systems, unlike the prevalent nonlinear nature of many real-world applications. To address these limitations, we introduce a unified residual form that unifies collocation and variational methods, enabling the incorporation of incomplete and complex physical constraints in hybrid learning settings. Within this formulation, we establish that the generalization performance of physics-informed regression in such hybrid settings is governed by the dimension of the affine variety associated with the physical constraint, rather than by the number of parameters. This enables a unified analysis that is applicable to both linear and nonlinear equations. We also present a method to approximate this dimension and provide experimental validation of our theoretical findings.

Paperid: 680, https://arxiv.org/pdf/2501.13271.pdf

Abstract:
The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate reconstruction capability and strict adherence to physical laws. In this study, we proposed a hybrid two-stage framework that uses multiscale basis functions and physics-guided deep learning to solve the Darcy flow problem in high-contrast fractured porous media. In the first stage, a data-driven model is used to reconstruct the multiscale basis function based on the permeability field to achieve effective dimensionality reduction while preserving the necessary multiscale features. In the second stage, the physics-informed neural network, together with Transformer-based global information extractor is used to reconstruct the pressure field by integrating the physical constraints derived from the Darcy equation, ensuring consistency with the physical laws of the real world. The model was evaluated on datasets with different combinations of permeability and basis functions and performed well in terms of reconstruction accuracy. Specifically, the framework achieves R2 values above 0.9 in terms of basis function fitting and pressure reconstruction, and the residual indicator is on the order of $1\times 10^{-4}$. These results validate the ability of the proposed framework to achieve accurate reconstruction while maintaining physical consistency.

Paperid: 681, https://arxiv.org/pdf/2412.13993.pdf

Abstract:
In machine learning and statistical modeling, the mean square or absolute error is commonly used as an error metric, also called a "loss function." While effective in reducing the average error, this approach may fail to address localized outliers, leading to significant inaccuracies in regions with sharp gradients or discontinuities. This issue is particularly evident in physics-informed neural networks (PINNs), where such localized errors are expected and affect the overall solution. To overcome this limitation, we propose a novel loss function that combines the mean and the standard deviation of the chosen error metric. By minimizing this combined loss function, the method ensures a more uniform error distribution and reduces the impact of localized high-error regions. The proposed loss function is easy to implement and tested on problems of varying complexity: the 1D Poisson equation, the unsteady Burgers' equation, 2D linear elastic solid mechanics, and 2D steady Navier-Stokes equations. Results demonstrate improved solution quality and lower maximum error compared to the standard mean-based loss, with minimal impact on computational time.

Paperid: 682, https://arxiv.org/pdf/2411.19374.pdf

Abstract:
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these methods are computationally expensive, particularly for applications requiring repeated integration, such as parameter estimation, Bayesian inference, neural ODEs, physics-informed neural networks, and MeshGraphNets. Explicit exponential integration methods have been proposed as a potential alternative, leveraging the matrix exponential to address stiffness without requiring nonlinear solvers. This study evaluates several state-of-the-art explicit single-step exponential schemes against classical implicit methods on benchmark stiff ODE problems, analyzing their accuracy, stability, and scalability with step size. Despite their initial appeal, our results reveal that explicit exponential methods significantly lag behind implicit schemes in accuracy and scalability for stiff ODEs. The backward Euler method consistently outperformed higher-order exponential methods in accuracy at small step sizes, with none surpassing the accuracy of the first-order integrating factor Euler method. Exponential methods fail to improve upon first-order accuracy, revealing the integrating factor Euler method as the only reliable choice for repeated, inexpensive integration in applications such as neural ODEs and parameter estimation. This study exposes the limitations of explicit exponential methods and calls for the development of improved algorithms.

Paperid: 683, https://arxiv.org/pdf/2411.17039.pdf

Abstract:
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling points, which is a robust approach specifically designed to handle partial differential equations with rough solutions or in high dimensions. The sample points are generated by the generating vector to achieve the smallest discrepancy. The architecture integrates Physics-Informed Neural Networks (PINNs) with rigorous mathematical guarantees demonstrating lower error bounds compared to conventional uniform random sampling. Numerical validation includes low-regularity Poisson equations, two-dimensional inverse Helmholtz problems, and high-dimensional linear/nonlinear PDEs, systematically demonstrating the algorithm's superior performance and generalization capabilities.

Paperid: 684, https://arxiv.org/pdf/2411.14942.pdf

Abstract:
Topological solitons, which are stable, localized solutions of nonlinear differential equations, are crucial in various fields of physics and mathematics, including particle physics and cosmology. However, solving these solitons presents significant challenges due to the complexity of the underlying equations and the computational resources required for accurate solutions. To address this, we have developed a novel method using neural network (NN) to efficiently solve solitons. A similar NN approach is Physics-Informed Neural Networks (PINN). In a comparative analysis between our method and PINN, we find that our method achieves shorter computation times while maintaining the same level of accuracy. This advancement in computational efficiency not only overcomes current limitations but also opens new avenues for studying topological solitons and their dynamical behavior.

Paperid: 685, https://arxiv.org/pdf/2411.09237.pdf

Abstract:
Contraction analysis offers, through elegant mathematical developments, a unified way of designing observers for a general class of nonlinear systems, where the observer correction term is obtained by solving an infinite dimensional inequality that guarantees global exponential convergence. However, solving the matrix partial differential inequality involved in contraction analysis design is both analytically and numerically challenging and represents a long-lasting challenge that prevented its wide use. Therefore, the present paper proposes a novel approach that relies on an unsupervised Physics Informed Neural Network (PINN) to design the observer's correction term by enforcing the partial differential inequality in the loss function. The performance of the proposed PINN-based nonlinear observer is assessed in numerical simulation as well as its robustness to measurement noise and neural network approximation error.

Paperid: 686, https://arxiv.org/pdf/2411.08326.pdf

Abstract:
We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous group, but are also universal approximators for flows of ordinary differential equation (ODEs). Furthermore, topological properties of these flows can be enforced by the architecture in an interpretable manner. We demonstrate in numerical experiments how this topological group structure leads to concrete computational gains over other physics informed neural networks in estimating and extrapolating latent dynamics of ODEs, while training up to five times faster than other flow-based architectures.

Paperid: 687, https://arxiv.org/pdf/2410.17445.pdf

Abstract:
Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are also important to consider in modeling physical systems. To address this, we proposed PINN-Proj, a PINN-based model that uses a novel projection method to enforce conservation laws. We found that PINN-Proj substantially outperformed PINN in conserving momentum and lowered prediction error by three to four orders of magnitude from the best benchmark tested. PINN-Proj also performed marginally better in the separate task of state prediction on three PDE datasets.

Paperid: 688, https://arxiv.org/pdf/2409.13644.pdf

Abstract:
We present a non-overlapping, Schwarz-type domain decomposition method with a generalized interface condition, designed for physics-informed machine learning of partial differential equations (PDEs) in both forward and inverse contexts. Our approach employs physics and equality-constrained artificial neural networks (PECANN) within each subdomain. Unlike the original PECANN method, which relies solely on initial and boundary conditions to constrain PDEs, our method uses both boundary conditions and the governing PDE to constrain a unique interface loss function for each subdomain. This modification improves the learning of subdomain-specific interface parameters while reducing communication overhead by delaying information exchange between neighboring subdomains. To address the constrained optimization in each subdomain, we apply an augmented Lagrangian method with a conditionally adaptive update strategy, transforming the problem into an unconstrained dual optimization. A distinct advantage of our domain decomposition method is its ability to learn solutions to both Poisson's and Helmholtz equations, even in cases with high-wavenumber and complex-valued solutions. Through numerical experiments with up to 64 subdomains, we demonstrate that our method consistently generalizes well as the number of subdomains increases.

Paperid: 689, https://arxiv.org/pdf/2601.19905.pdf

Abstract:
Silicon-based analog neural networks physically embody the ideal neural network model in an approximate way. We show that by retraining the neural network using a physics-informed hardware-aware model one can fully recover the inference accuracy of the ideal network model even in the presence of significant non-idealities. This is way more promising for scalability and integration density than the default option of improving the fidelity of the analog neural network at the cost of significant energy, area, and design overhead, through extensive calibration and conservative analog design. We first present a physics-informed hardware-aware model for a time-domain vector-matrix multiplier implemented with single-transistor floating-gate memory cells that explicitly accounts for two dominant non-idealities of the physical implementation - capacitive crosstalk and bit-line voltage drop - and integrates seamlessly with modern deep-learning workflows. The model discretizes each operation into adaptive time slots, processes activation patterns in parallel, and accumulates their contributions to predict effective multiplier outputs. Using measurements from a 16x16 silicon array, we calibrate the model, show that crosstalk is layout-dependent and often dominant, and introduce an improved weight-extraction procedure that doubles signal-to-error ratio versus an ideal vector-matrix multiplier model. Finally, we show that by training silicon-based analog neural networks using an hardware-aware model in the forward pass we can recover the accuracy of the ideal software networks across three architectures -- custom MLP on low-resolution MNIST, LeNet-5 on MNIST, and a VGG-style CNN on CIFAR-10 - establishing a complete design-to-deployment workflow for time-domain analog neuromorphic chips.

Paperid: 690, https://arxiv.org/pdf/2601.12675.pdf

Abstract:
In this paper, we develop a novel mesh-free framework, termed physics-informed neural networks with invariant measure score matching (PINN-IMSM), for reconstructing dynamical systems from unlabeled point-cloud data that capture the system's invariant measure. The invariant density satisfies the steady-state Fokker-Planck (FP) equation. We reformulate this equation in terms of its score function (the gradient of the log-density), which is estimated directly from data via denoising score matching, thereby bypassing explicit density estimation. This learned score is then embedded into a physics-informed neural network (PINN) to reconstruct the drift velocity field under the resulting score-based FP equation. The mesh-free nature of PINNs allows the framework to scale to higher dimensions, avoiding the curse of dimensionality inherent in mesh-based methods. To address the ill-posedness of high-dimensional inverse problems, we recast the problem as a PDE-constrained optimization that seeks the minimal-energy velocity field. Under suitable conditions, we prove that this problem admits a unique solution that depends continuously on the score function. The constrained formulation is solved using a stochastic augmented Lagrangian method. Numerical experiments on representative dynamical systems, including the Van der Pol oscillator, an active swimmer in an anharmonic trap, and the chaotic Lorenz-63 and Lorenz-96 systems, demonstrate that PINN-IMSM accurately recovers invariant measures and reconstructs faithful dynamical behavior for problems in up to five dimensions.

Paperid: 691, https://arxiv.org/pdf/2601.07760.pdf

Abstract:
Kolmogorov-Arnold Networks (KANs) have shown strong potential for efficiently approximating complex nonlinear functions. However, the original KAN formulation relies on B-spline basis functions, which incur substantial computational overhead due to De Boor's algorithm. To address this limitation, recent work has explored alternative basis functions such as radial basis functions (RBFs) that can improve computational efficiency and flexibility. Yet, standard RBF-KANs often sacrifice accuracy relative to the original KAN design. In this work, we propose Free-RBF-KAN, a RBF-based KAN architecture that incorporates adaptive learning grids and trainable smoothness to close this performance gap. Our method employs freely learnable RBF shapes that dynamically align grid representations with activation patterns, enabling expressive and adaptive function approximation. Additionally, we treat smoothness as a kernel parameter optimized jointly with network weights, without increasing computational complexity. We provide a general universality proof for RBF-KANs, which encompasses our Free-RBF-KAN formulation. Through a broad set of experiments, including multiscale function approximation, physics-informed machine learning, and PDE solution operator learning, Free-RBF-KAN achieves accuracy comparable to the original B-spline-based KAN while delivering faster training and inference. These results highlight Free-RBF-KAN as a compelling balance between computational efficiency and adaptive resolution, particularly for high-dimensional structured modeling tasks.

Paperid: 692, https://arxiv.org/pdf/2601.06244.pdf

Abstract:
In this work, we embed hard constraints in a physics informed neural network (PINN) which predicts solutions to the 2D incompressible Navier Stokes equations. We extend the hard constraint method introduced by Chen et al. (arXiv:2012.06148) from a linear PDE to a strongly non-linear PDE. The PINN is used to estimate the stream function and pressure of the fluid, and by differentiating the stream function we can recover an incompressible velocity field. An unlearnable hard constraint projection (HCP) layer projects the predicted velocity and pressure to a hyperplane that admits only exact solutions to a discretised form of the governing equations.

Paperid: 693, https://arxiv.org/pdf/2601.03040.pdf

Abstract:
A fundamental requirement for full autonomy is the ability to sustain accurate navigation in the absence of external data, such as GNSS signals or visual information. In these challenging environments, the platform must rely exclusively on inertial sensors, leading to pure inertial navigation. However, the inherent noise and other error terms of the inertial sensors in such real-world scenarios will cause the navigation solution to drift over time. Although conventional deep-learning models have emerged as a possible approach to inertial navigation, they are inherently black-box in nature. Furthermore, they struggle to learn effectively with limited supervised sensor data and often fail to preserve physical principles. To address these limitations, we propose PiDR, a physics-informed inertial dead-reckoning framework for autonomous platforms in situations of pure inertial navigation. PiDR offers transparency by explicitly integrating inertial navigation principles into the network training process through the physics-informed residual component. PiDR plays a crucial role in mitigating abrupt trajectory deviations even under limited or sparse supervision. We evaluated PiDR on real-world datasets collected by a mobile robot and an autonomous underwater vehicle. We obtained more than 29% positioning improvement in both datasets, demonstrating the ability of PiDR to generalize different platforms operating in various environments and dynamics. Thus, PiDR offers a robust, lightweight, yet effective architecture and can be deployed on resource-constrained platforms, enabling real-time pure inertial navigation in adverse scenarios.

Paperid: 694, https://arxiv.org/pdf/2601.00820.pdf

Abstract:
Ka-band low-Earth-orbit (LEO) downlinks can suffer second-scale reliability collapses during flare-driven ionospheric disturbances, where fixed fade margins and reactive adaptive coding and modulation (ACM) are either overly conservative or too slow. This paper presents a GNSS-free, link-internal predictive controller that senses the same downlink via a geometry-free dual-carrier phase observable at 10~Hz: a high-pass filter and template-based onset detector, followed by a four-state nearly-constant-velocity Kalman filter, estimate $Δ$VTEC and its rate, and a short look-ahead (60~s) yields an endpoint outage probability used as a risk gate to trigger one-step discrete MCS down-switch and pilot-time update with hysteresis. Evaluation uses physics-informed log replay driven by real GOES X-ray flare morphologies under a disjoint-day frozen-calibration protocol, with uncertainty reported via paired moving-block bootstrap. Across stressed 60~s windows, the controller reduces peak BLER by 25--30\% and increases goodput by 0.10--0.15~bps/Hz versus no-adaptation baselines under a unified link-level abstraction. The loop runs in $\mathcal{O}(1)$ per 0.1~s epoch (about 0.042~ms measured), making on-board implementation feasible, and scope and deployment considerations for dispersion-dominated events are discussed.

Paperid: 695, https://arxiv.org/pdf/2512.22421.pdf

Abstract:
We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an end-to-end differentiable numerical solver to reconstruct unknown heterogeneous parameter fields in a low-dimensional nonlinear manifold, improving numerical conditioning and enabling stable gradient-based optimization under sparse observations. The proposed framework integrates a latent diffusion model (LDM), trained in a compact latent space, with a differentiable finite-volume discretization of the forward PDE. Sensitivities are propagated through the discretization using adjoint-based gradients combined with reverse-mode automatic differentiation. Inversion is performed directly in latent space, which implicitly suppresses ill-conditioned degrees of freedom while preserving dominant structural modes, including sharp material interfaces. The effectiveness of LD-DIM is demonstrated using a representative inverse problem for flow in porous media, where heterogeneous conductivity fields are reconstructed from spatially sparse hydraulic head measurements. Numerical experiments assess convergence behavior and reconstruction quality for both Gaussian random fields and bimaterial coefficient distributions. The results show that LD-DIM achieves consistently improved numerical stability and reconstruction accuracy of both parameter fields and corresponding PDE solutions compared with physics-informed neural networks (PINNs) and physics-embedded variational autoencoder (VAE) baselines, while maintaining sharp discontinuities and reducing sensitivity to initialization.

Paperid: 696, https://arxiv.org/pdf/2512.17198.pdf

Abstract:
We introduce BumpNet, a sparse neural network framework for PDE numerical solution and operator learning. BumpNet is based on meshless basis function expansion, in a similar fashion to radial-basis function (RBF) networks. Unlike RBF networks, the basis functions in BumpNet are constructed from ordinary sigmoid activation functions. This enables the efficient use of modern training techniques optimized for such networks. All parameters of the basis functions, including shape, location, and amplitude, are fully trainable. Model parsimony and h-adaptivity are effectively achieved through dynamically pruning basis functions during training. BumpNet is a general framework that can be combined with existing neural architectures for learning PDE solutions: here, we propose Bump-PINNs (BumpNet with physics-informed neural networks) for solving general PDEs; Bump-EDNN (BumpNet with evolutionary deep neural networks) to solve time-evolution PDEs; and Bump-DeepONet (BumpNet with deep operator networks) for PDE operator learning. Bump-PINNs are trained using the same collocation-based approach used by PINNs, Bump-EDNN uses a BumpNet only in the spatial domain and uses EDNNs to advance the solution in time, while Bump-DeepONets employ a BumpNet regression network as the trunk network of a DeepONet. Extensive numerical experiments demonstrate the efficiency and accuracy of the proposed architecture.

Paperid: 697, https://arxiv.org/pdf/2512.14929.pdf

Abstract:
Purpose: Magnetic Resonance Spectroscopic Imaging (MRSI) maps endogenous brain metabolism while suppressing the overwhelming water signal. Water-unsuppressed MRSI (wu-MRSI) allows simultaneous imaging of water and metabolites, but large water sidebands cause challenges for metabolic fitting. We developed an end-to-end deep-learning pipeline to overcome these challenges at ultra-high field. Methods:Fast high-resolution wu-MRSI was acquired at 7T with non-cartesian ECCENTRIC sampling and ultra-short echo time. A water and lipid removal network (WALINET+) was developed to remove lipids, water signal, and sidebands. MRSI reconstruction was performed by DeepER and a physics-informed network for metabolite fitting. Water signal was used for absolute metabolite quantification, quantitative susceptibility mapping (QSM), and myelin water fraction imaging (MWF). Results: WALINET+ provided the lowest NRMSE (< 2%) in simulations and in vivo the smallest bias (< 20%) and limits-of-agreement (+-63%) between wu-MRSI and ws-MRSI scans. Several metabolites such as creatine and glutamate showed higher SNR in wu-MRSI. QSM and MWF obtained from wu-MRSI and GRE showed good agreement with 0 ppm/5.5% bias and +-0.05 ppm/ +- 12.75% limits-of-agreement. Conclusion: High-quality metabolic, QSM, and MWF mapping of the human brain can be obtained simultaneously by ECCENTRIC wu-MRSI at 7T with 2 mm isotropic resolution in 12 min. WALINET+ robustly removes water sidebands while preserving metabolite signal, eliminating the need for water suppression and separate water acquisitions.

Paperid: 698, https://arxiv.org/pdf/2512.12445.pdf

Abstract:
Integrating domain knowledge into deep learning has emerged as a promising direction for improving model interpretability, generalization, and data efficiency. In this work, we present a novel knowledge-guided ViT-based Masked Autoencoder that embeds scientific domain knowledge within the self-supervised reconstruction process. Instead of relying solely on data-driven optimization, our proposed approach incorporates the Linear Spectral Mixing Model (LSMM) as a physical constraint and physically-based Spectral Angle Mapper (SAM), ensuring that learned representations adhere to known structural relationships between observed signals and their latent components. The framework jointly optimizes LSMM and SAM loss with a conventional Huber loss objective, promoting both numerical accuracy and geometric consistency in the feature space. This knowledge-guided design enhances reconstruction fidelity, stabilizes training under limited supervision, and yields interpretable latent representations grounded in physical principles. The experimental findings indicate that the proposed model substantially enhances reconstruction quality and improves downstream task performance, highlighting the promise of embedding physics-informed inductive biases within transformer-based self-supervised learning.

Paperid: 699, https://arxiv.org/pdf/2512.11048.pdf

Abstract:
The trade-off between model fidelity and computational cost remains a central challenge in the computational modeling of extrusion-based 3D printing, particularly for real time optimization and control. Although high fidelity simulations have advanced considerably for offline analysis, dynamical modeling tailored for online, control-oriented applications is still significantly underdeveloped. In this study, we propose a reduced order dynamical flow model that captures the transient behavior of extrusion-based 3D printing. The model is grounded in physics-based principles derived from the Navier Stokes equations and further simplified through spatial averaging and input dependent parameterization. To assess its performance, the model is identified via a nonlinear least squares approach using Computational Fluid Dynamics (CFD) simulation data spanning a range of printing conditions and subsequently validated across multiple combinations of training and testing scenarios. The results demonstrate strong agreement with the CFD data within the nozzle, the nozzle substrate gap, and the deposited layer regions. Overall, the proposed reduced order model successfully captures the dominant flow dynamics of the process while maintaining a level of simplicity compatible with real time control and optimization.

Paperid: 700, https://arxiv.org/pdf/2512.00712.pdf

Abstract:
Analog circuit optimization is typically framed as black-box search over arbitrary smooth functions, yet device physics constrains performance mappings to structured families: exponential device laws, rational transfer functions, and regime-dependent dynamics. Off-the-shelf Gaussian-process surrogates impose globally smooth, stationary priors that are misaligned with these regime-switching primitives and can severely misfit highly nonlinear circuits at realistic sample sizes (50--100 evaluations). We demonstrate that pre-trained tabular models encoding these primitives enable reliable optimization without per-circuit engineering. Circuit Prior Network (CPN) combines a tabular foundation model (TabPFN v2) with Direct Expected Improvement (DEI), computing expected improvement exactly under discrete posteriors rather than Gaussian approximations. Across 6 circuits and 25 baselines, structure-matched priors achieve $R^2 \approx 0.99$ in small-sample regimes where GP-Matérn attains only $R^2 = 0.16$ on Bandgap, deliver $1.05$--$3.81\times$ higher FoM with $3.34$--$11.89\times$ fewer iterations, and suggest a shift from hand-crafting models as priors toward systematic physics-informed structure identification. Our code will be made publicly available upon paper acceptance.

Paperid: 701, https://arxiv.org/pdf/2511.22343.pdf

Abstract:
Power Flow (PF) calculation based on machine learning (ML) techniques offer significant computational advantages over traditional numerical methods but often struggle to maintain full physical consistency. This paper introduces a physics-informed test-time training (PI-TTT) framework that enhances the accuracy and feasibility of ML-based PF surrogates by enforcing AC power flow equalities and operational constraints directly at inference time. The proposed method performs a lightweight self-supervised refinement of the surrogate outputs through few gradient-based updates, enabling local adaptation to unseen operating conditions without requiring labeled data. Extensive experiments on the IEEE 14-, 118-, and 300-bus systems and the PEGASE 1354-bus network show that PI-TTT reduces power flow residuals and operational constraint violations by one to two orders of magnitude compared with purely ML-based models, while preserving their computational advantage. The results demonstrate that PI-TTT provides fast, accurate, and physically reliable predictions, representing a promising direction for scalable and physics-consistent learning in power system analysis.

Paperid: 702, https://arxiv.org/pdf/2511.05216.pdf

Abstract:
Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a neural-operator framework for surrogate modeling of power system components, using Deep Operator Networks (DeepONets) to learn mappings from system states and time-varying inputs to full trajectories without step-by-step integration. To enhance generalization and data efficiency, we introduce Physics-Informed DeepONets (PI-DeepONets), which embed the residuals of governing equations into the training loss. Our results show that DeepONets, and especially PI-DeepONets, achieve accurate predictions under diverse scenarios, providing over 30 times speedup compared to high-order ODE solvers. Benchmarking against Physics-Informed Neural Networks (PINNs) highlights superior stability and scalability. Our results demonstrate neural operators as a promising path toward real-time, physics-aware simulation of power system dynamics.

Paperid: 703, https://arxiv.org/pdf/2510.21736.pdf

Abstract:
This study introduces a novel control framework for adaptive cruise control (ACC) in automated driving, leveraging Long Short-Term Memory (LSTM) networks and physics-informed constraints. As automated vehicles (AVs) adopt advanced features like ACC, transportation systems are becoming increasingly intelligent and efficient. However, existing AV control strategies primarily focus on optimizing the performance of individual vehicles or platoons, often neglecting their interactions with human-driven vehicles (HVs) and the broader impact on traffic flow. This oversight can exacerbate congestion and reduce overall system efficiency. To address this critical research gap, we propose a neural network-based, socially compliant AV control framework that incorporates social value orientation (SVO). This framework enables AVs to account for their influence on HVs and traffic dynamics. By leveraging AVs as mobile traffic regulators, the proposed approach promotes adaptive driving behaviors that reduce congestion, improve traffic efficiency, and lower energy consumption. Within this framework, we define utility functions for both AVs and HVs, which are optimized based on the SVO of each AV to balance its own control objectives with broader traffic flow considerations. Numerical results demonstrate the effectiveness of the proposed method in adapting to varying traffic conditions, thereby enhancing system-wide efficiency. Specifically, when the AV's control mode shifts from prioritizing energy consumption to optimizing traffic flow efficiency, vehicles in the following platoon experience at least a 58.99% increase in individual energy consumption alongside at least a 38.39% improvement in individual average speed, indicating significant enhancements in traffic dynamics.

Paperid: 704, https://arxiv.org/pdf/2510.19364.pdf

Abstract:
Uncertainty-aware robot motion prediction is crucial for downstream traversability estimation and safe autonomous navigation in unstructured, off-road environments, where terrain is heterogeneous and perceptual uncertainty is high. Most existing methods assume deterministic or spatially independent terrain uncertainties, ignoring the inherent local correlations of 3D spatial data and often producing unreliable predictions. In this work, we introduce an efficient probabilistic framework that explicitly models spatially correlated aleatoric uncertainty over terrain parameters as a probabilistic world model and propagates this uncertainty through a differentiable physics engine for probabilistic trajectory forecasting. By leveraging structured convolutional operators, our approach provides high-resolution multivariate predictions at manageable computational cost. Experimental evaluation on a publicly available dataset shows significantly improved uncertainty estimation and trajectory prediction accuracy over aleatoric uncertainty estimation baselines.

Paperid: 705, https://arxiv.org/pdf/2510.18195.pdf

Abstract:
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal control system design. However, numerical solutions to this equation are computationally intensive, and analytical solutions are frequently unavailable. Knowledge-guided machine learning methodologies, such as physics-informed neural networks (PINNs), offer new alternative approaches that can alleviate the difficulties of solving the HJB equation numerically. This work presents a multistage ensemble framework to learn the optimal cost-to-go, and subsequently the corresponding optimal control signal, through the HJB equation. Prior PINN-based approaches rely on a stabilizing the HJB enforcement during training. Our framework does not use stabilizer terms and offers a means of controlling the nonlinear system, via either a singular learned control signal or an ensemble control signal policy. Success is demonstrated in closed-loop control, using both ensemble- and singular-control, of a steady-state time-invariant two-state continuous nonlinear system with an infinite time horizon, accounting of noisy, perturbed system states and varying initial conditions.

Paperid: 706, https://arxiv.org/pdf/2510.16817.pdf

Abstract:
We propose an enhanced physics-informed neural network (PINN), the Trace Regularity Physics-Informed Neural Network (TRPINN), which enforces the boundary loss in the Sobolev-Slobodeckij norm $H^{1/2}(\partial Ω)$, the correct trace space associated with $H^1(Ω)$. We reduce computational cost by computing only the theoretically essential portion of the semi-norm and enhance convergence stability by avoiding denominator evaluations in the discretization. By incorporating the exact $H^{1/2}(\partial Ω)$ norm, we show that the approximation converges to the true solution in the $H^{1}(Ω)$ sense, and, through Neural Tangent Kernel (NTK) analysis, we demonstrate that TRPINN can converge faster than standard PINNs. Numerical experiments on the Laplace equation with highly oscillatory Dirichlet boundary conditions exhibit cases where TRPINN succeeds even when standard PINNs fail, and show performance improvements of one to three decimal digits.

Paperid: 707, https://arxiv.org/pdf/2510.14297.pdf

Abstract:
The Keller-Segel (KS) chemotaxis system is used to describe the overall behavior of a collection of cells under the influence of chemotaxis. However, solving the KS chemotaxis system and generating its aggregation patterns remain challenging due to the emergence of solutions exhibiting near-singular behavior, such as finite-time blow-up or concentration phenomena. Building on a Lagrangian framework of the KS system, we develop DeepLagrangian, a self-adaptive density estimation method that learns and generates aggregation patterns and near-singular solutions of the KS system in two- and three-dimensional (2D and 3D) space under different physical parameters. The main advantage of the Lagrangian framework is its inherent ability to adapt to near-singular solutions. To develop this framework, we normalize the KS solution into a probability density function (PDF), derive the corresponding normalized KS system, and utilize the property of the continuity equation to rewrite the system into a Lagrangian framework. We then define a physics-informed Lagrangian loss to enforce this framework and incorporate a flow-based generative model, called the time-dependent KRnet, to approximate the PDF by minimizing the loss. Furthermore, we integrate time-marching strategies with the time-dependent KRnet to enhance the accuracy of the PDF approximation. After obtaining the approximate PDF, we recover the original KS solution. We also prove that the Lagrangian loss effectively controls the Kullback-Leibler (KL) divergence between the approximate PDF and the exact PDF. In the numerical experiments, we demonstrate the accuracy of our DeepLagrangian method for the 2D and 3D KS chemotaxis system with/without advection.

Paperid: 708, https://arxiv.org/pdf/2510.13386.pdf

Abstract:
Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires uniform grids of regular domains, which limits its application on non-uniform grids or irregular domains. To address the limitation, we develop a functional tensor train neural network (FTTNN) for solving high-dimensional PDEs, which can represent PDE solutions on non-uniform grids or irregular domains. An essential ingredient of our approach is to represent the PDE solutions by the functional tensor train format whose TT-core functions are approximated by neural networks. To give the functional tensor train representation, we propose and study functional tensor train rank and employ it into a physics-informed loss function for training. Because of tensor train representation, the resulting high-dimensional integral in the loss function can be computed via one-dimensional integrals by Gauss quadrature rules. Numerical examples including high-dimensional PDEs on regular or irregular domains are presented to demonstrate that the performance of the proposed FTTNN is better than that of Physics Informed Neural Networks (PINN).

Paperid: 709, https://arxiv.org/pdf/2510.10483.pdf

Abstract:
Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches like Physics$-$Informed Neural Networks (PINNs) have been developed, offering a mesh$-$free, analytic type framework for efficiently solving PDEs across a wide range of applications. However, traditional PINNs often struggle with challenges such as limited precision, slow training dynamics, lack of labeled data availability, and inadequate handling of multi$-$physics interactions. To overcome these challenging issues of PINNs, we proposed a Gradient Enhanced Self$-$Training PINN (gST$-$PINN) method that specifically introduces a gradient based pseudo point self$-$learning algorithm for solving PDEs. We tested the proposed method on three different types of PDE problems from various fields, each representing distinct scenarios. The effectiveness of the proposed method is evident, as the PINN approach for solving the Burgers$'$ equation attains a mean square error (MSE) on the order of $10^{-3}$, while the diffusion$-$sorption equation achieves an MSE on the order of $10^{-4}$ after 12,500 iterations, with no further improvement as the iterations increase. In contrast, the MSE for both PDEs in the gST$-$PINN model continues to decrease, demonstrating better generalization and reaching an MSE on the order of $10^{-5}$ after 18,500 iterations. Furthermore, the results show that the proposed purely semi$-$supervised gST$-$PINN consistently outperforms the standard PINN method in all cases, even when solution of the PDEs are unavailable. It generalizes both PINN and Gradient$-$enhanced PINN (gPINN), and can be effectively applied in scenarios prone to low accuracy and convergence issues, particularly in the absence of labeled data.

Paperid: 710, https://arxiv.org/pdf/2510.08795.pdf

Abstract:
We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep Operator Network (DeepONet) architecture that incorporates Chunkwise Rational Kolmogorov--Arnold Network (CKAN) sub-networks for enhanced function approximation. The principles of Physics-Informed Neural Networks (PINNs) are integrated into the operator learning framework to enforce physical consistency. This design enables the efficient learning of physically consistent spatio-temporal solution operators and allows for rapid prediction for parametric time-dependent PDEs with varying inputs (e.g., parameters, initial/boundary conditions) after training. Validated on challenging benchmark problems, PO-CKAN demonstrates accurate operator learning with results closely matching high-fidelity solutions. PO-CKAN adopts a DeepONet-style branch--trunk architecture with its sub-networks instantiated as rational KAN modules, and enforces physical consistency via a PDE residual (PINN-style) loss. On Burgers' equation with $ν=0.01$, PO-CKAN reduces the mean relative $L^2$ error by approximately 48\% compared to PI-DeepONet, and achieves competitive accuracy on the Eikonal and diffusion--reaction benchmarks.

Paperid: 711, https://arxiv.org/pdf/2510.06355.pdf

Abstract:
Unmanned aerial vehicle (UAV) communications demand accurate yet interpretable air-to-ground (A2G) channel models that can adapt to nonstationary propagation environments. While deterministic models offer interpretability and deep learning (DL) models provide accuracy, both approaches suffer from either rigidity or a lack of explainability. To bridge this gap, we propose the Physics-Inspired Kolmogorov-Arnold Network (PIKAN) that embeds physical principles (e.g., free-space path loss, two-ray reflections) into the learning process. Unlike physics-informed neural networks (PINNs), PIKAN is more flexible for applying physical information because it introduces them as flexible inductive biases. Thus, it enables a more flexible training process. Experiments on UAV A2G measurement data show that PIKAN achieves comparable accuracy to DL models while providing symbolic and explainable expressions aligned with propagation laws. Remarkably, PIKAN achieves this performance with only 232 parameters, making it up to 37 times lighter than multilayer perceptron (MLP) baselines with thousands of parameters, without sacrificing correlation with measurements and also providing symbolic expressions. These results highlight PIKAN as an efficient, interpretable, and scalable solution for UAV channel modelling in beyond-5G and 6G networks.

Paperid: 712, https://arxiv.org/pdf/2510.04459.pdf

Abstract:
Sound field reconstruction involves estimating sound fields from a limited number of spatially distributed observations. This work introduces a differentiable physics approach for sound field reconstruction, where the initial conditions of the wave equation are approximated with a neural network, and the differential operator is computed with a differentiable numerical solver. The use of a numerical solver enables a stable network training while enforcing the physics as a strong constraint, in contrast to conventional physics-informed neural networks, which include the physics as a constraint in the loss function. We introduce an additional sparsity-promoting constraint to achieve meaningful solutions even under severe undersampling conditions. Experiments demonstrate that the proposed approach can reconstruct sound fields under extreme data scarcity, achieving higher accuracy and better convergence compared to physics-informed neural networks.

Paperid: 713, https://arxiv.org/pdf/2510.03305.pdf

Abstract:
Machine learning has been increasingly applied in climate modeling on system emulation acceleration, data-driven parameter inference, forecasting, and knowledge discovery, addressing challenges such as physical consistency, multi-scale coupling, data sparsity, robust generalization, and integration with scientific workflows. This paper analyzes a series of case studies from applied machine learning research in climate modeling, with a focus on design choices and workflow structure. Rather than reviewing technical details, we aim to synthesize workflow design patterns across diverse projects in ML-enabled climate modeling: from surrogate modeling, ML parameterization, probabilistic programming, to simulation-based inference, and physics-informed transfer learning. We unpack how these workflows are grounded in physical knowledge, informed by simulation data, and designed to integrate observations. We aim to offer a framework for ensuring rigor in scientific machine learning through more transparent model development, critical evaluation, informed adaptation, and reproducibility, and to contribute to lowering the barrier for interdisciplinary collaboration at the interface of data science and climate modeling.

Paperid: 714, https://arxiv.org/pdf/2510.02414.pdf

Abstract:
Reconstructing high-resolution rainfall fields is essential for flood forecasting, hydrological modeling, and climate analysis. However, existing spatial interpolation methods-whether based on automatic weather station (AWS) measurements or enhanced with satellite/radar observations often over-smooth critical structures, failing to capture sharp transitions and localized extremes. We introduce RainSeer, a structure-aware reconstruction framework that reinterprets radar reflectivity as a physically grounded structural prior-capturing when, where, and how rain develops. This shift, however, introduces two fundamental challenges: (i) translating high-resolution volumetric radar fields into sparse point-wise rainfall observations, and (ii) bridging the physical disconnect between aloft hydro-meteors and ground-level precipitation. RainSeer addresses these through a physics-informed two-stage architecture: a Structure-to-Point Mapper performs spatial alignment by projecting mesoscale radar structures into localized ground-level rainfall, through a bidirectional mapping, and a Geo-Aware Rain Decoder captures the semantic transformation of hydro-meteors through descent, melting, and evaporation via a causal spatiotemporal attention mechanism. We evaluate RainSeer on two public datasets-RAIN-F (Korea, 2017-2019) and MeteoNet (France, 2016-2018)-and observe consistent improvements over state-of-the-art baselines, reducing MAE by over 13.31% and significantly enhancing structural fidelity in reconstructed rainfall fields.

Paperid: 715, https://arxiv.org/pdf/2509.25158.pdf

Abstract:
Voltage prediction in distribution grids is a critical yet difficult task for maintaining power system stability. Machine learning approaches, particularly Graph Neural Networks (GNNs), offer significant speedups but suffer from poor generalization when trained on limited or incomplete data. In this work, we systematically investigate the role of inductive biases in improving a model's ability to reliably learn power flow. Specifically, we evaluate three physics-informed strategies: (i) power-flow-constrained loss functions, (ii) complex-valued neural networks, and (iii) residual-based task reformulation. Using the ENGAGE dataset, which spans multiple low- and medium-voltage grid configurations, we conduct controlled experiments to isolate the effect of each inductive bias and assess both standard predictive performance and out-of-distribution generalization. Our study provides practical insights into which model assumptions most effectively guide learning for reliable and efficient voltage prediction in modern distribution networks.

Paperid: 716, https://arxiv.org/pdf/2509.21405.pdf

Abstract:
This work addresses object identification under known dynamics in unmanned aerial vehicle applications, where learning and classification are combined through a physics-informed residual neural network. The proposed framework leverages physics-informed learning for state mapping and state-derivative prediction, while a softmax layer enables multi-class confidence estimation. Quadcopter, fixed-wing, and helicopter aerial vehicles are considered as case studies. The results demonstrate high classification accuracy with reduced training time, offering a promising solution for system identification problems in domains where the underlying dynamics are well understood.

Paperid: 717, https://arxiv.org/pdf/2509.20191.pdf

Abstract:
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for which many properties and limitations remain unknown. PINNs are widely accepted as inferior to traditional methods for solving PDEs, such as the finite element method, both with regard to computation time and accuracy. However, PINNs are commonly claimed to show promise in solving inverse problems and handling noisy or incomplete data. We compare the performance of PINNs in solving inverse problems with that of a traditional approach using the finite element method combined with a numerical optimizer. The models are tested on a series of increasingly difficult fluid mechanics problems, with and without noise. We find that while PINNs may require less human effort and specialized knowledge, they are outperformed by the traditional approach. However, the difference appears to decrease with higher dimensions and more data. We identify common failures during training to be addressed if the performance of PINNs on noisy inverse problems is to become more competitive.

Paperid: 718, https://arxiv.org/pdf/2509.19233.pdf

Abstract:
In the context of the energy transition, with increasing integration of renewable sources and cross-border electricity exchanges, power grids are encountering greater uncertainty and operational risk. Maintaining grid stability under varying conditions is a complex task, and power flow simulators are commonly used to support operators by evaluating potential actions before implementation. However, traditional physical solvers, while accurate, are often too slow for near real-time use. Machine learning models have emerged as fast surrogates, and to improve their adherence to physical laws (e.g., Kirchhoff's laws), they are often trained with embedded constraints which are also known as physics-informed or hybrid models. This paper presents an ablation study to demystify hybridization strategies, ranging from incorporating physical constraints as regularization terms or unsupervised losses, and exploring model architectures from simple multilayer perceptrons to advanced graph-based networks enabling the direct optimization of physics equations. Using our custom benchmarking pipeline for hybrid models called LIPS, we evaluate these models across four dimensions: accuracy, physical compliance, industrial readiness, and out-of-distribution generalization. The results highlight how integrating physical knowledge impacts performance across these criteria. All the implementations are reproducible and provided in the corresponding Github page.

Paperid: 719, https://arxiv.org/pdf/2509.14559.pdf

Abstract:
In this paper, we propose a novel physics-informed deep learning architecture for predicting radio maps over lunar terrain. Our approach integrates a physics-based lunar terrain generator, which produces realistic topography informed by publicly available NASA data, with a ray-tracing engine to create a high-fidelity dataset of radio propagation scenarios. Building on this dataset, we introduce a triplet-UNet architecture, consisting of two standard UNets and a diffusion network, to model complex propagation effects. Experimental results demonstrate that our method outperforms existing deep learning approaches on our terrain dataset across various metrics.

Paperid: 720, https://arxiv.org/pdf/2509.11284.pdf

Abstract:
We introduce PINGS (Physics-Informed Neural Network for Fast Generative Sampling), a framework that amortizes diffusion sampling by training a physics-informed network to approximate reverse-time probability-flow dynamics, reducing sampling to a single forward pass (NFE = 1). As a proof of concept, we learn a direct map from a 3D standard normal to a non-Gaussian Gaussian Mixture Model (GMM). PINGS preserves the target's distributional structure (multi-bandwidth kernel $MMD^2 = 1.88 \times 10^{-2}$ with small errors in mean, covariance, skewness, and excess kurtosis) and achieves constant-time generation: $10^4$ samples in $16.54 \pm 0.56$ millisecond on an RTX 3090, versus 468-843 millisecond for DPM-Solver (10/20) and 960 millisecond for DDIM (50) under matched conditions. We also sanity-check the PINN/automatic-differentiation pipeline on a damped harmonic oscillator, obtaining MSEs down to $\mathcal{O}(10^{-5})$. Compared to fast but iterative ODE solvers and direct-map families (Flow, Rectified-Flow, Consistency), PINGS frames generative sampling as a PINN-style residual problem with endpoint anchoring, yielding a white-box, differentiable map with NFE = 1. These proof-of-concept results position PINGS as a promising route to fast, function-based generative sampling with potential extensions to scientific simulation (e.g., fast calorimetry).

Paperid: 721, https://arxiv.org/pdf/2509.09135.pdf

Abstract:
Existing reinforcement learning (RL) methods struggle with complex dynamical systems that demand interactions at high frequencies or irregular time intervals. Continuous-time RL (CTRL) has emerged as a promising alternative by replacing discrete-time Bellman recursion with differential value functions defined as viscosity solutions of the Hamilton--Jacobi--Bellman (HJB) equation. While CTRL has shown promise, its applications have been largely limited to the single-agent domain. This limitation stems from two key challenges: (i) conventional solution methods for HJB equations suffer from the curse of dimensionality (CoD), making them intractable in high-dimensional systems; and (ii) even with HJB-based learning approaches, accurately approximating centralized value functions in multi-agent settings remains difficult, which in turn destabilizes policy training. In this paper, we propose a CT-MARL framework that uses physics-informed neural networks (PINNs) to approximate HJB-based value functions at scale. To ensure the value is consistent with its differential structure, we align value learning with value-gradient learning by introducing a Value Gradient Iteration (VGI) module that iteratively refines value gradients along trajectories. This improves gradient fidelity, in turn yielding more accurate values and stronger policy learning. We evaluate our method using continuous-time variants of standard benchmarks, including multi-agent particle environment (MPE) and multi-agent MuJoCo. Our results demonstrate that our approach consistently outperforms existing continuous-time RL baselines and scales to complex multi-agent dynamics.

Paperid: 722, https://arxiv.org/pdf/2509.08607.pdf

Abstract:
The geodesy of irregularly shaped small bodies presents fundamental challenges for gravitational field modeling, particularly as deep space exploration missions increasingly target asteroids and comets. Traditional approaches suffer from critical limitations: spherical harmonics diverge within the Brillouin sphere where spacecraft typically operate, polyhedral models assume unrealistic homogeneous density distributions, and existing machine learning methods like GeodesyNets and Physics-Informed Neural Networks (PINN-GM) require extensive computational resources and training time. This work introduces MasconCubes, a novel self-supervised learning approach that formulates gravity inversion as a direct optimization problem over a regular 3D grid of point masses (mascons). Unlike implicit neural representations, MasconCubes explicitly model mass distributions while leveraging known asteroid shape information to constrain the solution space. Comprehensive evaluation on diverse asteroid models including Bennu, Eros, Itokawa, and synthetic planetesimals demonstrates that MasconCubes achieve superior performance across multiple metrics. Most notably, MasconCubes demonstrate computational efficiency advantages with training times approximately 40 times faster than GeodesyNets while maintaining physical interpretability through explicit mass distributions. These results establish MasconCubes as a promising approach for mission-critical gravitational modeling applications requiring high accuracy, computational efficiency, and physical insight into internal mass distributions of irregular celestial bodies.

Paperid: 723, https://arxiv.org/pdf/2509.07245.pdf

Abstract:
Solving inverse problems with Physics-Informed Neural Networks (PINNs) is computationally expensive for multi-query scenarios, as each new set of observed data requires a new, expensive training procedure. We present Inverse-Parameter Basis PINNs (IP-Basis PINNs), a meta-learning framework that extends the foundational work of Desai et al. (2022) to enable rapid and efficient inference for inverse problems. Our method employs an offline-online decomposition: a deep network is first trained offline to produce a rich set of basis functions that span the solution space of a parametric differential equation. For each new inverse problem online, this network is frozen, and solutions and parameters are inferred by training only a lightweight linear output layer against observed data. Key innovations that make our approach effective for inverse problems include: (1) a novel online loss formulation for simultaneous solution reconstruction and parameter identification, (2) a significant reduction in computational overhead via forward-mode automatic differentiation for PDE loss evaluation, and (3) a non-trivial validation and early-stopping mechanism for robust offline training. We demonstrate the efficacy of IP-Basis PINNs on three diverse benchmarks, including an extension to universal PINNs for unknown functional terms-showing consistent performance across constant and functional parameter estimation, a significant speedup per query over standard PINNs, and robust operation with scarce and noisy data.

Paperid: 724, https://arxiv.org/pdf/2509.04402.pdf

Abstract:
X-ray ptychography provides exceptional nanoscale resolution and is widely applied in materials science, biology, and nanotechnology. However, its full potential is constrained by the critical challenge of accurately reconstructing images when the illuminating probe is unknown. Conventional iterative methods and deep learning approaches are often suboptimal, particularly under the low-signal conditions inherent to low-dose and high-speed experiments. These limitations compromise reconstruction fidelity and restrict the broader adoption of the technique. In this work, we introduce the Ptychographic Implicit Neural Representation (PtyINR), a self-supervised framework that simultaneously addresses the object and probe recovery problem. By parameterizing both as continuous neural representations, PtyINR performs end-to-end reconstruction directly from raw diffraction patterns without requiring any pre-characterization of the probe. Extensive evaluations demonstrate that PtyINR achieves superior reconstruction quality on both simulated and experimental data, with remarkable robustness under challenging low-signal conditions. Furthermore, PtyINR offers a generalizable, physics-informed framework for addressing probe-dependent inverse problems, making it applicable to a wide range of computational microscopy problems.

Paperid: 725, https://arxiv.org/pdf/2509.03084.pdf

Abstract:
Self-supervised pretraining from static structures of drug-like compounds and proteins enable powerful learned feature representations. Learned features demonstrate state of the art performance on a range of predictive tasks including molecular properties, structure generation, and protein-ligand interactions. The majority of approaches are limited by their use of static structures and it remains an open question, how best to use atomistic molecular dynamics (MD) simulations to develop more generalized models to improve prediction accuracy for novel molecular structures. We present SURrogate mmGBSA (SurGBSA) as a new modeling approach for MD-based representation learning, which learns a surrogate function of the Molecular Mechanics Generalized Born Surface Area (MMGBSA). We show for the first time the benefits of physics-informed pre-training to train a surrogate MMGBSA model on a collection of over 1.4 million 3D trajectories collected from MD simulations of the CASF-2016 benchmark. SurGBSA demonstrates a dramatic 27,927x speedup versus a traditional physics-based single-point MMGBSA calculation while nearly matching single-point MMGBSA accuracy on the challenging pose ranking problem for identification of the correct top pose (-0.4% difference). Our work advances the development of molecular foundation models by showing model improvements when training on MD simulations. Models, code and training data are made publicly available.

Paperid: 726, https://arxiv.org/pdf/2509.02091.pdf

Abstract:
Physics-informed Neural Network (PINN) faces significant challenges when approximating solutions to conservation laws, particularly in ensuring conservation and accurately resolving discontinuities. To address these limitations, we propose Conservation Law-informed Neural Network (CLINN), a novel framework that incorporates the boundedness constraint, implicit solution form, and Rankine-Hugoniot condition of scalar conservation laws into the loss function, thereby enforcing exact conservation properties. Furthermore, we integrate a residual-based adaptive refinement (RAR) strategy to dynamically prioritize training near discontinuities, substantially improving the network's ability to capture sharp gradients. Numerical experiments are conducted on benchmark problems, including the inviscid Burgers equation, the Lighthill-Whitham-Richards (LWR) traffic flow model, and the Buckley-Leverett problem. Results demonstrate that CLINN achieves superior accuracy in resolving solution profiles and discontinuity locations while reducing numeral oscillations. Compared to conventional PINN, CLINN yields a maximum reduction of 99.2% in mean squared error (MSE).

Paperid: 727, https://arxiv.org/pdf/2508.21618.pdf

Abstract:
We present PhISM, a physics-informed deep learning architecture that learns without supervision to explicitly disentangle hyperspectral observations and model them with continuous basis functions. \mname outperforms prior methods on several classification and regression benchmarks, requires limited labeled data, and provides additional insights thanks to interpretable latent representation.

Paperid: 728, https://arxiv.org/pdf/2508.21571.pdf

Abstract:
Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore, the convergence guarantee of stochastic gradient descent is of fundamental importance. In this work, we establish the linear convergence of stochastic gradient descent / flow in training over-parameterized two layer PINNs for a general class of activation functions in the sense of high probability. These results extend the existing result [18] in which gradient descent was analyzed. The challenge of the analysis lies in handling the dynamic randomness introduced by stochastic optimization methods. The key of the analysis lies in ensuring the positive definiteness of suitable Gram matrices during the training. The analysis sheds insight into the dynamics of the optimization process, and provides guarantees on the neural networks trained by stochastic algorithms.

Paperid: 729, https://arxiv.org/pdf/2508.20440.pdf

Abstract:
In this paper, we propose a novel framework, Dynamic Domain Decomposition Physics-Informed Neural Networks (D3PINNs), for solving time-dependent partial differential equations (PDEs). In this framework, solutions of time-dependent PDEs are dynamically captured. First, an approximate solution is obtained by the Physics-Informed Neural Networks (PINNs) containing the domain decomposition, then the time derivative terms in the PDE will be retained and the other terms associated with the solution will be replaced with the approximate solution. As a result, the PDE reduces to an ordinary differential equations (ODEs). Finally, the time-varying solution will be solved by the classical numerical methods for ODEs. D3PINNs retain the computational efffciency and ffexibility inherent to PINNs and enhance the ability for capturing solutions of time-dependent PDEs. Numerical experiments validate the effectiveness of the proposed methods.

Paperid: 730, https://arxiv.org/pdf/2508.19419.pdf

Abstract:
Accurate subsurface reservoir pressure control is extremely challenging due to geological heterogeneity and multiphase fluid-flow dynamics. Predicting behavior in this setting relies on high-fidelity physics-based simulations that are computationally expensive. Yet, the uncertain, heterogeneous properties that control these flows make it necessary to perform many of these expensive simulations, which is often prohibitive. To address these challenges, we introduce a physics-informed machine learning workflow that couples a fully differentiable multiphase flow simulator, which is implemented in the DPFEHM framework with a convolutional neural network (CNN). The CNN learns to predict fluid extraction rates from heterogeneous permeability fields to enforce pressure limits at critical reservoir locations. By incorporating transient multiphase flow physics into the training process, our method enables more practical and accurate predictions for realistic injection-extraction scenarios compare to previous works. To speed up training, we pretrain the model on single-phase, steady-state simulations and then fine-tune it on full multiphase scenarios, which dramatically reduces the computational cost. We demonstrate that high-accuracy training can be achieved with fewer than three thousand full-physics multiphase flow simulations -- compared to previous estimates requiring up to ten million. This drastic reduction in the number of simulations is achieved by leveraging transfer learning from much less expensive single-phase simulations.

Paperid: 731, https://arxiv.org/pdf/2508.14688.pdf

Abstract:
Perceptualizing tool interactions with deformable structures in surgical procedures remains challenging, as unimodal visualization techniques often fail to capture the complexity of these interactions due to constraints such as occlusion and limited depth perception. This paper presents a novel approach to augment tool navigation in mixed reality environments by providing auditory representations of tool-tissue dynamics, particularly for interactions with soft tissue. BioSonix, a physics-informed design framework, utilizes tissue displacements in 3D space to compute excitation forces for a sound model encoding tissue properties such as stiffness and density. Biomechanical simulations were employed to model particle displacements resulting from tool-tissue interactions, establishing a robust foundation for the method. An optimization approach was used to define configurations for capturing diverse interaction scenarios with varying tool trajectories. Experiments were conducted to validate the accuracy of the sound-displacement mappings. Additionally, two user studies were performed: the first involved two clinical professionals (a neuroradiologist and a cardiologist), who confirmed the method's impact and achieved high task accuracy; the second included 22 biomedical experts, who demonstrated high discrimination accuracy in tissue differentiation and targeting tasks. The results revealed a strong correlation between tool-tissue dynamics and their corresponding auditory profiles, highlighting the potential of these sound representations to enhance the intuitive understanding of complex interactions.

Paperid: 732, https://arxiv.org/pdf/2508.11542.pdf

Abstract:
This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy within the reduced space to iteratively construct initial guesses for the OpInf learning problem that prioritize the interactions of the dominant modes. The initial guess computed for any target reduced dimension corresponds to a ROM with provably smaller or equal snapshot reconstruction error than with standard OpInf. Moreover, our nested OpInf algorithm can be warm-started from previously learned models, enabling versatile application scenarios involving dynamic basis and model form updates. We demonstrate the performance of our algorithm on a cubic heat conduction problem, with nested OpInf achieving a four times smaller error than standard OpInf at a comparable offline time. Further, we apply nested OpInf to a large-scale, parameterized model of the Greenland ice sheet where, despite model form approximation errors, it learns a ROM with, on average, 3% error and computational speed-up factor above 19,000.

Paperid: 733, https://arxiv.org/pdf/2508.10921.pdf

Abstract:
This study proposes a self-optimization physics-informed Fourier-features randomized neural network (SO-PIFRNN) framework, which significantly improves the numerical solving accuracy of PDEs through hyperparameter optimization mechanism. The framework employs a bi-level optimization architecture: the outer-level optimization utilizes a multi-strategy collaborated particle swarm optimization (MSC-PSO) algorithm to search for optimal hyperparameters of physics-informed Fourier-features randomized neural network, while the inner-level optimization determines the output layer weights of the neural network via the least squares method. The core innovation of this study is embodied in the following three aspects: First, the Fourier basis function activation mechanism is introduced in the hidden layer of neural network, which significantly enhances the ability of the network to capture multi-frequency components of the solution. Secondly, a novel derivative neural network method is proposed, which improves the calculation accuracy and efficiency of PIFRNN method. Finally, the MSC-PSO algorithm of the hybrid optimization strategy is designed to improve the global search ability and convergence accuracy through the synergistic effect of dynamic parameter adjustment, elitist and mutation strategies. Through a series of numerical experiments, including multiscale equations in complex regions, high-order equations, high-dimensional equations and nonlinear equations, the validity of SO-PIFRNN is verified. The experimental results affirm that SO-PIFRNN exhibits superior approximation accuracy and frequency capture capability.

Paperid: 734, https://arxiv.org/pdf/2508.03421.pdf

Abstract:
Physics-informed neural networks (PINNs) have recently emerged as a popular approach for solving forward and inverse problems involving partial differential equations (PDEs). Compared to fully connected neural networks, PINNs based on convolutional neural networks offer advantages in the hard enforcement of boundary conditions and in reducing the computational cost of partial derivatives. However, the latter still struggles with slow convergence and even failure in some scenarios. In this study, we propose a matrix preconditioning method to improve the convergence of the latter. Specifically, we combine automatic differentiation with matrix coloring to compute the Jacobian matrix of the PDE system, which is used to construct the preconditioner via incomplete LU factorization. We subsequently use the preconditioner to scale the PDE residual in the loss function in order to reduce the condition number of the Jacobian matrix, which is key to improving the convergence of PINNs. To overcome the incompatibility between automatic differentiation and triangular solves in the preconditioning, we also design a framework based on the adjoint method to compute the gradients of the loss function with respect to the network parameters. By numerical experiments, we validate that the proposed method successfully and efficiently solves the multi-scale problem and the high Reynolds number problem, in both of which PINNs fail to obtain satisfactory results.

Paperid: 735, https://arxiv.org/pdf/2508.03326.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth velocity and pressure fields from synthetic 4D flow Magnetic Resonance Imaging (MRI) data. We analyze five non-Newtonian dynamic 3D blood flow cases within a realistic aortic model, covering a range of hematocrit values from anemic to polycythemic conditions. To enhance state estimation results, we consider various design and training techniques for PINNs, including adaptive loss balancing, curriculum training, and a realistic measurement operator. Regarding blood rheology, the PINN approach accurately estimates viscosity globally and locally under peak systolic conditions. It also provides a clear pattern recognition for diastolic stages. Regarding mass conservation, PINN estimations effectively reproduce the bifurcation of flow through the different branches of the aorta, demonstrate an excellent representation of the non-slip conditions at the walls, and accurately estimate pressure drops with relative errors below the 5% in the whole pressure field. We test our pressure drop estimations against the state of the art Virtual Work Energy Relative Pressure (vWERP) estimator, and we observe how our results outperform vWERP in terms of both accuracy and time resolution. Additionally, we find that the best results are achieved by computing the velocity field using the PINN, which is then integrated into the vWERP framework, leading to time super-sampled and high-order approximations, with a clinically admissible accuracy.

Paperid: 736, https://arxiv.org/pdf/2508.02712.pdf

Abstract:
Modern engineering systems are increasingly equipped with sensors for real-time monitoring and decision-making. However, the data collected by these sensors is often noisy and difficult to interpret, limiting its utility for control and diagnostics. In this work, we propose a physics-informed denoising framework that integrates energy-based model and Fisher score regularization to jointly reduce data noise and enforce physical consistency with a physics-based model. The approach is first validated on benchmark problems, including the simple harmonic oscillator, Burgers' equation, and Laplace's equation, across varying noise levels. We then apply the denoising framework to real thermal emission data from laser powder bed fusion (LPBF) additive manufacturing experiments, using a trained Physics-Informed Neural Network (PINN) surrogate model of the LPBF process to guide denoising. Results show that the proposed method outperforms baseline neural network denoisers, effectively reducing noise under a range of LPBF processing conditions. This physics-guided denoising strategy enables robust, real-time interpretation of low-cost sensor data, facilitating predictive control and improved defect mitigation in additive manufacturing.

Paperid: 737, https://arxiv.org/pdf/2508.02692.pdf

Abstract:
Optimization-based PDE solvers that minimize scalar loss functions have gained increasing attention in recent years. These methods either define the loss directly over discrete variables, as in Optimizing a Discrete Loss (ODIL), or indirectly through a neural network surrogate, as in Physics-Informed Neural Networks (PINNs). However, despite their promise, such methods often converge much more slowly than classical iterative solvers and are commonly regarded as inefficient. This work provides a theoretical insight, attributing the inefficiency to the use of the mean squared error (MSE) loss, which implicitly forms the normal equations, squares the condition number, and severely impairs optimization. To address this, we propose a novel Stabilized Gradient Residual (SGR) loss. By tuning a weight parameter, it flexibly modulates the condition number between the original system and its normal equations, while reducing to the MSE loss in the limiting case. We systematically benchmark the convergence behavior and optimization stability of the SGR loss within both the ODIL framework and PINNs-employing either numerical or automatic differentiation-and compare its performance against classical iterative solvers. Numerical experiments on a range of benchmark problems demonstrate that, within the ODIL framework, the proposed SGR loss achieves orders-of-magnitude faster convergence than the MSE loss. Further validation within the PINNs framework shows that, despite the high nonlinearity of neural networks, SGR consistently outperforms the MSE loss. These theoretical and empirical findings help bridge the performance gap between classical iterative solvers and optimization-based solvers, highlighting the central role of loss conditioning, and provide key insights for the design of more efficient PDE solvers.

Paperid: 738, https://arxiv.org/pdf/2507.22678.pdf

Abstract:
Physics-informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to satisfy boundary conditions, often resulting in significantly improved accuracy and computational efficiency compared to traditional physics-informed neural networks (PINNs). In this work, we improve and extend the application of PIHNNs to two-dimensional problems. First, we introduce a novel holomorphic network architecture based on the Kolmogorov-Arnold representation (PIHKAN), which achieves higher accuracy with reduced model complexity. Second, we develop mathematical extensions that broaden the applicability of PIHNNs to a wider class of elliptic partial differential equations, including the Helmholtz equation. Finally, we propose a new method based on Laurent series theory that enables the application of holomorphic networks to multiply-connected plane domains, thereby removing the previous limitation to simply-connected geometries.

Paperid: 739, https://arxiv.org/pdf/2507.22279.pdf

Abstract:
In the rapidly evolving domain of autonomous systems, interaction among agents within a shared environment is both inevitable and essential for enhancing overall system capabilities. A key requirement in such multi-agent systems is the ability of each agent to reliably predict the future positions of its nearest neighbors. Traditionally, graphs and graph theory have served as effective tools for modeling inter agent communication and relationships. While this approach is widely used, the present work proposes a novel method that leverages dynamic graphs in a forward looking manner. Specifically, the employment of EvolveGCN, a dynamic graph convolutional network, to forecast the evolution of inter-agent relationships over time. To improve prediction accuracy and ensure physical plausibility, this research incorporates physics constrained loss functions based on the Clohessy-Wiltshire equations of motion. This integrated approach enhances the reliability of future state estimations in multi-agent scenarios.

Paperid: 740, https://arxiv.org/pdf/2507.21749.pdf

Abstract:
Training neural networks can be challenging, especially as the complexity of the problem increases. Despite using wider or deeper networks, training them can be a tedious process, especially if a wrong choice of the hyperparameter is made. The learning rate is one of such crucial hyperparameters, which is usually kept static during the training process. Learning dynamics in complex systems often requires a more adaptive approach to the learning rate. This adaptability becomes crucial to effectively navigate varying gradients and optimize the learning process during the training process. In this paper, a dynamic learning rate scheduler (DLRS) algorithm is presented that adapts the learning rate based on the loss values calculated during the training process. Experiments are conducted on problems related to physics-informed neural networks (PINNs) and image classification using multilayer perceptrons and convolutional neural networks, respectively. The results demonstrate that the proposed DLRS accelerates training and improves stability.

Paperid: 741, https://arxiv.org/pdf/2507.21350.pdf

Abstract:
Neural networks have emerged as a powerful tool for modeling physical systems, offering the ability to learn complex representations from limited data while integrating foundational scientific knowledge. In particular, neuro-symbolic approaches that combine data-driven learning, the neuro, with symbolic equations and rules, the symbolic, address the tension between methods that are purely empirical, which risk straying from established physical principles, and traditional numerical solvers that demand complete geometric knowledge and can be prohibitively expensive for high-fidelity simulations. In this work, we present a novel neuro-symbolic framework for reconstructing and simulating elastic objects directly from sparse multi-view image sequences, without requiring explicit geometric information. Specifically, we integrate a neural radiance field (NeRF) for object reconstruction with physics-informed neural networks (PINN) that incorporate the governing partial differential equations of elasticity. In doing so, our method learns a spatiotemporal representation of deforming objects that leverages both image supervision and symbolic physical constraints. To handle complex boundary and initial conditions, which are traditionally confronted using finite element methods, boundary element methods, or sensor-based measurements, we employ an energy-constrained Physics-Informed Neural Network architecture. This design enhances both simulation accuracy and the explainability of results.

Paperid: 742, https://arxiv.org/pdf/2507.18206.pdf

Abstract:
A fundamental requirement for full autonomy in mobile robots is accurate navigation even in situations where satellite navigation or cameras are unavailable. In such practical situations, relying only on inertial sensors will result in navigation solution drift due to the sensors' inherent noise and error terms. One of the emerging solutions to mitigate drift is to maneuver the robot in a snake-like slithering motion to increase the inertial signal-to-noise ratio, allowing the regression of the mobile robot position. In this work, we propose MoRPI-PINN as a physics-informed neural network framework for accurate inertial-based mobile robot navigation. By embedding physical laws and constraints into the training process, MoRPI-PINN is capable of providing an accurate and robust navigation solution. Using real-world experiments, we show accuracy improvements of over 85% compared to other approaches. MoRPI-PINN is a lightweight approach that can be implemented even on edge devices and used in any typical mobile robot application.

Paperid: 743, https://arxiv.org/pdf/2507.04419.pdf

Abstract:
Acoustic data provide scientific and engineering insights in fields ranging from bioacoustics and communications to ocean and earth sciences. In this review, we survey recent advances and the transformative potential of machine learning (ML) in acoustics, including deep learning (DL). Using the Python high-level programming language, we demonstrate a broad collection of ML techniques to detect and find patterns for classification, regression, and generation in acoustics data automatically. We have ML examples including acoustic data classification, generative modeling for spatial audio, and physics-informed neural networks. This work includes AcousticsML, a set of practical Jupyter notebook examples on GitHub demonstrating ML benefits and encouraging researchers and practitioners to apply reproducible data-driven approaches to acoustic challenges.

Paperid: 744, https://arxiv.org/pdf/2507.02887.pdf

Abstract:
Proton exchange membrane (PEM) electrolyzers are pivotal for sustainable hydrogen production, yet their long-term performance is hindered by membrane degradation, which poses reliability and safety challenges. Therefore, accurate modeling of this degradation is essential for optimizing durability and performance. To address these concerns, traditional physics-based models have been developed, offering interpretability but requiring numerous parameters that are often difficult to measure and calibrate. Conversely, data-driven approaches, such as machine learning, offer flexibility but may lack physical consistency and generalizability. To address these limitations, this study presents the first application of Physics-Informed Neural Networks (PINNs) to model membrane degradation in PEM electrolyzers. The proposed PINN framework couples two ordinary differential equations, one modeling membrane thinning via a first-order degradation law and another governing the time evolution of the cell voltage under membrane degradation. Results demonstrate that the PINN accurately captures the long-term system's degradation dynamics while preserving physical interpretability with limited noisy data. Consequently, this work introduces a novel hybrid modeling approach for estimating and understanding membrane degradation mechanisms in PEM electrolyzers, offering a foundation for more robust predictive tools in electrochemical system diagnostics.

Paperid: 745, https://arxiv.org/pdf/2506.20537.pdf

Abstract:
Efficient simulation of Laser Powder Bed Fusion (LPBF) is crucial for process prediction due to the lasting issue of high computation cost using traditional numerical methods such as finite element analysis (FEA). This study presents an efficient modeling framework termed FEA-Regulated Physics-Informed Neural Network (FEA-PINN) to accelerate the thermal field prediction in a LPBF process while maintaining the FEA accuracy. A novel dynamic material updating strategy is developed to capture the dynamic phase change of powder-liquid-solid in the PINN model. The PINN model incorporates temperature-dependent material properties and phase change behavior using the apparent heat capacity method. While the PINN model demonstrates high accuracy with a small training data and enables generalization of new process parameters via transfer learning, it faces the challenge of high computation cost in time-dependent problems due to the residual accumulation. To overcome this issue, the FEA-PINN framework integrates corrective FEA simulations during inference to enforce physical consistency and reduce error drift. A comparative analysis shows that FEA-PINN achieves equivalent accuracy to FEA while significantly reducing computational cost. The framework has been validated using the benchmark FEA data and demonstrated through single-track scanning in LPBF.

Paperid: 746, https://arxiv.org/pdf/2506.06188.pdf

Abstract:
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC) framework, originally proposed to modeling and control of Ordinary Differential Equations (ODE) without the need of any labeled data, to the PDE case, particularly to single-phase incompressible and compressible flows, integrating neural networks with physical conservation laws. The PINC model for PDEs is structured into two stages: a steady-state network, which learns equilibrium solutions for a wide range of control inputs, and a transient network, which captures dynamic responses under time-varying boundary conditions. We propose a simplifying assumption that reduces the dimensionality of the spatial coordinate regarding the initial condition, allowing the efficient training of the PINC network. This simplification enables the derivation of optimal control policies using Model Predictive Control (MPC). We validate our approach through numerical experiments, demonstrating that the PINC model, which is trained exclusively using physical laws, i.e., without labeled data, accurately represents flow dynamics and enables real-time control applications. The results highlight the PINC's capability to efficiently approximate PDE solutions without requiring iterative solvers, making it a promising alternative for fluid flow monitoring and optimization in engineering applications.

Paperid: 747, https://arxiv.org/pdf/2505.21994.pdf

Abstract:
Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible homogeneous elasticity equations deteriorates as the LamÃ© coefficient $Î»\to\infty$, or equivalently as the Poisson ratio $Î½\to1/2$. This phenomenon, known as locking or non-robustness, remains not fully understood despite extensive investigation. In this paper, we propose a robust method based on a fundamentally different, machine-learning-driven approach. Leveraging recently developed Physics-Informed Neural Networks (PINNs), we address the numerical solution of linear elasticity equations governing nearly incompressible materials. The core idea of our method is to appropriately decompose the given equations to alleviate the extreme imbalance in the coefficients, while simultaneously solving both the forward and inverse problems to recover the solutions of the decomposed systems as well as the associated external conditions. Through various numerical experiments, including constant, variable and parametric LamÃ© coefficients, we illustrate the efficiency of the proposed methodology.

Paperid: 748, https://arxiv.org/pdf/2505.20327.pdf

Abstract:
Data-driven discovery of dynamics in biological systems allows for better observation and characterization of processes, such as calcium signaling in cell culture. Recent advancements in techniques allow the exploration of previously unattainable insights of dynamical systems, such as the Sparse Identification of Non-Linear Dynamics (SINDy), overcoming the limitations of more classic methodologies. The latter requires some prior knowledge of an effective library of candidate terms, which is not realistic for a real case study. Using inspiration from fields like traffic density estimation and control theory, we propose a methodology for characterization and performance analysis of calcium delivery in a family of cells. In this work, we compare the performance of the Constrained Regularized Least-Squares Method (CRLSM) and Physics-Informed Neural Networks (PINN) for system identification and parameter discovery for governing ordinary differential equations (ODEs). The CRLSM achieves a fairly good parameter estimate and a good data fit when using the learned parameters in the Consensus problem. On the other hand, despite the initial hypothesis, PINNs fail to match the CRLSM performance and, under the current configuration, do not provide fair parameter estimation. However, we have only studied a limited number of PINN architectures, and it is expected that additional hyperparameter tuning, as well as uncertainty quantification, could significantly improve the performance in future works.

Paperid: 749, https://arxiv.org/pdf/2505.19036.pdf

Abstract:
Physics-informed neural networks (PINNs), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability effectively circumvents the challenges of mesh generation that traditional numerical methods face in high-dimensional or geometrically intricate settings. While recent studies have extended PINNs to manifolds, the theoretical foundations remain scarce. Existing theoretical analyses of PINNs in Euclidean space often rely on smoothness assumptions for the solutions. However, recent empirical evidence indicates that PINNs may struggle to approximate solutions with low regularity, such as those arising from nonlinear hyperbolic equations. In this paper, we develop a framework for PINNs tailored to the efficient approximation of weak solutions, particularly nonlinear hyperbolic equations defined on manifolds. We introduce a novel weak PINN (wPINN) formulation on manifolds that leverages the well-posedness theory to approximate entropy solutions of geometry-compatible hyperbolic conservation laws on manifolds. Employing tools from approximation theory, we establish a convergence analysis of the algorithm, including an analysis of approximation errors for time-dependent entropy solutions. This analysis provides insight into the accumulation of approximation errors over long time horizons. Notably, the network complexity depends only on the intrinsic dimension, independent of the ambient space dimension. Our results match the minimax rate in the d-dimensional Euclidean space, demonstrating that PINNs can alleviate the curse of dimensionality in the context of low-dimensional manifolds. Finally, we validate the performance of the proposed wPINN framework through numerical experiments, confirming its ability to efficiently approximate entropy solutions on manifolds.

Paperid: 750, https://arxiv.org/pdf/2505.17919.pdf

Abstract:
Despite the widely recognized success of residual connections in modern neural networks, their design principles remain largely heuristic. This paper introduces KITINet (Kinetics Theory Inspired Network), a novel architecture that reinterprets feature propagation through the lens of non-equilibrium particle dynamics and partial differential equation (PDE) simulation. At its core, we propose a residual module that models feature updates as the stochastic evolution of a particle system, numerically simulated via a discretized solver for the Boltzmann transport equation (BTE). This formulation mimics particle collisions and energy exchange, enabling adaptive feature refinement via physics-informed interactions. Additionally, we reveal that this mechanism induces network parameter condensation during training, where parameters progressively concentrate into a sparse subset of dominant channels. Experiments on scientific computation (PDE operator), image classification (CIFAR-10/100), and text classification (IMDb/SNLI) show consistent improvements over classic network baselines, with negligible increase of FLOPs.

Paperid: 751, https://arxiv.org/pdf/2505.16996.pdf

Abstract:
Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and Universal Physics-Informed Neural Networks (UPINNs), are effective at isolating either parameters or functions but can face challenges when applied simultaneously due to solution non-uniqueness. In this work, we introduce a framework that addresses these limitations by establishing conditions under which unique solutions can be guaranteed. To illustrate, we apply it to examples from biological systems and ecological dynamics, demonstrating accurate and interpretable results. Our approach significantly enhances the potential of machine learning techniques in modeling complex systems in science and engineering.

Paperid: 752, https://arxiv.org/pdf/2505.14002.pdf

Abstract:
We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we extend the neural tangent kernel (NTK) framework for PINNs to establish global convergence guarantees for a broad class of linear operators. For nonlinear PDEs, we prove convergence to critical points via the Åojasiewicz inequality under the random feature model, eliminating the need for strong over-parameterization and encompassing both gradient flow and implicit gradient descent dynamics. Our results further reveal that the random feature model exhibits an implicit regularization effect, preventing parameter divergence to infinity. Theoretical findings are corroborated by numerical experiments, providing new insights into the training dynamics and robustness of neural network PDE solvers.

Paperid: 753, https://arxiv.org/pdf/2505.10925.pdf

Abstract:
This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style mesh discretization, the dPINN accurately evaluates system energy through Gaussian quadrature-based element-wise integration. To ensure physical field continuity across subdomain interfaces, the EIC mechanism enforces interfacial displacement constraints without requiring auxiliary sampling or loss penalties.This formulation supports independent meshing in each subdomain, simplifying preprocessing and improving computational flexibility. Additionally, by eliminating the influence of weak spatial constraints (WSC) commonly observed in traditional PINNs, the EIC-dPINN delivers more stable and physically consistent predictions.Extensive two- and three-dimensional numerical experiments validate the proposed framework's accuracy and demonstrate the computational efficiency gains achieved through parallel training. The results highlight the framework's scalability, robustness, and potential for solving large-scale, geometrically complex problems.

Paperid: 754, https://arxiv.org/pdf/2505.01424.pdf

Abstract:
Metal additive manufacturing enables unprecedented design freedom and the production of customized, complex components. However, the rapid melting and solidification dynamics inherent to metal AM processes generate heterogeneous, non-equilibrium microstructures that significantly impact mechanical properties and subsequent functionality. Predicting microstructure and its evolution across spatial and temporal scales remains a central challenge for process optimization and defect mitigation. While conventional experimental techniques and physics-based simulations provide a physical foundation and valuable insights, they face critical limitations. In contrast, data-driven machine learning offers an alternative prediction approach and powerful pattern recognition but often operate as black-box, lacking generalizability and physical consistency. To overcome these limitations, physics-informed machine learning, including physics-informed neural networks, has emerged as a promising paradigm by embedding governing physical laws into neural network architectures, thereby enhancing accuracy, transparency, data efficiency, and extrapolation capabilities. This work presents a comprehensive evaluation of modeling strategies for microstructure prediction in metal AM. The strengths and limitations of experimental, computational, and data-driven methods are analyzed in depth, and highlight recent advances in hybrid PIML frameworks that integrate physical knowledge with ML. Key challenges, such as data scarcity, multi-scale coupling, and uncertainty quantification, are discussed alongside future directions. Ultimately, this assessment underscores the importance of PIML-based hybrid approaches in enabling predictive, scalable, and physically consistent microstructure modeling for site-specific, microstructure-aware process control and the reliable production of high-performance AM components.

Paperid: 755, https://arxiv.org/pdf/2504.20241.pdf

Abstract:
Detecting ship presence via wake signatures in SAR imagery is attracting considerable research interest, but limited annotated data availability poses significant challenges for supervised learning. Physics-based simulations are commonly used to address this data scarcity, although they are slow and constrain end-to-end learning. In this work, we explore a new direction for more efficient and end-to-end SAR ship wake simulation using a diffusion model trained on data generated by a physics-based simulator. The training dataset is built by pairing images produced by the simulator with text prompts derived from simulation parameters. Experimental result show that the model generates realistic Kelvin wake patterns and achieves significantly faster inference than the physics-based simulator. These results highlight the potential of diffusion models for fast and controllable wake image generation, opening new possibilities for end-to-end downstream tasks in maritime SAR analysis.

Paperid: 756, https://arxiv.org/pdf/2504.19013.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric uncertainties in big multi-scale problems remains challenging. We propose \$PINN a novel method of computing global uncertainty in PDEs using a Bayesian framework, by combining local Bayesian Physics-Informed Neural Networks (BPINN) with domain decomposition. The solution continuity across subdomains is obtained by imposing the flux continuity across the interface of neighboring subdomains. To demonstrate the effectiveness of \$PINN, we conduct a series of computational experiments on PDEs in 1D and 2D spatial domains. Although we have adopted conservative PINNs (cPINNs), the method can be seamlessly extended to other domain decomposition techniques. The results infer that the proposed method recovers the global uncertainty by computing the local uncertainty exactly more efficiently as the uncertainty in each subdomain can be computed concurrently. The robustness of \$PINN is verified by adding uncorrelated random noise to the training data up to 15% and testing for different domain sizes.

Paperid: 757, https://arxiv.org/pdf/2504.07058.pdf

Abstract:
In this work, we propose the Residual-Weighted Physics-Informed Neural Network (RW-PINN), a new method designed to enhance the accuracy of Physics-Informed Neural Network (PINN) based algorithms. We construct a deep learning framework with two residual-weighting schemes to solve reaction diffusion equations and evaluate its performance on both forward and inverse problems. The approach computes weights proportional to the PDE residuals, rescales them, and incorporates these scaled residuals into the loss function, leading to more stable training. Furthermore, we establish generalized error bounds that account for training and quadrature errors, and we analyze the convergence and stability of the method. The proposed algorithms are validated through numerical experiments on nonlinear equations, supported by statistical error analysis. To further demonstrate the effectiveness of our methodology, we implemented PINN-based forward and inverse frameworks for the nonlinear equations and conducted a comparative analysis with the proposed RW-PINN approach.

Paperid: 758, https://arxiv.org/pdf/2504.03484.pdf

Abstract:
The degree of polymerization (DP) is one of the methods for estimating the aging of the polymer based insulation systems, such as cellulose insulation in power components. The main degradation mechanisms in polymers are hydrolysis, pyrolysis, and oxidation. These mechanisms combined cause a reduction of the DP. However, the data availability for these types of problems is usually scarce. This study analyzes insulation aging using cellulose degradation data from power transformers. The aging problem for the cellulose immersed in mineral oil inside power transformers is modeled with ordinary differential equations (ODEs). We recover the governing equations of the degradation system using Physics-Informed Neural Networks (PINNs) and symbolic regression. We apply PINNs to discover the Arrhenius equation's unknown parameters in the Ekenstam ODE describing cellulose contamination content and the material aging process related to temperature for synthetic data and real DP values. A modification of the Ekenstam ODE is given by Emsley's system of ODEs, where the rate constant expressed by the Arrhenius equation decreases in time with the new formulation. We use PINNs and symbolic regression to recover the functional form of one of the ODEs of the system and to identify an unknown parameter.

Paperid: 759, https://arxiv.org/pdf/2503.22528.pdf

Abstract:
We introduce MixFunn, a novel neural network architecture designed to solve differential equations with enhanced precision, interpretability, and generalization capability. The architecture comprises two key components: the mixed-function neuron, which integrates multiple parameterized nonlinear functions to improve representational flexibility, and the second-order neuron, which combines a linear transformation of its inputs with a quadratic term to capture cross-combinations of input variables. These features significantly enhance the expressive power of the network, enabling it to achieve comparable or superior results with drastically fewer parameters and a reduction of up to four orders of magnitude compared to conventional approaches. We applied MixFunn in a physics-informed setting to solve differential equations in classical mechanics, quantum mechanics, and fluid dynamics, demonstrating its effectiveness in achieving higher accuracy and improved generalization to regions outside the training domain relative to standard machine learning models. Furthermore, the architecture facilitates the extraction of interpretable analytical expressions, offering valuable insights into the underlying solutions.

Paperid: 760, https://arxiv.org/pdf/2503.20222.pdf

Abstract:
Physics-informed neural networks offered an alternate way to solve several differential equations that govern complicated physics. However, their success in predicting the acoustic field is limited by the vanishing-gradient problem that occurs when solving the Helmholtz equation. In this paper, a formulation is presented that addresses this difficulty. The problem of solving the two-dimensional Helmholtz equation with the prescribed boundary conditions is posed as an unconstrained optimization problem using trial solution method. According to this method, a trial neural network that satisfies the given boundary conditions prior to the training process is constructed using the technique of transfinite interpolation and the theory of R-functions. This ansatz is initially applied to the rectangular domain and later extended to the circular and elliptical domains. The acoustic field predicted from the proposed formulation is compared with that obtained from the two-dimensional finite element methods. Good agreement is observed in all three domains considered. Minor limitations associated with the proposed formulation and their remedies are also discussed.

Paperid: 761, https://arxiv.org/pdf/2503.15679.pdf

Abstract:
For a data-driven and physics combined modelling of unsteady flow systems with moving immersed boundaries, Sundar {\it et al.} introduced an immersed boundary-aware (IBA) framework, combining Physics-Informed Neural Networks (PINNs) and the immersed boundary method (IBM). This approach was beneficial because it avoided case-specific transformations to a body-attached reference frame. Building on this, we now address the challenges of long time integration in velocity reconstruction and pressure recovery by extending this IBA framework with sequential learning strategies. Key difficulties for PINNs in long time integration include temporal sparsity, long temporal domains and rich spectral content. To tackle these, a moving boundary-enabled PINN is developed, proposing two sequential learning strategies: - a time marching with gradual increase in time domain size, however, this approach struggles with error accumulation over long time domains; and - a time decomposition which divides the temporal domain into smaller segments, combined with transfer learning it effectively reduces error propagation and computational complexity. The key findings for modelling of incompressible unsteady flows past a flapping airfoil include: - for quasi-periodic flows, the time decomposition approach with preferential spatio-temporal sampling improves accuracy and efficiency for pressure recovery and aerodynamic load reconstruction, and, - for long time domains, decomposing it into smaller temporal segments and employing multiple sub-networks, simplifies the problem ensuring stability and reduced network sizes. This study highlights the limitations of traditional PINNs for long time integration of flow-structure interaction problems and demonstrates the benefits of decomposition-based strategies for addressing error accumulation, computational cost, and complex dynamics.

Paperid: 762, https://arxiv.org/pdf/2503.14222.pdf

Abstract:
In a more connected world, modeling multi-agent systems with hyperbolic partial differential equations (PDEs) offers a compact, physics-consistent description of collective dynamics. However, classical control tools need adaptation for these complex systems. Physics-informed neural networks (PINNs) provide a powerful framework to fix this issue by inferring solutions to PDEs by embedding governing equations into the neural network. A major limitation of original PINNs is their inability to capture steep gradients and discontinuities in hyperbolic PDEs. To tackle this problem, we propose a stacked residual PINN method enhanced with a vanishing viscosity mechanism. Initially, a basic PINN with a small viscosity coefficient provides a stable, low-fidelity solution. Residual correction blocks with learnable scaling parameters then iteratively refine this solution, progressively decreasing the viscosity coefficient to transition from parabolic to hyperbolic PDEs. Applying this method to traffic state reconstruction improved results by an order of magnitude in relative $\mathcal{L}^2$ error, demonstrating its potential to accurately estimate solutions where original PINNs struggle with instability and low fidelity.

Paperid: 763, https://arxiv.org/pdf/2503.10032.pdf

Abstract:
Extreme learning machines (ELMs), which preset hidden layer parameters and solve for last layer coefficients via a least squares method, can typically solve partial differential equations faster and more accurately than Physics Informed Neural Networks. However, they remain computationally expensive when high accuracy requires large least squares problems to be solved. Domain decomposition methods (DDMs) for ELMs have allowed parallel computation to reduce training times of large systems. This paper constructs a coarse space for ELMs, which enables further acceleration of their training. By partitioning interface variables into coarse and non-coarse variables, selective elimination introduces a Schur complement system on the non-coarse variables with the coarse problem embedded. Key to the performance of the proposed method is a Neumann-Neumann acceleration that utilizes the coarse space. Numerical experiments demonstrate significant speedup compared to a previous DDM method for ELMs.

Paperid: 764, https://arxiv.org/pdf/2503.09418.pdf

Abstract:
Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force characteristics, or inaccessible load points. This paper presents an efficient dynamic load reconstruction method using physics-informed Gaussian processes (GP) based on frequency-sparse Fourier basis functions. The GP's covariance matrices are built using the description of the system dynamics, and the model is trained using structural response measurements. This provides support and interpretability to the machine learning model, in contrast to purely data-driven methods. In addition, the model filters out irrelevant components in the Fourier basis function by leveraging the sparsity of structural responses in the frequency domain, thereby reducing computational complexity during optimization. The trained model for structural responses is then integrated with the differential equation for a harmonic oscillator, creating a probabilistic dynamic load model that predicts load patterns without requiring force data during training. The model's effectiveness is validated through two case studies: a numerical model of a wind-excited 76-story building and an experiment using a physical scale model of the LillebÃ¦lt Bridge in Denmark, excited by a servo motor. For both cases, validation of the reconstructed forces is provided using comparison metrics for several signal properties. The developed model holds potential for applications in structural health monitoring, damage prognosis, and load model validation.

Paperid: 765, https://arxiv.org/pdf/2503.05716.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have gained significant attention for their simplicity and flexibility in engineering and scientific computing. In this study, we introduce a normalized PINN (NPINN) framework to solve a class of wave propagation equations in non-unitized domains over extended time ranges. This is achieved through a normalization technique that involves either spatial or temporal variable normalization. To enhance the capability of NPINN in solving wave equations, we integrate a Fourier-induced deep neural network as the solver, leading to a novel architecture termed NFPINN. Furthermore, we explore different normalization strategies for spatial and temporal variables and identify the optimal normalization approach for our method. To assess the effectiveness and robustness of the proposed NFPINN, we present numerical experiments in both two-dimensional and three-dimensional Euclidean spaces, considering regular and irregular domains. The results confirm the accuracy and stability of our approach.

Paperid: 766, https://arxiv.org/pdf/2503.04585.pdf

Abstract:
First formulated by Sir Isaac Newton in his work "Philosophiae Naturalis Principia Mathematica", the concept of the Three-Body Problem was put forth as a study of the motion of the three celestial bodies within the Earth-Sun-Moon system. In a generalized definition, it seeks to predict the motion for an isolated system composed of three point masses freely interacting under Newton's law of universal attraction. This proves to be analogous to a multitude of interactions between celestial bodies, and thus, the problem finds applicability within the studies of celestial mechanics. Despite numerous attempts by renowned physicists to solve it throughout the last three centuries, no general closed-form solutions have been reached due to its inherently chaotic nature for most initial conditions. Current state-of-the-art solutions are based on two approaches, either numerical high-precision integration or machine learning-based. Notwithstanding the breakthroughs of neural networks, these present a significant limitation, which is their ignorance of any prior knowledge of the chaotic systems presented. Thus, in this work, we propose a novel method that utilizes Physics-Informed Neural Networks (PINNs). These deep neural networks are able to incorporate any prior system knowledge expressible as an Ordinary Differential Equation (ODE) into their learning processes as a regularizing agent. Our findings showcase that PINNs surpass current state-of-the-art machine learning methods with comparable prediction quality. Despite a better prediction quality, the usability of numerical integrators suffers due to their prohibitively high computational cost. These findings confirm that PINNs are both effective and time-efficient open-form solvers of the Three-Body Problem that capitalize on the extensive knowledge we hold of classical mechanics.

Paperid: 767, https://arxiv.org/pdf/2503.00331.pdf

Abstract:
The advancement of smart grid technologies necessitates the integration of cutting-edge computational methods to enhance predictive energy optimization. This study proposes a multi-faceted approach by incorporating (1) Deep Reinforcement Learning (DRL) agents trained using data from Digital Twins (DTs) to optimize energy consumption in real time, (2) Physics-Informed Neural Networks (PINNs) to seamlessly embed physical laws within the optimization process, ensuring model accuracy and interpretability, and (3) Blockchain (BC) technology to facilitate secure and transparent communication across the smart grid infrastructure. The model was trained and validated using comprehensive datasets, including smart meter energy consumption data, renewable energy outputs, dynamic pricing, and user preferences collected from IoT devices. The proposed framework achieved superior predictive performance with a Mean Absolute Error (MAE) of 0.237 kWh, Root Mean Square Error (RMSE) of 0.298 kWh, and an R-squared (R2) value of 0.978, indicating a 97.8% explanation of data variance. Classification metrics further demonstrated the model's robustness, achieving 97.7% accuracy, 97.8% precision, 97.6% recall, and an F1 Score of 97.7%. Comparative analysis with traditional models like Linear Regression, Random Forest, SVM, LSTM, and XGBoost revealed the superior accuracy and real-time adaptability of the proposed method. In addition to enhancing energy efficiency, the model reduced energy costs by 35%, maintained a 96% user comfort index, and increased renewable energy utilization to 40%. This study demonstrates the transformative potential of integrating PINNs, DT, and Blockchain technologies to optimize energy consumption in smart grids, paving the way for sustainable, secure, and efficient energy management systems.

Paperid: 768, https://arxiv.org/pdf/2503.00213.pdf

Abstract:
Physics-informed machine learning is one of the most commonly used methods for fusing physical knowledge in the form of partial differential equations with experimental data. The idea is to construct a loss function where the physical laws take the place of a regularizer and minimize it to reconstruct the underlying physical fields and any missing parameters. However, there is a noticeable lack of a direct connection between physics-informed loss functions and an overarching Bayesian framework. In this work, we demonstrate that Brownian bridge Gaussian processes can be viewed as a softly-enforced physics-constrained prior for the Poisson equation. We first show equivalence between the variational form of the physics-informed loss function for the Poisson equation and a kernel ridge regression objective. Then, through the connection between Gaussian process regression and kernel methods, we identify a Gaussian process for which the posterior mean function and physics-informed loss function minimizer agree. This connection allows us to probe different theoretical questions, such as convergence and behavior of inverse problems. We also connect the method to the important problem of identifying model-form error in applications.

Paperid: 769, https://arxiv.org/pdf/2502.00552.pdf

Abstract:
Our work aims at simulating and predicting the temperature conditions inside a power transformer using Physics-Informed Neural Networks (PINNs). The predictions obtained are then used to determine the optimal placement for temperature sensors inside the transformer under the constraint of a limited number of sensors, enabling efficient performance monitoring. The method consists of combining PINNs with Mixed Integer Optimization Programming to obtain the optimal temperature reconstruction inside the transformer. First, we extend our PINN model for the thermal modeling of power transformers to solve the heat diffusion equation from 1D to 2D space. Finally, we construct an optimal sensor placement model inside the transformer that can be applied to problems in 1D and 2D.

Paperid: 770, https://arxiv.org/pdf/2501.16370.pdf

Abstract:
In this paper, we present the Residual Integral Solver Network (RISN), a novel neural network architecture designed to solve a wide range of integral and integro-differential equations, including one-dimensional, multi-dimensional, ordinary and partial integro-differential, systems, fractional types, and Helmholtz-type integral equations involving oscillatory kernels. RISN integrates residual connections with high-accuracy numerical methods such as Gaussian quadrature and fractional derivative operational matrices, enabling it to achieve higher accuracy and stability than traditional Physics-Informed Neural Networks (PINN). The residual connections help mitigate vanishing gradient issues, allowing RISN to handle deeper networks and more complex kernels, particularly in multi-dimensional problems. Through extensive experiments, we demonstrate that RISN consistently outperforms not only classical PINNs but also advanced variants such as Auxiliary PINN (A-PINN) and Self-Adaptive PINN (SA-PINN), achieving significantly lower Mean Absolute Errors (MAE) across various types of equations. These results highlight RISN's robustness and efficiency in solving challenging integral and integro-differential problems, making it a valuable tool for real-world applications where traditional methods often struggle.

Paperid: 771, https://arxiv.org/pdf/2501.16153.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are a powerful deep learning method capable of providing solutions and parameter estimations of physical systems. Given the complexity of their neural network structure, the convergence speed is still limited compared to numerical methods, mainly when used in applications that model realistic systems. The network initialization follows a random distribution of the initial weights, as in the case of traditional neural networks, which could lead to severe model convergence bottlenecks. To overcome this problem, we follow current studies that deal with optimal initial weights in traditional neural networks. In this paper, we use a convex optimization model to improve the initialization of the weights in PINNs and accelerate convergence. We investigate two optimization models as a first training step, defined as pre-training, one involving only the boundaries and one including physics. The optimization is focused on the first layer of the neural network part of the PINN model, while the other weights are randomly initialized. We test the methods using a practical application of the heat diffusion equation to model the temperature distribution of power transformers. The PINN model with boundary pre-training is the fastest converging method at the current stage.

Paperid: 772, https://arxiv.org/pdf/2501.15186.pdf

Abstract:
In this work, we present a novel iterative deep Ritz method (IDRM) for solving a general class of elliptic problems. It is inspired by the iterative procedure for minimizing the loss during the training of the neural network, but at each step encodes the geometry of the underlying function space and incorporates a convex penalty to enhance the performance of the algorithm. The algorithm is applicable to elliptic problems involving a monotone operator (not necessarily of variational form) and does not impose any stringent regularity assumption on the solution. It improves several existing neural PDE solvers, e.g., physics informed neural network and deep Ritz method, in terms of the accuracy for the concerned class of elliptic problems. Further, we establish a convergence rate for the method using tools from geometry of Banach spaces and theory of monotone operators, and also analyze the learning error. To illustrate the effectiveness of the method, we present several challenging examples, including a comparative study with existing techniques.

Paperid: 773, https://arxiv.org/pdf/2501.14573.pdf

Abstract:
The techno-economic and safety concerns of battery capacity knee occurrence call for developing online knee detection and prediction methods as an advanced battery management system (BMS) function. To address this, a transferable physics-informed framework that consists of a histogram-based feature engineering method, a hybrid physics-informed model, and a fine-tuning strategy, is proposed for online battery degradation diagnosis and knee-onset detection. The hybrid model is first developed and evaluated using a scenario-aware pipeline in protocol cycling scenarios and then fine-tuned to create local models deployed in a dynamic cycling scenario. A 2D histogram-based 17-feature set is found to be the best choice in both source and target scenarios. The fine-tuning strategy is proven to be effective in improving battery degradation mode estimation and degradation phase detection performance in the target scenario. Again, a strong linear correlation was found between the identified knee-onset and knee points. As a result, advanced BMS functions, such as online degradation diagnosis and prognosis, online knee-onset detection and knee prediction, aging-aware battery classification, and second-life repurposing, can be enabled through a battery performance digital twin in the cloud.

Paperid: 774, https://arxiv.org/pdf/2501.10162.pdf

Abstract:
Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neuralnetwork method is advocated here for the solution of the corresponding generalized Monge-Amp`ere equation. Convex neural networks are advocated to enforce the convexity of the solution to the Monge-AmpÃ¨re equation and obtain a suitable approximation of the optimal transport map. A particular focus is set on the enforcement of transport boundary conditions in the loss function. Numerical experiments illustrate the solution to the optimal transport problem in several configurations, and sensitivity analyses are performed.

Paperid: 775, https://arxiv.org/pdf/2501.08428.pdf

Abstract:
Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, for complex, high-dimensional systems, these models often require heavily overparameterized networks, leading to long training times and convergence difficulties. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. In this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of high-dimensional parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Paperid: 776, https://arxiv.org/pdf/2412.20851.pdf

Abstract:
The article is devoted to the study of neural networks with one hidden layer and a modified activation function for solving physical problems. A rectified sigmoid activation function has been proposed to solve physical problems described by the ODE with neural networks. Algorithms for physics-informed data-driven initialization of a neural network and a neuron-by-neuron gradient-free fitting method have been presented for the neural network with this activation function. Numerical experiments demonstrate the superiority of neural networks with a rectified sigmoid function over neural networks with a sigmoid function in the accuracy of solving physical problems (harmonic oscillator, relativistic slingshot, and Lorentz system).

Paperid: 777, https://arxiv.org/pdf/2412.19517.pdf

Abstract:
Differential equations (DEs) are crucial for modeling the evolution of natural or engineered systems. Traditionally, the parameters in DEs are adjusted to fit data from system observations. However, in fields such as politics, economics, and biology, available data are often independently collected at distinct time points from different subjects (i.e., repeated cross-sectional (RCS) data). Conventional optimization techniques struggle to accurately estimate DE parameters when RCS data exhibit various heterogeneities, leading to a significant loss of information. To address this issue, we propose a new estimation method called the emulator-informed deep-generative model (EIDGM), designed to handle RCS data. Specifically, EIDGM integrates a physics-informed neural network-based emulator that immediately generates DE solutions and a Wasserstein generative adversarial network-based parameter generator that can effectively mimic the RCS data. We evaluated EIDGM on exponential growth, logistic population models, and the Lorenz system, demonstrating its superior ability to accurately capture parameter distributions. Additionally, we applied EIDGM to an experimental dataset of Amyloid beta 40 and beta 42, successfully capturing diverse parameter distribution shapes. This shows that EIDGM can be applied to model a wide range of systems and extended to uncover the operating principles of systems based on limited data.

Paperid: 778, https://arxiv.org/pdf/2412.19235.pdf

Abstract:
The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks with a single hidden layer to solve physical problems described by ordinary differential equations (ODEs) and partial differential equations (PDEs). A method for strictly deterministic initialization of a neural network with one hidden layer for solving physical problems described by an ODE is proposed. Modifications to existing methods for weighting the loss function are given, as well as new methods developed for training strictly deterministic-initialized neural networks to solve ODEs (detaching, additional weighting based on the second derivative, predicted solution-based weighting, relative residuals). An algorithm for physics-informed data-driven initialization of a neural network with one hidden layer is proposed. A neural network with pronounced generalizing properties is presented, whose generalizing abilities of which can be precisely controlled by adjusting network parameters. A metric for measuring the generalization of such neural network has been introduced. A gradient-free neuron-by-neuron fitting method has been developed for adjusting the parameters of a single-hidden-layer neural network, which does not require the use of an optimizer or solver for its implementation. The proposed methods have been extended to 2D problems using the separable physics-informed neural networks approach. Numerous experiments have been carried out to develop the above methods and approaches. Experiments on physical problems, such as solving various ODEs and PDEs, have demonstrated that these methods for initializing and training neural networks with one or two hidden layers (SPINN) achieve competitive accuracy and, in some cases, state-of-the-art results.

Paperid: 779, https://arxiv.org/pdf/2412.18786.pdf

Abstract:
Understanding thermal stress evolution in metal additive manufacturing (AM) is crucial for producing high-quality components. Recent advancements in machine learning (ML) have shown great potential for modeling complex multiphysics problems in metal AM. While physics-based simulations face the challenge of high computational costs, conventional data-driven ML models require large, labeled training datasets to achieve accurate predictions. Unfortunately, generating large datasets for ML model training through time-consuming experiments or high-fidelity simulations is highly expensive in metal AM. To address these challenges, this study introduces a physics-informed neural network (PINN) framework that incorporates governing physical laws into deep neural networks (NNs) to predict temperature and thermal stress evolution during the laser metal deposition (LMD) process. The study also discusses the enhanced accuracy and efficiency of the PINN model when supplemented with small simulation data. Furthermore, it highlights the PINN transferability, enabling fast predictions with a set of new process parameters using a pre-trained PINN model as an online soft sensor, significantly reducing computation time compared to physics-based numerical models while maintaining accuracy.

Paperid: 780, https://arxiv.org/pdf/2412.14699.pdf

Abstract:
Radiation heat transfer in a graded-index medium often suffers accuracy problems due to the gradual changes in the refractive index. The finite element method, meshfree, and other numerical methods often struggle to maintain accuracy when applied to this medium. To address this issue, we apply physics-informed neural networks (PINNs)-based machine learning algorithms to simulate forward and inverse problems for this medium. We also provide the theoretical upper bounds. This theoretical framework is validated through numerical experiments of predefined and newly developed models that demonstrate the accuracy and robustness of the algorithms in solving radiation transport problems in the medium. The simulations show that the novel algorithm goes on with numerical stability and effectively mitigates oscillatory errors, even in cases with more pronounced variations in the refractive index.

Paperid: 781, https://arxiv.org/pdf/2412.00087.pdf

Abstract:
Rapid reconstruction of 2D plasma profiles from line-integral measurements is important in nuclear fusion. This paper introduces a physics-informed model architecture called Onion, that can enhance the performance of models and be adapted to various backbone networks. The model under Onion incorporates physical information by a multiplication process and applies the physics-informed loss function according to the principle of line integration. Prediction results demonstrate that the additional input of physical information improves the deep learning model's ability, leading to a reduction in the average relative error E_1 between the reconstruction profiles and the target profiles by approximately 0.84x10^(-2) on synthetic datasets and about 0.06x10^(-2) on experimental datasets. Furthermore, the implementation of the Softplus activation function in the final two fully connected layers improves model performance. This enhancement results in a reduction in the E_1 by approximately 1.06x10^(-2) on synthetic datasets and about 0.11x10^(-2) on experimental datasets. The incorporation of the physics-informed loss function has been shown to correct the model's predictions, bringing the back-projections closer to the actual inputs and reducing the errors associated with inversion algorithms. Besides, we have developed a synthetic data model to generate customized line-integral diagnostic datasets and have also collected soft x-ray diagnostic datasets from EAST and HL-2A. This study achieves reductions in reconstruction errors, and accelerates the development of surrogate models in fusion research.

Paperid: 782, https://arxiv.org/pdf/2411.18050.pdf

Abstract:
Electricity grid's resiliency and climate change strongly impact one another due to an array of technical and policy-related decisions that impact both. This paper introduces a physics-informed machine learning-based framework to enhance grid's resiliency. Specifically, when encountering disruptive events, this paper designs remedial control actions to prevent blackouts. The proposed Physics-Guided Reinforcement Learning (PG-RL) framework determines effective real-time remedial line-switching actions, considering their impact on power balance, system security, and grid reliability. To identify an effective blackout mitigation policy, PG-RL leverages power-flow sensitivity factors to guide the RL exploration during agent training. Comprehensive evaluations using the Grid2Op platform demonstrate that incorporating physical signals into RL significantly improves resource utilization within electric grids and achieves better blackout mitigation policies - both of which are critical in addressing climate change.

Paperid: 783, https://arxiv.org/pdf/2410.23388.pdf

Abstract:
The anisotropic structure of the myocardium is a key determinant of the cardiac function. To date, there is no imaging modality to assess in-vivo the cardiac fiber structure. We recently proposed Fibernet, a method for the automatic identification of the anisotropic conduction -- and thus fibers -- in the atria from local electrical recordings. Fibernet uses cardiac activation as recorded during electroanatomical mappings to infer local conduction properties using physics-informed neural networks. In this work, we extend Fibernet to cope with the uncertainty in the estimated fiber field. Specifically, we use an ensemble of neural networks to produce multiple samples, all fitting the observed data, and compute posterior statistics. We also introduce a methodology to select the best fiber orientation members and define the input of the neural networks directly on the atrial surface. With these improvements, we outperform the previous methodology in terms of fiber orientation error in 8 different atrial anatomies. Currently, our approach can estimate the fiber orientation and conduction velocities in under 7 minutes with quantified uncertainty, which opens the door to its application in clinical practice. We hope the proposed methodology will enable further personalization of cardiac digital twins for precision medicine.

Paperid: 784, https://arxiv.org/pdf/2410.19027.pdf

Abstract:
A novel physics-informed operator learning technique based on spectral methods is introduced to model the complex behavior of heterogeneous materials. The Lippmann-Schwinger operator in Fourier space is employed to construct physical constraints with minimal computational overhead, effectively eliminating the need for automatic differentiation. The introduced methodology accelerates the training process by enabling gradient construction on a fixed, finite discretization in Fourier space. Later, the spectral physics-informed finite operator learning (SPiFOL) framework is built based on this discretization and trained to map the arbitrary shape of microstructures to their mechanical responses (strain fields) without relying on labeled data. The training is done by minimizing equilibrium in Fourier space concerning the macroscopic loading condition, which also guarantees the periodicity. SPiFOL, as a physics-informed operator learning method, enables rapid predictions through forward inference after training. To ensure accuracy, we incorporate physical constraints and diversify the training data. However, performance may still degrade for out-of-distribution microstructures. SPiFOL is further enhanced by integrating a Fourier Neural Operator (FNO). Compared to the standard data-driven FNO, SPiFOL shows higher accuracy in predicting stress fields and provides nearly resolution-independent results. Additionally, its zero-shot super-resolution capabilities are explored in heterogeneous domains. Finally, SPiFOL is extended to handle 3D problems and further adapted to finite elasticity, demonstrating the robustness of the framework in handling nonlinear mechanical behavior. The framework shows great potential for efficient and scalable prediction of mechanical responses in complex material systems while also reducing the training time required for training physics-informed neural operators.

Paperid: 785, https://arxiv.org/pdf/2410.05507.pdf

Abstract:
When the physics is wrong, physics-informed machine learning becomes physics-misinformed machine learning. A powerful black-box model should not be able to conceal misconceived physics. We propose two criteria that can be used to assert integrity that a hybrid (physics plus black-box) model: 0) the black-box model should be unable to replicate the physical model, and 1) any best-fit hybrid model has the same physical parameter as a best-fit standalone physics model. We demonstrate them for a sample nonlinear mechanical system approximated by its small-signal linearization.

Paperid: 786, https://arxiv.org/pdf/2409.19140.pdf

Abstract:
Echo State Networks (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs) were proposed initially to model chaotic dynamic systems without external inputs. They require less data for training since Ordinary Differential Equations (ODEs) of the considered system help to regularize the ESN. In this work, the PI-ESN is extended with external inputs to model controllable nonlinear dynamic systems. Additionally, an existing self-adaptive balancing loss method is employed to balance the contributions of the residual regression term and the physics-informed loss term in the total loss function. The experiments with two nonlinear systems modeled by ODEs, the Van der Pol oscillator and the four-tank system, and with one differential-algebraic (DAE) system, an electric submersible pump, revealed that the proposed PI-ESN outperforms the conventional ESN, especially in scenarios with limited data availability, showing that PI-ESNs can regularize an ESN model with external inputs previously trained on just a few datapoints, reducing its overfitting and improving its generalization error (up to 92% relative reduction in the test error). Further experiments demonstrated that the proposed PI-ESN is robust to parametric uncertainties in the ODE equations and that model predictive control using PI-ESN outperforms the one using plain ESN, particularly when training data is scarce.

Paperid: 787, https://arxiv.org/pdf/2409.09466.pdf

Abstract:
Power flow analysis plays a critical role in the control and operation of power systems. The high computational burden of traditional solution methods led to a shift towards data-driven approaches, exploiting the availability of digital metering data. However, data-driven approaches, such as deep learning, have not yet won the trust of operators as they are agnostic to the underlying physical model and have poor performances in regimes with limited observability. To address these challenges, this paper proposes a new, physics-informed model. More specifically, a novel physics-informed loss function is developed that can be used to train (deep) neural networks aimed at power flow simulation. The loss function is not only based on the theoretical AC power flow equations that govern the problem but also incorporates real physical line losses, resulting in higher loss accuracy and increased learning potential. The proposed model is used to train a Graph Neural Network (GNN) and is evaluated on a small 3-bus test case both against another physics-informed GNN that does not incorporate physical losses and against a model-free technique. The validation results show that the proposed model outperforms the conventional physics-informed network on all used performance metrics. Even more interesting is that the model shows strong prediction capabilities when tested on scenarios outside the training sample set, something that is a substantial deficiency of model-free techniques.

Paperid: 788, https://arxiv.org/pdf/2409.02345.pdf

Abstract:
This paper addresses integrated design of engineering systems, where physical structure of the plant and controller design are optimized simultaneously. To cope with uncertainties due to noises acting on the dynamics and modeling errors, an Uncertain Control Co-design (UCCD) problem formulation is proposed. Existing UCCD methods usually rely on uncertainty propagation analyses using Monte Calro methods for open-loop solutions of optimal control, which suffer from stringent trade-offs among accuracy, time horizon, and computational time. The proposed method utilizes closed-loop solutions characterized by the Hamilton-Jacobi-Bellman equation, a Partial Differential Equation (PDE) defined on the state space. A solution algorithm for the proposed UCCD formulation is developed based on PDE solutions of Physics-informed Neural Networks (PINNs). Numerical examples of regulator design problems are provided, and it is shown that simultaneous update of PINN weights and the design parameters effectively works for solving UCCD problems.

Paperid: 789, https://arxiv.org/pdf/2409.02339.pdf

Abstract:
In this paper, we develop a systematic deep learning approach to solve two-dimensional (2D) stationary quantum droplets (QDs) and investigate their wave propagation in the 2D amended Gross-Pitaevskii equation with Lee-Huang-Yang correction and two kinds of potentials. Firstly, we use the initial-value iterative neural network (IINN) algorithm for 2D stationary quantum droplets of stationary equations. Then the learned stationary QDs are used as the initial value conditions for physics-informed neural networks (PINNs) to explore their evolutions in the some space-time region. Especially, we consider two types of potentials, one is the 2D quadruple-well Gaussian potential and the other is the PT-symmetric HO-Gaussian potential, which lead to spontaneous symmetry breaking and the generation of multi-component QDs. The used deep learning method can also be applied to study wave propagations of other nonlinear physical models.

Paperid: 790, https://arxiv.org/pdf/2409.01124.pdf

Abstract:
We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs). Specifically, the IINN framework consists of two subnetworks, one of which is used to fit a given initial value, and the other incorporates physical information and continues training on the basis of the first subnetwork. Importantly, the IINN method does not require any additional data information including boundary conditions, apart from the given initial value. Corresponding theoretical guarantees are provided to demonstrate the effectiveness of our IINN method. The proposed IINN method is efficiently applied to learn some types of solutions in different nonlinear wave equations, including the one-dimensional (1D) nonlinear SchrÃ¶dinger equations (NLS) equation (with and without potentials), the 1D saturable NLS equation with PT -symmetric optical lattices, the 1D focusing-defocusing coupled NLS equations, the KdV equation, the two-dimensional (2D) NLS equation with potentials, the 2D amended GP equation with a potential, the (2+1)-dimensional KP equation, and the 3D NLS equation with a potential. These applications serve as evidence for the efficacy of our method. Finally, by comparing with the traditional methods, we demonstrate the advantages of the proposed IINN method.

Paperid: 791, https://arxiv.org/pdf/2601.02264.pdf

Abstract:
Earthquake prediction and seismic hazard assessment remain fundamental challenges in geophysics, with existing machine learning approaches often operating as black boxes that ignore established physical laws. We introduce POSEIDON (Physics-Optimized Seismic Energy Inference and Detection Operating Network), a physics-informed energy-based model for unified multi-task seismic event prediction, alongside the Poseidon dataset -- the largest open-source global earthquake catalog comprising 2.8 million events spanning 30 years. POSEIDON embeds fundamental seismological principles, including the Gutenberg-Richter magnitude-frequency relationship and Omori-Utsu aftershock decay law, as learnable constraints within an energy-based modeling framework. The architecture simultaneously addresses three interconnected prediction tasks: aftershock sequence identification, tsunami generation potential, and foreshock detection. Extensive experiments demonstrate that POSEIDON achieves state-of-the-art performance across all tasks, outperforming gradient boosting, random forest, and CNN baselines with the highest average F1 score among all compared methods. Crucially, the learned physics parameters converge to scientifically interpretable values -- Gutenberg-Richter b-value of 0.752 and Omori-Utsu parameters p=0.835, c=0.1948 days -- falling within established seismological ranges while enhancing rather than compromising predictive accuracy. The Poseidon dataset is publicly available at https://huggingface.co/datasets/BorisKriuk/Poseidon, providing pre-computed energy features, spatial grid indices, and standardized quality metrics to advance physics-informed seismic research.

Paperid: 792, https://arxiv.org/pdf/2512.24686.pdf

Abstract:
Fault diagnosis of lithium-ion batteries is critical for system safety. While existing deep learning methods exhibit superior detection accuracy, their "black-box" nature hinders interpretability. Furthermore, restricted by binary classification paradigms, they struggle to provide root cause analysis and maintenance recommendations. To address these limitations, this paper proposes BatteryAgent, a hierarchical framework that integrates physical knowledge features with the reasoning capabilities of Large Language Models (LLMs). The framework comprises three core modules: (1) A Physical Perception Layer that utilizes 10 mechanism-based features derived from electrochemical principles, balancing dimensionality reduction with physical fidelity; (2) A Detection and Attribution Layer that employs Gradient Boosting Decision Trees and SHAP to quantify feature contributions; and (3) A Reasoning and Diagnosis Layer that leverages an LLM as the agent core. This layer constructs a "numerical-semantic" bridge, combining SHAP attributions with a mechanism knowledge base to generate comprehensive reports containing fault types, root cause analysis, and maintenance suggestions. Experimental results demonstrate that BatteryAgent effectively corrects misclassifications on hard boundary samples, achieving an AUROC of 0.986, which significantly outperforms current state-of-the-art methods. Moreover, the framework extends traditional binary detection to multi-type interpretable diagnosis, offering a new paradigm shift from "passive detection" to "intelligent diagnosis" for battery safety management.

Paperid: 793, https://arxiv.org/pdf/2512.15706.pdf

Abstract:
In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is further exacerbated by the fact that experimental data are often sparse and sometimes are composed of a few time points of tumor volume. In this paper, we propose to learn time-varying interactions between cells, such as those of bladder cancer tumors and immune cells, and their response to a combination of anticancer treatments in a limited data scenario. We employ the physics-informed neural network (PINN) approach to predict possible subpopulation trajectories at time points where no observed data are available. We demonstrate that our approach is consistent with the biological explanation of subpopulation trajectories. Our method provides a framework for learning evolving interactions among biological organisms when external interventions are applied to their environment.

Paperid: 794, https://arxiv.org/pdf/2512.14941.pdf

Abstract:
Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of the solution field is naturally adaptive and avoids meshing the computational domain, which can both improve the accuracy of the numerical solution and streamline implementation. However, there have been limited studies of PINNs on complex three-dimensional geometries, as the lack of mesh and the reliance on the strong form of the partial differential equation (PDE) make boundary condition (BC) enforcement challenging. Techniques to enforce BCs with PINNs have proliferated in the literature, but a comprehensive side-by-side comparison of these techniques and a study of their efficacy on geometrically complex three-dimensional test problems are lacking. In this work, we i) systematically compare BC enforcement techniques for PINNs, ii) propose a general solution framework for arbitrary three-dimensional geometries, and iii) verify the methodology on three-dimensional, linear and nonlinear test problems with combinations of Dirichlet, Neumann, and Robin boundaries. Our approach is agnostic to the underlying PDE, the geometry of the computational domain, and the nature of the BCs, while requiring minimal hyperparameter tuning. This work represents a step in the direction of establishing PINNs as a mature numerical method, capable of competing head-to-head with incumbents such as the finite element method.

Paperid: 795, https://arxiv.org/pdf/2512.11327.pdf

Abstract:
Lens flare is a degradation phenomenon caused by strong light sources. Existing researches on flare removal have mainly focused on images, while the spatiotemporal characteristics of video flare remain largely unexplored. Video flare synthesis and removal pose significantly greater challenges than in image, owing to the complex and mutually independent motion of flare, light sources, and scene content. This motion independence further affects restoration performance, often resulting in flicker and artifacts. To address this issue, we propose a physics-informed dynamic flare synthesis pipeline, which simulates light source motion using optical flow and models the temporal behaviors of both scattering and reflective flares. Meanwhile, we design a video flare removal network that employs an attention module to spatially suppress flare regions and incorporates a Mamba-based temporal modeling component to capture long range spatio-temporal dependencies. This motion-independent spatiotemporal representation effectively eliminates the need for multi-frame alignment, alleviating temporal aliasing between flares and scene content and thereby improving video flare removal performance. Building upon this, we construct the first video flare dataset to comprehensively evaluate our method, which includes a large set of synthetic paired videos and additional real-world videos collected from the Internet to assess generalization capability. Extensive experiments demonstrate that our method consistently outperforms existing video-based restoration and image-based flare removal methods on both real and synthetic videos, effectively removing dynamic flares while preserving light source integrity and maintaining spatiotemporal consistency of scene.

Paperid: 796, https://arxiv.org/pdf/2512.02495.pdf

Abstract:
Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

Paperid: 797, https://arxiv.org/pdf/2512.01170.pdf

Abstract:
The requirements of modern sensing are rapidly evolving, driven by increasing demands for data efficiency, real-time processing, and deployment under limited sensing coverage. Complex physical systems are often characterized through the integration of a limited number of point sensors in combination with scientific computations which approximate the dominant, full-state dynamics. Simulation models, however, inevitably neglect small-scale or hidden processes, are sensitive to perturbations, or oversimplify parameter correlations, leading to reconstructions that often diverge from the reality measured by sensors. This creates a critical need for data assimilation, the process of integrating observational data with predictive simulation models to produce coherent and accurate estimates of the full state of complex physical systems. We propose a machine learning framework for Data Assimilation with a SHallow REcurrent Decoder (DA-SHRED) which bridges the simulation-to-real (SIM2REAL) gap between computational modeling and experimental sensor data. For real-world physics systems modeling high-dimensional spatiotemporal fields, where the full state cannot be directly observed and must be inferred from sparse sensor measurements, we leverage the latent space learned from a reduced simulation model via SHRED, and update these latent variables using real sensor data to accurately reconstruct the full system state. Furthermore, our algorithm incorporates a sparse identification of nonlinear dynamics based regression model in the latent space to identify functionals corresponding to missing dynamics in the simulation model. We demonstrate that DA-SHRED successfully closes the SIM2REAL gap and additionally recovers missing dynamics in highly complex systems, demonstrating that the combination of efficient temporal encoding and physics-informed correction enables robust data assimilation.

Paperid: 798, https://arxiv.org/pdf/2511.17258.pdf

Abstract:
Neural PDE solvers used for scientific simulation often violate governing equation constraints. While linear constraints can be projected cheaply, many constraints are nonlinear, complicating projection onto the feasible set. Dynamical PDEs are especially difficult because constraints induce long-range dependencies in time. In this work, we evaluate two training-free, post hoc projections of approximate solutions: a nonlinear optimization-based projection, and a local linearization-based projection using Jacobian-vector and vector-Jacobian products. We analyze constraints across representative PDEs and find that both projections substantially reduce violations and improve accuracy over physics-informed baselines.

Paperid: 799, https://arxiv.org/pdf/2511.12092.pdf

Abstract:
Modeling indoor radio propagation is crucial for wireless network planning and optimization. However, existing approaches often rely on labor-intensive manual modeling of geometry and material properties, resulting in limited scalability and efficiency. To overcome these challenges, this paper presents SenseRay-3D, a generalizable and physics-informed end-to-end framework that predicts three-dimensional (3D) path-loss heatmaps directly from RGB-D scans, thereby eliminating the need for explicit geometry reconstruction or material annotation. The proposed framework builds a sensing-driven voxelized scene representation that jointly encodes occupancy, electromagnetic material characteristics, and transmitter-receiver geometry, which is processed by a SwinUNETR-based neural network to infer environmental path-loss relative to free-space path-loss. A comprehensive synthetic indoor propagation dataset is further developed to validate the framework and to serve as a standardized benchmark for future research. Experimental results show that SenseRay-3D achieves a mean absolute error of 4.27 dB on unseen environments and supports real-time inference at 217 ms per sample, demonstrating its scalability, efficiency, and physical consistency. SenseRay-3D paves a new path for sense-driven, generalizable, and physics-consistent modeling of indoor propagation, marking a major leap beyond our pioneering EM DeepRay framework.

Paperid: 800, https://arxiv.org/pdf/2511.10158.pdf

Abstract:
Vessels navigating in confined waters are subject to banking effects, which are hydrodynamic forces and moments arising from pressure differentials between the vessel sides, significantly affecting manoeuvrability and safety. Existing numerical approaches such as computational fluid dynamics (CFD) can accurately capture these effects but are computationally expensive and unsuitable for real-time control or estimation. This paper presents a closed-form, first-principles model of banking effects. The model coefficients are identified using physics-informed regression on towing tank experiment data for a scaled container vessel. Validation through Shapley value analysis confirms the significance of the banking terms in reproducing the measured forces and moments. Lastly, the derived coefficients are shown to be non-dimensional, making the model applicable across different scales that preserve vessel geometry.

Paperid: 801, https://arxiv.org/pdf/2511.09048.pdf

Abstract:
We propose a novel projection method that guarantees the conservation of integral quantities in Physics-Informed Neural Networks (PINNs). While the soft constraint that PINNs use to enforce the structure of partial differential equations (PDEs) enables necessary flexibility during training, it also permits the discovered solution to violate physical laws. To address this, we introduce a projection method that guarantees the conservation of the linear and quadratic integrals, both separately and jointly. We derived the projection formulae by solving constrained non-linear optimization problems and found that our PINN modified with the projection, which we call PINN-Proj, reduced the error in the conservation of these quantities by three to four orders of magnitude compared to the soft constraint and marginally reduced the PDE solution error. We also found evidence that the projection improved convergence through improving the conditioning of the loss landscape. Our method holds promise as a general framework to guarantee the conservation of any integral quantity in a PINN if a tractable solution exists.

Paperid: 802, https://arxiv.org/pdf/2511.06299.pdf

Abstract:
Recently, 3D Gaussian Splatting (3DGS), an explicit scene representation technique, has shown significant promise for dynamic novel-view synthesis from monocular video input. However, purely data-driven 3DGS often struggles to capture the diverse physics-driven motion patterns in dynamic scenes. To fill this gap, we propose Physics-Informed Deformable Gaussian Splatting (PIDG), which treats each Gaussian particle as a Lagrangian material point with time-varying constitutive parameters and is supervised by 2D optical flow via motion projection. Specifically, we adopt static-dynamic decoupled 4D decomposed hash encoding to reconstruct geometry and motion efficiently. Subsequently, we impose the Cauchy momentum residual as a physics constraint, enabling independent prediction of each particle's velocity and constitutive stress via a time-evolving material field. Finally, we further supervise data fitting by matching Lagrangian particle flow to camera-compensated optical flow, which accelerates convergence and improves generalization. Experiments on a custom physics-driven dataset as well as on standard synthetic and real-world datasets demonstrate significant gains in physical consistency and monocular dynamic reconstruction quality.

Paperid: 803, https://arxiv.org/pdf/2510.27658.pdf

Abstract:
We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions. In particular, we study the numerical ill-conditioning, frequency bias, and the balance between the differential operator and the shallow network representation for different formulations of the PDEs and with various activation functions. Our study shows that the performance of Physics-Informed Neural Networks (PINNs) or Deep Ritz Method (DRM) using linear SNNs with power ReLU activation is dominated by their inherent ill-conditioning and spectral bias against high frequencies. Although this can be alleviated by using non-homogeneous activation functions with proper scaling, achieving such adaptivity for nonlinear SNNs remains costly due to ill-conditioning.

Paperid: 804, https://arxiv.org/pdf/2510.22955.pdf

Abstract:
Accurate prediction of remaining useful life (RUL) is essential to enhance system reliability and reduce maintenance risk. Yet many strong contemporary models are fragile around fault onset and opaque to engineers: short, high-energy spikes are smoothed away or misread, fixed thresholds blunt sensitivity, and physics-based explanations are scarce. To remedy this, we introduce SARNet (Spike-Aware Consecutive Validation Framework), which builds on a Modern Temporal Convolutional Network (ModernTCN) and adds spike-aware detection to provide physics-informed interpretability. ModernTCN forecasts degradation-sensitive indicators; an adaptive consecutive threshold validates true spikes while suppressing noise. Failure-prone segments then receive targeted feature engineering (spectral slopes, statistical derivatives, energy ratios), and the final RUL is produced by a stacked RF--LGBM regressor. Across benchmark-ported datasets under an event-triggered protocol, SARNet consistently lowers error compared to recent baselines (RMSE 0.0365, MAE 0.0204) while remaining lightweight, robust, and easy to deploy.

Paperid: 805, https://arxiv.org/pdf/2510.18299.pdf

Abstract:
In millimeter wave (mmWave) communications, beam alignment and tracking are crucial to combat the significant path loss. As scanning the entire directional space is inefficient, designing an efficient and robust method to identify the optimal beam directions is essential. Since traditional bandit algorithms require a long time horizon to converge under large beam spaces, many existing works propose efficient bandit algorithms for beam alignment by relying on unimodality or multimodality assumptions on the reward function's structure. However, such assumptions often do not hold (or cannot be strictly satisfied) in practice, which causes such algorithms to converge to choosing suboptimal beams. In this work, we propose two physics-informed bandit algorithms \textit{pretc} and \textit{prgreedy} that exploit the sparse multipath property of mmWave channels - a generic but realistic assumption - which is connected to the Phase Retrieval Bandit problem. Our algorithms treat the parameters of each path as black boxes and maintain optimal estimates of them based on sampled historical rewards. \textit{pretc} starts with a random exploration phase and then commits to the optimal beam under the estimated reward function. \textit{prgreedy} performs such estimation in an online manner and chooses the best beam under current estimates. Our algorithms can also be easily adapted to beam tracking in the mobile setting. Through experiments using both the synthetic DeepMIMO dataset and the real-world DeepSense6G dataset, we demonstrate that both algorithms outperform existing approaches in a wide range of scenarios across diverse channel environments, showing their generalizability and robustness.

Paperid: 806, https://arxiv.org/pdf/2510.17146.pdf

Abstract:
Heating, Ventilation, and Air-Conditioning (HVAC) systems account for a substantial share of global building energy use, making reliable anomaly detection essential for improving efficiency and reducing emissions. Classical rule-based approaches offer explainability but lack adaptability, while deep learning methods provide predictive power at the cost of transparency, efficiency, and physical plausibility. Recent attempts to use Large Language Models (LLMs) for anomaly detection improve interpretability but largely ignore the physical principles that govern HVAC operations. We present PILLM, a Physics-Informed LLM framework that operates within an evolutionary loop to automatically generate, evaluate, and refine anomaly detection rules. Our approach introduces physics-informed reflection and crossover operators that embed thermodynamic and control-theoretic constraints, enabling rules that are both adaptive and physically grounded. Experiments on the public Building Fault Detection dataset show that PILLM achieves state-of-the-art performance while producing diagnostic rules that are interpretable and actionable, advancing trustworthy and deployable AI for smart building systems.

Paperid: 807, https://arxiv.org/pdf/2510.15998.pdf

Abstract:
Recent works have shown that natural gradient methods can significantly outperform standard optimizers when training physics-informed neural networks (PINNs). In this paper, we analyze the training dynamics of PINNs optimized with ANaGRAM, a natural-gradient-inspired approach employing singular value decomposition with cutoff regularization. Building on this analysis, we propose a multi-cutoff adaptation strategy that further enhances ANaGRAM's performance. Experiments on benchmark PDEs validate the effectiveness of our method, which allows to reach machine precision on some experiments. To provide theoretical grounding, we develop a framework based on spectral theory that explains the necessity of regularization and extend previous shown connections with Green's functions theory.

Paperid: 808, https://arxiv.org/pdf/2510.13431.pdf

Abstract:
Physics-informed neural networks (PINNs) are neural networks that embed the laws of dynamical systems modeled by differential equations into their loss function as constraints. In this work, we present a PINN framework applied to oncology. Here, we seek to learn time-varying interactions due to a combination therapy in a tumor microenvironment. In oncology, experimental data are often sparse and composed of a few time points of tumor volume. By embedding inductive biases derived from prior information about a dynamical system, we extend the physics-informed neural networks (PINN) and incorporate observed biological constraints as regularization agents. The modified PINN algorithm is able to steer itself to a reasonable solution and can generalize well with only a few training examples. We demonstrate the merit of our approach by learning the dynamics of treatment applied intermittently in an ordinary differential equation (ODE) model of a combination therapy. The algorithm yields a solution to the ODE and time-varying forms of some of the ODE model parameters. We demonstrate a strong convergence using metrics such as the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).

Paperid: 809, https://arxiv.org/pdf/2510.06286.pdf

Abstract:
To reliably project future sea level rise, ice sheet models require inputs that respect physics. Embedding physical principles like mass conservation into models that interpolate Antarctic ice flow vector fields from sparse & noisy measurements not only promotes physical adherence but can also improve accuracy and robustness. While physics-informed neural networks (PINNs) impose physics as soft penalties, offering flexibility but no physical guarantees, we instead propose divergence-free neural networks (dfNNs), which enforce local mass conservation exactly via a vector calculus trick. Our comparison of dfNNs, PINNs, and unconstrained NNs on ice flux interpolation over Byrd Glacier suggests that "mass conservation on rails" yields more reliable estimates, and that directional guidance, a learning strategy leveraging continent-wide satellite velocity data, boosts performance across models.

Paperid: 810, https://arxiv.org/pdf/2510.05385.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are a useful framework for approximating partial differential equation solutions using deep learning methods. In this paper, we propose a principled redesign of the PINNsformer, a Transformer-based PINN architecture. We present the Spectral PINNSformer (S-Pformer), a refinement of encoder-decoder PINNSformers that addresses two key issues; 1. the redundancy (i.e. increased parameter count) of the encoder, and 2. the mitigation of spectral bias. We find that the encoder is unnecessary for capturing spatiotemporal correlations when relying solely on self-attention, thereby reducing parameter count. Further, we integrate Fourier feature embeddings to explicitly mitigate spectral bias, enabling adaptive encoding of multiscale behaviors in the frequency domain. Our model outperforms encoder-decoder PINNSformer architectures across all benchmarks, achieving or outperforming MLP performance while reducing parameter count significantly.

Paperid: 811, https://arxiv.org/pdf/2510.04591.pdf

Abstract:
This article proposes a data-driven PID controller design based on the principle of adaptive gain optimization, leveraging Physics-Informed Neural Networks (PINNs) generated for predictive modeling purposes. The proposed control design method utilizes gradients of the PID gain optimization, achieved through the automatic differentiation of PINNs, to apply model predictive control using a cost function based on tracking error and control inputs. By optimizing PINNs-based PID gains, the method achieves adaptive gain tuning that ensures stability while accounting for system nonlinearities. The proposed method features a systematic framework for integrating PINNs-based models of dynamical control systems into closed-loop control systems, enabling direct application to PID control design. A series of numerical experiments is conducted to demonstrate the effectiveness of the proposed method from the control perspectives based on both time and frequency domains.

Paperid: 812, https://arxiv.org/pdf/2510.04094.pdf

Abstract:
A major problem of kernel-based methods (e.g., least squares support vector machines, LS-SVMs) for solving linear/nonlinear ordinary differential equations (ODEs) is the prohibitive $O(an^3)$ ($a=1$ for linear ODEs and 27 for nonlinear ODEs) part of their computational complexity with increasing temporal discretization points $n$. We propose a novel Nyström-accelerated LS-SVMs framework that breaks this bottleneck by reformulating ODEs as primal-space constraints. Specifically, we derive for the first time an explicit Nyström-based mapping and its derivatives from one-dimensional temporal discretization points to a higher $m$-dimensional feature space ($1< m\le n$), enabling the learning process to solve linear/nonlinear equation systems with $m$-dependent complexity. Numerical experiments on sixteen benchmark ODEs demonstrate: 1) $10-6000$ times faster computation than classical LS-SVMs and physics-informed neural networks (PINNs), 2) comparable accuracy to LS-SVMs ($<0.13\%$ relative MAE, RMSE, and $\left \| y-\hat{y} \right \| _{\infty } $difference) while maximum surpassing PINNs by 72\% in RMSE, and 3) scalability to $n=10^4$ time steps with $m=50$ features. This work establishes a new paradigm for efficient kernel-based ODEs learning without significantly sacrificing the accuracy of the solution.

Paperid: 813, https://arxiv.org/pdf/2510.03416.pdf

Abstract:
A successful deep learning network is highly dependent not only on the training dataset, but the training algorithm used to condition the network for a given task. The loss function, dataset, and tuning of hyperparameters all play an essential role in training a network, yet there is not much discussion on the reliability or reproducibility of a training algorithm. With the rise in popularity of physics-informed loss functions, this raises the question of how reliable one's loss function is in conditioning a network to enforce a particular boundary condition. Reporting the model variation is needed to assess a loss function's ability to consistently train a network to obey a given boundary condition, and provides a fairer comparison among different methods. In this work, a Pix2Pix network predicting the stress fields of high elastic contrast composites is used as a case study. Several different loss functions enforcing stress equilibrium are implemented, with each displaying different levels of variation in convergence, accuracy, and enforcing stress equilibrium across many training sessions. Suggested practices in reporting model variation are also shared.

Paperid: 814, https://arxiv.org/pdf/2510.01091.pdf

Abstract:
We present a data-driven framework for turbulence modeling, applied to flow prediction in the FDA nozzle. In this study, the standard RANS equations have been modified using an implicit-explicit hybrid approach. New variables were introduced, and a solver was developed within the OpenFOAM framework, integrating a machine learning module to estimate these variables. The invariant input features were derived based on Hilbert's basis theorem, and the outputs of the machine learning model were obtained through eigenvalue-vector decomposition of the Reynolds stress tensor. Validation was performed using DNS data for turbulent flow in a square channel at various Reynolds numbers. A baseline MLP was first trained at $Re=2900$ and tested at $Re=3500$ to assess its ability to reproduce turbulence anisotropy and secondary flows. To further enhance generalization, three benchmark DNS datasets were transformed into images via the Deep-Insight method, enabling the use of convolutional neural networks. The trained Deep-Insight network demonstrated improved prediction of turbulence structures in the FDA blood nozzle, highlighting the promise of data-driven augmentation in turbulence modeling.

Paperid: 815, https://arxiv.org/pdf/2510.00442.pdf

Abstract:
Neural network training relies on gradient computation through backpropagation, yet memory requirements for storing layer activations present significant scalability challenges. We present the first adaptation of control-theoretic matrix sketching to neural network layer activations, enabling memory-efficient gradient reconstruction in backpropagation. This work builds on recent matrix sketching frameworks for dynamic optimization problems, where similar state trajectory storage challenges motivate sketching techniques. Our approach sketches layer activations using three complementary sketch matrices maintained through exponential moving averages (EMA) with adaptive rank adjustment, automatically balancing memory efficiency against approximation quality. Empirical evaluation on MNIST, CIFAR-10, and physics-informed neural networks demonstrates a controllable accuracy-memory tradeoff. We demonstrate a gradient monitoring application on MNIST showing how sketched activations enable real-time gradient norm tracking with minimal memory overhead. These results establish that sketched activation storage provides a viable path toward memory-efficient neural network training and analysis.

Paperid: 816, https://arxiv.org/pdf/2509.21123.pdf

Abstract:
Future high-luminosity hadron colliders demand tracking detectors with extreme radiation tolerance, high spatial precision, and sub-nanosecond timing. 3D diamond pixel sensors offer these capabilities due to diamond's radiation hardness and high carrier mobility. Conductive electrodes, produced via femtosecond IR laser pulses, exhibit high resistivity that delays signal propagation. This effect necessitates extending the classical Ramo-Shockley weighting potential formalism. We model the phenomenon through a 3rd-order, 3+1D PDE derived as a quasi-stationary approximation of Maxwell's equations. The PDE is solved numerically and coupled with charge transport simulations for realistic 3D sensor geometries. A Mixture-of-Experts Physics-Informed Neural Network, trained on Spectral Method data, provides a meshless solver to assess timing degradation from electrode resistance.

Paperid: 817, https://arxiv.org/pdf/2509.19467.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that is consistent with the underlying fluctuation structure, as characterized by a large deviations principle. This approach yields a novel formulation of PINNs in which the penalty term is chosen to penalize improbable deviations, rather than being selected heuristically. The resulting thermodynamically consistent extension of PINNs, termed THINNs, is subsequently analyzed by establishing analytical a posteriori estimates, and providing empirical comparisons to established penalization strategies.

Paperid: 818, https://arxiv.org/pdf/2509.15029.pdf

Abstract:
This paper presents a physics-informed framework that integrates graph convolutional networks (GCN) with long short-term memory (LSTM) architecture to forecast microstructure evolution over long time horizons in both 2D and 3D with remarkable performance across varied metrics. The proposed framework is composition-aware, trained jointly on datasets with different compositions, and operates in latent graph space, which enables the model to capture compositions and morphological dynamics while remaining computationally efficient. Compressing and encoding phase-field simulation data with convolutional autoencoders and operating in Latent graph space facilitates efficient modeling of microstructural evolution across composition, dimensions, and long-term horizons. The framework captures the spatial and temporal patterns of evolving microstructures while enabling long-range forecasting at reduced computational cost after training.

Paperid: 819, https://arxiv.org/pdf/2509.15004.pdf

Abstract:
Physics-informed neural networks (PINNs) have been widely utilized for solving a range of partial differential equations (PDEs) in various scientific and engineering disciplines. This paper presents a Fourier heuristic-enhanced PINN (termed FCPINN) designed to address a specific class of biharmonic equations with Dirichlet and Navier boundary conditions. The method achieves this by decomposing the high-order equations into two Poisson equations. FCPINN integrates Fourier spectral theory with a reduced-order formulation for high-order PDEs, significantly improving approximation accuracy and reducing computational complexity. This approach is especially beneficial for problems with intricate boundary constraints and high-dimensional inputs. To assess the effectiveness and robustness of the FCPINN algorithm, we conducted several numerical experiments on both linear and nonlinear biharmonic problems across different Euclidean spaces. The results show that FCPINN provides an optimal trade-off between speed and accuracy for high-order PDEs, surpassing the performance of conventional PINN and deep mixed residual method (MIM) approaches, while also maintaining stability and robustness with varying numbers of hidden layer nodes.

Paperid: 820, https://arxiv.org/pdf/2509.14442.pdf

Abstract:
We develop a framework for non-invasive volumetric indoor airflow estimation from a single viewpoint using background-oriented schlieren (BOS) measurements and physics-informed reconstruction. Our framework utilizes a light projector that projects a pattern onto a target back-wall and a camera that observes small distortions in the light pattern. While the single-view BOS tomography problem is severely ill-posed, our proposed framework addresses this using: (1) improved ray tracing, (2) a physics-based light rendering approach and loss formulation, and (3) a physics-based regularization using a physics-informed neural network (PINN) to ensure that the reconstructed airflow is consistent with the governing equations for buoyancy-driven flows.

Paperid: 821, https://arxiv.org/pdf/2509.13952.pdf

Abstract:
This paper presents eXtended Physics-Informed Neural Network (X-PINN), a novel and robust framework for addressing fracture mechanics problems involving multiple cracks in fractured media. To address this, an energy-based loss function, customized integration schemes, and domain decomposition procedures are proposed. Inspired by the Extended Finite Element Method (XFEM), the neural network solution space is enriched with specialized functions that allow crack body discontinuities and singularities at crack tips to be explicitly captured. Furthermore, a structured framework is introduced in which standard and enriched solution components are modeled using distinct neural networks, enabling flexible and effective simulations of complex multiple-crack problems in 1D and 2D domains, with convenient extensibility to 3D problems. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed method.

Paperid: 822, https://arxiv.org/pdf/2509.13717.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this gap by introducing a distribution-free conformal prediction (CP) framework for UQ in PINNs. This framework calibrates prediction intervals by constructing nonconformity scores on a calibration set, thereby yielding distribution-free uncertainty estimates with rigorous finite-sample coverage guarantees for PINNs. To handle spatial heteroskedasticity, we further introduce local conformal quantile estimation, enabling spatially adaptive uncertainty bands while preserving theoretical guarantee. Through systematic evaluations on typical PDEs (damped harmonic oscillator, Poisson, Allen-Cahn, and Helmholtz equations) and comprehensive testing across multiple uncertainty metrics, our results demonstrate that the proposed framework achieves reliable calibration and locally adaptive uncertainty intervals, consistently outperforming heuristic UQ approaches. By bridging PINNs with distribution-free UQ, this work introduces a general framework that not only enhances calibration and reliability, but also opens new avenues for uncertainty-aware modeling of complex PDE systems.

Paperid: 823, https://arxiv.org/pdf/2509.12666.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) leverage machine learning with differential equations to solve direct and inverse problems, ensuring predictions follow physical laws. Physiologically based pharmacokinetic (PBPK) modeling advances beyond classical compartmental approaches by using a mechanistic, physiology focused framework. A PBPK model is based on a system of ODEs, with each equation representing the mass balance of a drug in a compartment, such as an organ or tissue. These ODEs include parameters that reflect physiological, biochemical, and drug-specific characteristics to simulate how the drug moves through the body. In this paper, we introduce PBPK-iPINN, a method to estimate drug-specific or patient-specific parameters and drug concentration profiles in PBPK brain compartment models using inverse PINNs. We demonstrate that, for the inverse problem to converge to the correct solution, the loss function components (data loss, initial conditions loss, and residual loss) must be appropriately weighted, and parameters (including number of layers, number of neurons, activation functions, learning rate, optimizer, and collocation points) must be carefully tuned. The performance of the PBPK-iPINN approach is then compared with established traditional numerical and statistical methods.

Paperid: 824, https://arxiv.org/pdf/2509.12483.pdf

Abstract:
Purpose - This study compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving the two-dimensional Helmholtz equation in wave scattering problems. The objective is to evaluate the performance of both methods under the same conditions. Design/methodology/approach - We solve the Helmholtz equation using BEM and PINNs for the same scattering problem. The PINNs are trained by minimizing the residual of the governing equations and boundary conditions, with their configuration determined through hyperparameter optimization, while the BEM is applied using boundary discretization. Both methods are evaluated in terms of solution accuracy, computation time, and generalization capacity. Findings - Numerical experiments were conducted by varying the number of integration points for BEM and the number of layers and neurons per layer for PINNs. Hyperparameter tuning provided further insight into suitable configurations for wave scattering problems. At comparable accuracy, PINNs produced consistent solutions but required training times approximately 42 times longer than BEM. However, once trained, PINNs achieved evaluation times up to 204 times faster. The generalization capacity was also assessed outside the PINN training domain, where the relative error increased from $7.46 \times 10^{-2}$ to 8.22, while BEM maintained a similar error level in the extended region. Originality/value - This work presents a direct comparison between PINNs and BEM for the Helmholtz equation. The analysis provides quantitative data on the performance of both methods, supporting their selection in future research on wave propagation problems and establishing future challenges and directions.

Paperid: 825, https://arxiv.org/pdf/2509.12271.pdf

Abstract:
This work proposes a Variational Physics-Informed Neural Network (VPINN) framework that integrates the Petrov-Galerkin formulation with deep neural networks (DNNs) for solving one-dimensional singularly perturbed boundary value problems (BVPs) and parabolic partial differential equations (PDEs) involving one or two small parameters. The method adopts a nonlinear approximation in which the trial space is defined by neural network functions, while the test space is constructed from hat functions. The weak formulation is constructed using localized test functions, with interface penalty terms introduced to enhance numerical stability and accurately capture boundary layers. Dirichlet boundary conditions are imposed via hard constraints, and source terms are computed using automatic differentiation. Numerical experiments on benchmark problems demonstrate the effectiveness of the proposed method, showing significantly improved accuracy in both the $L_2$ and maximum norms compared to the standard VPINN approach for one-dimensional singularly perturbed differential equations (SPDEs).

Paperid: 826, https://arxiv.org/pdf/2509.10945.pdf

Abstract:
In this article, we employ Chien-Physics Informed Neural Networks (C-PINNs) to obtain solutions for singularly perturbed convection-diffusion equations, reaction-diffusion equations, and their coupled forms in both one and two-dimensional settings. While PINNs have emerged as a powerful tool for solving various types of differential equations, their application to singular perturbation problems (SPPs) presents significant challenges. These challenges arise because a small perturbation parameter multiplies the highest-order derivatives, leading to sharp gradient changes near the boundary layer. To overcome these difficulties, we apply C-PINNs, a modified version of the standard PINNs framework, which is specifically designed to address singular perturbation problems. Our study shows that C-PINNs provide a more accurate solution for SPPs, demonstrating better performance than conventional methods.

Paperid: 827, https://arxiv.org/pdf/2509.09611.pdf

Abstract:
We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative Pre-Trained Physics-Informed Neural Networks, ReBaNO relies on a mathematically rigorous greedy algorithm to build its network structure offline adaptively from the ground up. Knowledge distillation via task-specific activation function allows ReBaNO to have a compact architecture requiring minimal computational cost online while embedding physics. In comparison to state-of-the-art operator learning algorithms such as PCA-Net, DeepONet, FNO, and CNO, numerical results demonstrate that ReBaNO significantly outperforms them in terms of eliminating/shrinking the generalization gap for both in- and out-of-distribution tests and being the only operator learning algorithm achieving strict discretization invariance.

Paperid: 828, https://arxiv.org/pdf/2509.08872.pdf

Abstract:
The contractile motion of the heart is strongly determined by the distribution of the fibers that constitute cardiac tissue. Strain analysis informed with the orientation of fibers allows to describe several pathologies that are typically associated with impaired mechanics of the myocardium, such as cardiovascular disease. Several methods have been developed to estimate strain-derived metrics from traditional imaging techniques. However, the physical models underlying these methods do not include fiber mechanics, restricting their capacity to accurately explain cardiac function. In this work, we introduce WarpPINN-fibers, a physics-informed neural network framework to accurately obtain cardiac motion and strains enhanced by fiber information. We train our neural network to satisfy a hyper-elastic model and promote fiber contraction with the goal to predict the deformation field of the heart from cine magnetic resonance images. For this purpose, we build a loss function composed of three terms: a data-similarity loss between the reference and the warped template images, a regularizer enforcing near-incompressibility of cardiac tissue and a fiber-stretch penalization that controls strain in the direction of synthetically produced fibers. We show that our neural network improves the former WarpPINN model and effectively controls fiber stretch in a synthetic phantom experiment. Then, we demonstrate that WarpPINN-fibers outperforms alternative methodologies in landmark-tracking and strain curve prediction for a cine-MRI benchmark with a cohort of 15 healthy volunteers. We expect that our method will enable a more precise quantification of cardiac strains through accurate deformation fields that are consistent with fiber physiology, without requiring imaging techniques more sophisticated than MRI.

Paperid: 829, https://arxiv.org/pdf/2509.07603.pdf

Abstract:
This paper presents an innovative Transformer-based deep learning strategy for optimizing the placement of sensors aiming at structural health monitoring of semiconductor probe cards. Failures in probe cards, including substrate cracks and loosened screws, would critically affect semiconductor manufacturing yield and reliability. Some failure modes could be detected by equipping a probe card with adequate sensors. Frequency response functions from simulated failure scenarios are adopted within a finite element model of a probe card. A comprehensive dataset, enriched by physics-informed scenario expansion and physics-aware statistical data augmentation, is exploited to train a hybrid Convolutional Neural Network and Transformer model. The model achieves high accuracy (99.83%) in classifying the probe card health states (baseline, loose screw, crack) and an excellent crack detection recall (99.73%). Model robustness is confirmed through a rigorous framework of 3 repetitions of 10-fold stratified cross-validation. The attention mechanism also pinpoints critical sensor locations: an analysis of the attention weights offers actionable insights for designing efficient, cost-effective monitoring systems by optimizing sensor configurations. This research highlights the capability of attention-based deep learning to advance proactive maintenance, enhancing operational reliability and yield in semiconductor manufacturing.

Paperid: 830, https://arxiv.org/pdf/2509.03370.pdf

Abstract:
We introduce the Neural Field Turing Machine (NFTM), a differentiable architecture that unifies symbolic computation, physical simulation, and perceptual inference within continuous spatial fields. NFTM combines a neural controller, continuous memory field, and movable read/write heads that perform local updates. At each timestep, the controller reads local patches, computes updates via learned rules, and writes them back while updating head positions. This design achieves linear O(N) scaling through fixed-radius neighborhoods while maintaining Turing completeness under bounded error. We demonstrate three example instantiations of NFTM: cellular automata simulation (Rule 110), physics-informed PDE solvers (2D heat equation), and iterative image refinement (CIFAR-10 inpainting). These instantiations learn local update rules that compose into global dynamics, exhibit stable long-horizon rollouts, and generalize beyond training horizons. NFTM provides a unified computational substrate bridging discrete algorithms and continuous field dynamics within a single differentiable framework.

Paperid: 831, https://arxiv.org/pdf/2509.03036.pdf

Abstract:
Symbolic regression (SR) has emerged as a powerful tool for automated scientific discovery, enabling the derivation of governing equations from experimental data. A growing body of work illustrates the promise of integrating domain knowledge into the SR to improve the discovered equation's generality and usefulness. Physics-informed SR (PiSR) addresses this by incorporating domain knowledge, but current methods often require specialized formulations and manual feature engineering, limiting their adaptability only to domain experts. In this study, we leverage pre-trained Large Language Models (LLMs) to facilitate knowledge integration in PiSR. By harnessing the contextual understanding of LLMs trained on vast scientific literature, we aim to automate the incorporation of domain knowledge, reducing the need for manual intervention and making the process more accessible to a broader range of scientific problems. Namely, the LLM is integrated into the SR's loss function, adding a term of the LLM's evaluation of the SR's produced equation. We extensively evaluate our method using three SR algorithms (DEAP, gplearn, and PySR) and three pre-trained LLMs (Falcon, Mistral, and LLama 2) across three physical dynamics (dropping ball, simple harmonic motion, and electromagnetic wave). The results demonstrate that LLM integration consistently improves the reconstruction of physical dynamics from data, enhancing the robustness of SR models to noise and complexity. We further explore the impact of prompt engineering, finding that more informative prompts significantly improve performance.

Paperid: 832, https://arxiv.org/pdf/2509.02607.pdf

Abstract:
Radioembolization is a localized liver cancer treatment that delivers radioactive microspheres (30 micron) to tumors via a catheter inserted in the hepatic arterial tree. The goal is to maximize therapeutic efficacy while minimizing damage to healthy liver tissue. However, optimization is challenging due to complex hepatic artery anatomy, variable blood flow, and uncertainty in microsphere transport. The creation of dynamic, patient-specific digital twins may provide a transformative solution to these challenges. This work outlines a framework for a liver radioembolization digital twin using high-fidelity computational fluid dynamics (CFD) and/or recent physics-informed machine learning approaches. The CFD approach involves microsphere transport calculations in the hepatic arterial tree with individual patient data, which enables personalized treatment planning. Although accurate, traditional CFD is computationally expensive and limits clinical applicability. To accelerate simulations, physics-informed neural networks (PINNs) and their generative extensions play an increasingly important role. PINNs integrate governing equations, such as the Navier-Stokes equations, directly into the neural network training process, enabling mesh-free, data-efficient approximation of blood flow and microsphere transport. Physics-informed generative adversarial networks (PI-GANs), diffusion models (PI-DMs), and transformer-based architectures further enable uncertainty-aware, temporally resolved predictions with reduced computational cost. These AI surrogates not only maintain physical fidelity but also support rapid sampling of diverse flow scenarios, facilitating real-time decision support. Together, CFD and physics-informed AI methods form the foundation of dynamic, patient-specific digital twin to optimize radioembolization planning and ultimately improve clinical outcomes.

Paperid: 833, https://arxiv.org/pdf/2509.01072.pdf

Abstract:
Diabetic retinopathy (DR) is a leading cause of blindness worldwide, necessitating early detection to prevent vision loss. Current automated DR detection systems often struggle with poor-quality images, lack interpretability, and insufficient integration of domain-specific knowledge. To address these challenges, we introduce a novel framework that integrates three innovative contributions: (1) Adaptive Retinal Image Enhancement Using Physics-Informed Neural Networks (PINNs): this technique dynamically enhances retinal images by incorporating physical constraints, improving the visibility of critical features such as microaneurysms, hemorrhages, and exudates; (2) Hybrid Feature Fusion Network (HFFN): by combining deep learning embeddings with handcrafted features, HFFN leverages both learned representations and domain-specific knowledge to enhance generalization and accuracy; (3) Multi-Stage Classifier with Uncertainty Quantification: this method breaks down the classification process into logical stages, providing interpretable predictions and confidence scores, thereby improving clinical trust. The proposed framework achieves an accuracy of 92.7%, a precision of 92.5%, a recall of 92.6%, an F1-score of 92.5%, an AUC of 97.8%, a mAP of 0.96, and an MCC of 0.85. Ophthalmologists rated the framework's predictions as highly clinically relevant (4.8/5), highlighting its alignment with real-world diagnostic needs. Qualitative analyses, including Grad-CAM visualizations and uncertainty heatmaps, further enhance the interpretability and trustworthiness of the system. The framework demonstrates robust performance across diverse conditions, including low-quality images, noisy data, and unseen datasets. These features make the proposed framework a promising tool for clinical adoption, enabling more accurate and reliable DR detection in resource-limited settings.

Paperid: 834, https://arxiv.org/pdf/2509.00808.pdf

Abstract:
Fetal ultrasound standard plane classification is essential for reliable prenatal diagnosis but faces inherent challenges, including low tissue contrast, boundary ambiguity, and operator-dependent image quality variations. To overcome these limitations, we propose a plug-and-play adaptive contrast adjustment module (ACAM), whose core design is inspired by the clinical practice of doctors adjusting image contrast to obtain clearer and more discriminative structural information. The module employs a shallow texture-sensitive network to predict clinically plausible contrast parameters, transforms input images into multiple contrast-enhanced views through differentiable mapping, and fuses them within downstream classifiers. Validated on a multi-center dataset of 12,400 images across six anatomical categories, the module consistently improves performance across diverse models, with accuracy of lightweight models increasing by 2.02 percent, accuracy of traditional models increasing by 1.29 percent, and accuracy of state-of-the-art models increasing by 1.15 percent. The innovation of the module lies in its content-aware adaptation capability, replacing random preprocessing with physics-informed transformations that align with sonographer workflows while improving robustness to imaging heterogeneity through multi-view fusion. This approach effectively bridges low-level image features with high-level semantics, establishing a new paradigm for medical image analysis under real-world image quality variations.

Paperid: 835, https://arxiv.org/pdf/2509.00049.pdf

Abstract:
Accurate prediction of hydrogen sorption in clays, shales, and coals is vital for advancing underground hydrogen storage, natural hydrogen exploration, and radioactive waste containment. Traditional experimental methods, while foundational, are time-consuming, error-prone, and limited in capturing geological heterogeneity. This study introduces an adaptive physics-informed neural network (PINN) framework with multi-category feature engineering to enhance hydrogen sorption prediction. The framework integrates classical isotherm models with thermodynamic constraints to ensure physical consistency while leveraging deep learning flexibility. A comprehensive dataset consisting of 155 samples, which includes 50 clays, 60 shales, and 45 coals, was employed, incorporating diverse compositional properties and experimental conditions. Multi-category feature engineering across seven categories captured complex sorption dynamics. The PINN employs deep residual networks with multi-head attention, optimized via adaptive loss functions and Monte Carlo dropout for uncertainty quantification. K-fold cross-validation and hyperparameter optimization achieve significant accuracy (R2 = 0.979, RMSE = 0.045 mol per kg) with 67% faster convergence despite 15-fold increased complexity. The framework demonstrates robust lithology-specific performance across clay minerals (R2 = 0.981), shales (R2 = 0.971), and coals (R2 = 0.978), maintaining 85-91% reliability scores. Interpretability analysis via SHAP, accumulated local effects, and Friedman's H-statistics reveal that hydrogen adsorption capacity dominates predictions, while 86.7% of feature pairs exhibit strong interactions, validating the necessity of non-linear modeling approaches. This adaptive physics-informed framework accelerates site screening and enables risk-informed decision-making through robust uncertainty quantification.

Paperid: 836, https://arxiv.org/pdf/2508.20612.pdf

Abstract:
In semiconductor manufacturing, defect detection and localization are critical to ensuring product quality and yield. While X-ray imaging is a reliable non-destructive testing method, it is memory-intensive and time-consuming for large-scale scanning, Magnetic Field Imaging (MFI) offers a more efficient means to localize regions of interest (ROI) for targeted X-ray scanning. However, the limited availability of MFI datasets due to proprietary concerns presents a significant bottleneck for training machine learning (ML) models using MFI. To address this challenge, we consider an ML-driven approach leveraging diffusion models with two physical constraints. We propose Physics Informed Generative Models for Magnetic Field Images (PI-GenMFI) to generate synthetic MFI samples by integrating specific physical information. We generate MFI images for the most common defect types: power shorts. These synthetic images will serve as training data for ML algorithms designed to localize defect areas efficiently. To evaluate generated MFIs, we compare our model to SOTA generative models from both variational autoencoder (VAE) and diffusion methods. We present a domain expert evaluation to assess the generated samples. In addition, we present qualitative and quantitative evaluation using various metrics used for image generation and signal processing, showing promising results to optimize the defect localization process.

Paperid: 837, https://arxiv.org/pdf/2508.18653.pdf

Abstract:
Information asymmetry in financial markets, often amplified by strategically crafted corporate narratives, undermines the effectiveness of conventional textual analysis. We propose a novel multimodal framework for financial risk assessment that integrates textual sentiment with paralinguistic cues derived from executive vocal tract dynamics in earnings calls. Central to this framework is the Physics-Informed Acoustic Model (PIAM), which applies nonlinear acoustics to robustly extract emotional signatures from raw teleconference sound subject to distortions such as signal clipping. Both acoustic and textual emotional states are projected onto an interpretable three-dimensional Affective State Label (ASL) space-Tension, Stability, and Arousal. Using a dataset of 1,795 earnings calls (approximately 1,800 hours), we construct features capturing dynamic shifts in executive affect between scripted presentation and spontaneous Q&A exchanges. Our key finding reveals a pronounced divergence in predictive capacity: while multimodal features do not forecast directional stock returns, they explain up to 43.8% of the out-of-sample variance in 30-day realized volatility. Importantly, volatility predictions are strongly driven by emotional dynamics during executive transitions from scripted to spontaneous speech, particularly reduced textual stability and heightened acoustic instability from CFOs, and significant arousal variability from CEOs. An ablation study confirms that our multimodal approach substantially outperforms a financials-only baseline, underscoring the complementary contributions of acoustic and textual modalities. By decoding latent markers of uncertainty from verifiable biometric signals, our methodology provides investors and regulators a powerful tool for enhancing market interpretability and identifying hidden corporate uncertainty.

Paperid: 838, https://arxiv.org/pdf/2508.16032.pdf

Abstract:
For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we introduce a hybrid computational framework by coupling discontinuous Galerkin (DG) discretizations with a temporally progressive neural network architecture. Our method incorporates a structure-preserving weak-form loss -- combining DG residuals and Rankine-Hugoniot jump conditions -- with a causality-respecting progressive training strategy. The proposed framework trains neural networks sequentially across temporally decomposed subintervals, leveraging pseudo-label supervision to ensure temporal coherence and solution continuity. This approach mitigates error accumulation and enhances the model's capacity to resolve shock waves and steep gradients without explicit limiters. Besides, a theoretical analysis establishes error bounds for the proposed framework, demonstrating convergence toward the physical solution under mesh refinement and regularized training. Numerical experiments on Burgers and Euler equations show that our method consistently outperforms standard PINNs, PINNs-WE, and first-order DG schemes in both accuracy and robustness, particularly in capturing shocks and steep gradients. These results highlight the promise of combining classical discretization techniques with machine learning to develop robust and accurate solvers for nonlinear hyperbolic systems.

Paperid: 839, https://arxiv.org/pdf/2508.07566.pdf

Abstract:
We present an evolved steerable version of the single-tail Fish-&-Ribbon-Inspired Small Swimming Harmonic roBot (FRISSHBot), a 59-mg biologically inspired swimmer, which is driven by a new shape-memory alloy (SMA)-based bimorph actuator. The new FRISSHBot is controllable in the two-dimensional (2D) space, which enabled the first demonstration of feedback-controlled trajectory tracking of a single-tail aquatic robot with onboard actuation at the subgram scale. These new capabilities are the result of a physics-informed design with an enlarged head and shortened tail relative to those of the original platform. Enhanced by its design, this new platform achieves forward swimming speeds of up to 13.6 mm/s (0.38 Bl/s), which is over four times that of the original platform. Furthermore, when following 2D references in closed loop, the tested FRISSHBot prototype attains forward swimming speeds of up to 9.1 mm/s, root-mean-square (RMS) tracking errors as low as 2.6 mm, turning rates of up to 13.1 Â°/s, and turning radii as small as 10 mm.

Paperid: 840, https://arxiv.org/pdf/2508.05418.pdf

Abstract:
Shockwave classification in shadowgraph imaging is challenging due to limited labeled data and complex flow structures. This study presents a hybrid framework that combines unsupervised autoencoder models with a fuzzy inference system to generate and interpret anomaly maps. Among the evaluated methods, the hybrid $Î²$-VAE autoencoder with a fuzzy rule-based system most effectively captured coherent shock features, integrating spatial context to enhance anomaly classification. The resulting approach enables interpretable, unsupervised classification of flow disruptions and lays the groundwork for real-time, physics-informed diagnostics in experimental and industrial fluid applications.

Paperid: 841, https://arxiv.org/pdf/2508.03315.pdf

Abstract:
Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for reconstructing initial conditions from sparse or indirect wave measurements. While recent advances in supervised deep learning have shown potential for this purpose, they require large labelled datasets of ground truth wave data, which are infeasible to obtain in real-world scenarios. To overcome this limitation, we propose a Physics-Informed Neural Operator (PINO) framework for reconstructing spatially and temporally phase-resolved, nonlinear ocean wave fields from sparse measurements, without the need for ground truth data during training. This is achieved by embedding residuals of the free surface boundary conditions of ocean gravity waves into the loss function of the PINO, constraining the solution space in a soft manner. After training, we validate our approach using highly realistic synthetic wave data and demonstrate the accurate reconstruction of nonlinear wave fields from both buoy time series and radar snapshots. Our results indicate that PINOs enable accurate, real-time reconstruction and generalize robustly across a wide range of wave conditions, thereby paving the way for operational, data-driven wave reconstruction and prediction in realistic marine environments.

Paperid: 842, https://arxiv.org/pdf/2508.02537.pdf

Abstract:
Physics-Informed Neural Networks offer a powerful framework for solving PDEs by embedding physical laws into the learning process. However, when applied to domains with irregular boundaries, PINNs often suffer from instability and slow convergence, which stems from (1) inconsistent normalization due to geometric anisotropy, (2) inaccurate boundary enforcements, and (3) imbalanced loss term competition. A common workaround is to map the domain to a regular space. Yet, conventional mapping methods rely on case-specific meshes, define Jacobians at pre-specified fixed nodes, reformulate PDEs via the chain rule-making them incompatible with modern automatic differentiation, tensor-based frameworks. To bridge this gap, we propose JacobiNet, a learning-based coordinate-transformed PINN framework that unifies domain mapping and PDE solving within an end-to-end differentiable architecture. Leveraging lightweight MLPs, JacobiNet learns continuous, differentiable mappings, enables direct Jacobian computation via autograd, shares computation graph with downstream PINNs. Its continuous nature and built-in Jacobian eliminate the need for meshing, explicit Jacobians computation/ storage, and PDE reformulation, while unlocking geometric-editing operations, reducing the mapping cost. Separating physical modeling from geometric complexity, JacobiNet (1) addresses normalization challenges in the original anisotropic coordinates, (2) facilitates hard constraints of boundary conditions, and (3) mitigates the long-standing imbalance among loss terms. Evaluated on various PDEs, JacobiNet reduces the L2 error from 0.11-0.73 to 0.01-0.09. In vessel-like domains with varying shapes, JacobiNet enables millisecond-level mapping inference for unseen geometries, improves prediction accuracy by an average of 3.65*, while delivering over 10* speed up-demonstrating strong generalization, accuracy, and efficiency.

Paperid: 843, https://arxiv.org/pdf/2507.19701.pdf

Abstract:
Accurate prediction of future agent trajectories is a critical challenge for ensuring safe and efficient autonomous navigation, particularly in complex urban environments characterized by multiple plausible future scenarios. In this paper, we present a novel hybrid approach that integrates learning-based with physics-based constraints to address the multi-modality inherent in trajectory prediction. Our method employs a variational Bayesian mixture model to effectively capture the diverse range of potential future behaviors, moving beyond traditional unimodal assumptions. Unlike prior approaches that predominantly treat trajectory prediction as a data-driven regression task, our framework incorporates physical realism through sector-specific boundary conditions and Model Predictive Control (MPC)-based smoothing. These constraints ensure that predicted trajectories are not only data-consistent but also physically plausible, adhering to kinematic and dynamic principles. Furthermore, our method produces interpretable and diverse trajectory predictions, enabling enhanced downstream decision-making and planning in autonomous driving systems. We evaluate our approach on two benchmark datasets, demonstrating superior performance compared to existing methods. Comprehensive ablation studies validate the contributions of each component and highlight their synergistic impact on prediction accuracy and reliability. By balancing data-driven insights with physics-informed constraints, our approach offers a robust and scalable solution for navigating the uncertainties of real-world urban environments.

Paperid: 844, https://arxiv.org/pdf/2507.16227.pdf

Abstract:
This work presents predictive hydrodynamic simulations empowered by artificial intelligence (AI) for laser driven implosion experiments, taking the double-cone ignition (DCI) scheme as an example. A Transformer-based deep learning model MULTI-Net is established to predict implosion features according to laser waveforms and target radius. A Physics-Informed Decoder (PID) is proposed for high-dimensional sampling, significantly reducing the prediction errors compared to Latin hypercube sampling. Applied to DCI experiments conducted on the SG-II Upgrade facility, the MULTI-Net model is able to predict the implosion dynamics measured by the x-ray streak camera. It is found that an effective laser absorption factor about 65\% is suitable for the one-dimensional simulations of the DCI-R10 experiments. For shot 33, the mean implosion velocity and collided plasma density reached 195 km/s and 117 g/cc, respectively. This study demonstrates a data-driven AI framework that enhances the prediction ability of simulations for complicated laser fusion experiments.

Paperid: 845, https://arxiv.org/pdf/2507.11853.pdf

Abstract:
The development of advanced packaging is essential in the semiconductor manufacturing industry. However, non-destructive testing (NDT) of advanced packaging becomes increasingly challenging due to the depth and complexity of the layers involved. In such a scenario, Magnetic field imaging (MFI) enables the imaging of magnetic fields generated by currents. For MFI to be effective in NDT, the magnetic fields must be converted into current density. This conversion has typically relied solely on a Fast Fourier Transform (FFT) for magnetic field inversion; however, the existing approach does not consider eddy current effects or image misalignment in the test setup. In this paper, we present a spatial-physics informed model (SPIM) designed for a 3D spiral sample scanned using Superconducting QUantum Interference Device (SQUID) microscopy. The SPIM encompasses three key components: i) magnetic image enhancement by aligning all the "sharp" wire field signals to mitigate the eddy current effect using both in-phase (I-channel) and quadrature-phase (Q-channel) images; (ii) magnetic image alignment that addresses skew effects caused by any misalignment of the scanning SQUID microscope relative to the wire segments; and (iii) an inversion method for converting magnetic fields to magnetic currents by integrating the Biot-Savart Law with FFT. The results show that the SPIM improves I-channel sharpness by 0.3% and reduces Q-channel sharpness by 25%. Also, we were able to remove rotational and skew misalignments of 0.30 in a real image. Overall, SPIM highlights the potential of combining spatial analysis with physics-driven models in practical applications.

Paperid: 846, https://arxiv.org/pdf/2507.10986.pdf

Abstract:
Stellar flare forecasting represents a critical frontier in astrophysics, offering profound insights into stellar activity mechanisms and exoplanetary habitability assessments. Yet the inherent unpredictability of flare activity, rooted in stellar diversity and evolutionary stages, underpins the field's core challenges: (1) sparse, incomplete, noisy lightcurve data from traditional observations; (2) ineffective multi-scale flare evolution capture via single representations; (3) poor physical interpretability in data-driven models lacking physics-informed priors. To address these challenges, we propose StellarF, a physics-informed framework synergizing general Al with astrophysical domain knowledge via three core components: a unified preprocessing pipeline for lightcurve refinement (missing-value imputation, temporal patch partitioning, adaptive sample filtering); a Low-Rank Adaptation (LoRA)-finetuned large language model (LLM) backbone enhanced by first-order difference augmentation, flare statistical information, and flare historical record modules for multimodal fusion instead of only simple representations; and a novel physics-informed loss embedding a minimum rising rate prior, appended to the cross-entropy loss, to align with flare physics. Extensive experiments on Kepler and TESS datasets show StellarF achieves state-of-the-art performance across key metrics, setting new benchmarks for flare forecasting. This work bridges general AI with astrophysics, offering a practical, physically interpretable paradigm for transient event forecasting in time-domain astronomy.

Paperid: 847, https://arxiv.org/pdf/2507.10884.pdf

Abstract:
System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we propose a Simulation-based Generative Model for Imperfect Data (SiGMoID) that enables precise and robust inference for dynamic systems. The proposed approach integrates two key methods: (1) physics-informed neural networks with hyper-networks that constructs an ODE solver, and (2) Wasserstein generative adversarial networks that estimates ODE parameters by effectively capturing noisy data distributions. We demonstrate that SiGMoID quantifies data noise, estimates system parameters, and infers unobserved system components. Its effectiveness is validated validated through realistic experimental examples, showcasing its broad applicability in various domains, from scientific research to engineered systems, and enabling the discovery of full system dynamics.

Paperid: 848, https://arxiv.org/pdf/2507.09782.pdf

Abstract:
This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We first employ PINNs to approximate solutions of nonlinear systems arising from lattice models, using the Levenberg-Marquardt algorithm to optimize network weights for greater accuracy. To enhance computational efficiency in high-dimensional settings, we integrate a stochastic sampling strategy. We then extend the method by coupling PINNs with a continuation approach to compute snaking bifurcation diagrams, incorporating an auxiliary equation to effectively track successive solution branches. For linear stability analysis, we adapt PINNs to compute eigenvectors, introducing output constraints to enforce positivity, in line with Sturm-Liouville theory. Numerical experiments are conducted on the discrete Allen-Cahn equation with cubic and quintic nonlinearities in one to five spatial dimensions. The results demonstrate that the proposed approach achieves accuracy comparable to, or better than, traditional numerical methods, especially in high-dimensional regimes where computational resources are a limiting factor. These findings highlight the potential of neural networks as scalable and efficient tools for the study of complex nonlinear lattice systems.

Paperid: 849, https://arxiv.org/pdf/2507.06712.pdf

Abstract:
State estimation for nonlinear dynamical systems is a critical challenge in control and engineering applications, particularly when only partial and noisy measurements are available. This paper introduces a novel Adaptive Physics-Informed Neural Network-based Observer (PINN-Obs) for accurate state estimation in nonlinear systems. Unlike traditional model-based observers, which require explicit system transformations or linearization, the proposed framework directly integrates system dynamics and sensor data into a physics-informed learning process. The observer adaptively learns an optimal gain matrix, ensuring convergence of the estimated states to the true system states. A rigorous theoretical analysis establishes formal convergence guarantees, demonstrating that the proposed approach achieves uniform error minimization under mild observability conditions. The effectiveness of PINN-Obs is validated through extensive numerical simulations on diverse nonlinear systems, including an induction motor model, a satellite motion system, and benchmark academic examples. Comparative experimental studies against existing observer designs highlight its superior accuracy, robustness, and adaptability.

Paperid: 850, https://arxiv.org/pdf/2507.02730.pdf

Abstract:
The industrialization of catalytic processes hinges on the availability of reliable kinetic models for design, optimization, and control. Traditional mechanistic models demand extensive domain expertise, while many data-driven approaches often lack interpretability and fail to enforce physical consistency. To overcome these limitations, we propose the Physics-Informed Automated Discovery of Kinetics (PI-ADoK) framework. By integrating physical constraints directly into a symbolic regression approach, PI-ADoK narrows the search space and substantially reduces the number of experiments required for model convergence. Additionally, the framework incorporates a robust uncertainty quantification strategy via the Metropolis-Hastings algorithm, which propagates parameter uncertainty to yield credible prediction intervals. Benchmarking our method against conventional approaches across several catalytic case studies demonstrates that PI-ADoK not only enhances model fidelity but also lowers the experimental burden, highlighting its potential for efficient and reliable kinetic model discovery in chemical reaction engineering.

Paperid: 851, https://arxiv.org/pdf/2506.23357.pdf

Abstract:
The current contribution develops a Variational Physics-Informed Neural Network (VPINN)-based framework for the analysis and design of multiphase architected solids. The elaborated VPINN methodology is based on the Petrov-Galerkin approach, with a deep neural network acting as trial function and local polynomials as test functions. For the analysis, a Galerkin Boundary Element Method (GBEM) scheme is developed to generate the mechanical field data, employing solely domain boundary information. The VPINN methodology is complemented by an adaptive, tree-based integration scheme for the evaluation of the weak-form integrals. Different double-phase material architectures are considered, with the VPINNs demonstrating their ability to capture the deformation fields with considerable accuracy. Moreover, the performance enhancement by the incorporation of additional semi-analytical information at auxiliary internal points is analyzed. Tree-based integration schemes are shown to be capable of robustly capturing inner material discontinuities upon substantial computational cost reductions. The results suggest that the proposed VPINN formulation offers comparative advantages in the modeling of multiphase architected materials compared to classical PINN formulations. The analysis paves the way for the development of variational physics-informed computational models for the mechanical analysis of complex architected multiphase materials and structures.

Paperid: 852, https://arxiv.org/pdf/2506.23311.pdf

Abstract:
We introduce MRF-DiPh, a novel physics informed denoising diffusion approach for multiparametric tissue mapping from highly accelerated, transient-state quantitative MRI acquisitions like Magnetic Resonance Fingerprinting (MRF). Our method is derived from a proximal splitting formulation, incorporating a pretrained denoising diffusion model as an effective image prior to regularize the MRF inverse problem. Further, during reconstruction it simultaneously enforces two key physical constraints: (1) k-space measurement consistency and (2) adherence to the Bloch response model. Numerical experiments on in-vivo brain scans data show that MRF-DiPh outperforms deep learning and compressed sensing MRF baselines, providing more accurate parameter maps while better preserving measurement fidelity and physical model consistency-critical for solving reliably inverse problems in medical imaging.

Paperid: 853, https://arxiv.org/pdf/2506.20441.pdf

Abstract:
Physics-informed Neural Networks (PINNs) have emerged as an efficient way to learn surrogate neural solvers of PDEs by embedding the physical model in the loss function and minimizing its residuals using automatic differentiation at so-called collocation points. Originally uniformly sampled, the choice of the latter has been the subject of recent advances leading to adaptive sampling refinements. In this paper, we propose a new quadrature method for approximating definite integrals based on the hessian of the considered function, and that we leverage to guide the selection of the collocation points during the training process of PINNs.

Paperid: 854, https://arxiv.org/pdf/2506.18954.pdf

Abstract:
This paper describes a sound source localization (SSL) technique that combines an $Î±$-stable model for the observed signal with a neural network-based approach for modeling steering vectors. Specifically, a physics-informed neural network, referred to as Neural Steerer, is used to interpolate measured steering vectors (SVs) on a fixed microphone array. This allows for a more robust estimation of the so-called $Î±$-stable spatial measure, which represents the most plausible direction of arrival (DOA) of a target signal. As an $Î±$-stable model for the non-Gaussian case ($Î±$ $\in$ (0, 2)) theoretically defines a unique spatial measure, we choose to leverage it to account for residual reconstruction error of the Neural Steerer in the downstream tasks. The objective scores indicate that our proposed technique outperforms state-of-the-art methods in the case of multiple sound sources.

Paperid: 855, https://arxiv.org/pdf/2506.18247.pdf

Abstract:
Quantifying and propagating modeling uncertainties is crucial for reliability analysis, robust optimization, and other model-based algorithmic processes in engineering design and control. Now, physics-informed machine learning (PIML) methods have emerged in recent years as a new alternative to traditional computational modeling and surrogate modeling methods, offering a balance between computing efficiency, modeling accuracy, and interpretability. However, their ability to predict and propagate modeling uncertainties remains mostly unexplored. In this paper, a promising class of auto-differentiable hybrid PIML architectures that combine partial physics and neural networks or ANNs (for input transformation or adaptive parameter estimation) is integrated with Bayesian Neural networks (replacing the ANNs); this is done with the goal to explore whether BNNs can successfully provision uncertainty propagation capabilities in the PIML architectures as well, further supported by the auto-differentiability of these architectures. A two-stage training process is used to alleviate the challenges traditionally encountered in training probabilistic ML models. The resulting BNN-integrated PIML architecture is evaluated on an analytical benchmark problem and flight experiments data for a fixed-wing RC aircraft, with prediction performance observed to be slightly worse or at par with purely data-driven ML and original PIML models. Moreover, Monte Carlo sampling of probabilistic BNN weights was found to be most effective in propagating uncertainty in the BNN-integrated PIML architectures.

Paperid: 856, https://arxiv.org/pdf/2506.17453.pdf

Abstract:
The UT GraphCast Hindcast Dataset from 1979 to 2024 is a comprehensive global weather forecast archive generated using the Google DeepMind GraphCast Operational model. Developed by researchers at The University of Texas at Austin under the WCRP umbrella, this dataset provides daily 15 day deterministic forecasts at 00UTC on an approximately 25 km global grid for a 45 year period. GraphCast is a physics informed graph neural network that was trained on ECMWF ERA5 reanalysis. It predicts more than a dozen key atmospheric and surface variables on 37 vertical levels, delivering a full medium range forecast in under one minute on modern hardware.

Paperid: 857, https://arxiv.org/pdf/2506.13833.pdf

Abstract:
This survey provides a comprehensive overview of the emerging field of world models grounded in the foundation of acoustic physical information. It examines the theoretical underpinnings, essential methodological frameworks, and recent technological advancements in leveraging acoustic signals for high-fidelity environmental perception, causal physical reasoning, and predictive simulation of dynamic events. The survey explains how acoustic signals, as direct carriers of mechanical wave energy from physical events, encode rich, latent information about material properties, internal geometric structures, and complex interaction dynamics. Specifically, this survey establishes the theoretical foundation by explaining how fundamental physical laws govern the encoding of physical information within acoustic signals. It then reviews the core methodological pillars, including Physics-Informed Neural Networks (PINNs), generative models, and self-supervised multimodal learning frameworks. Furthermore, the survey details the significant applications of acoustic world models in robotics, autonomous driving, healthcare, and finance. Finally, it systematically outlines the important technical and ethical challenges while proposing a concrete roadmap for future research directions toward robust, causal, uncertainty-aware, and responsible acoustic intelligence. These elements collectively point to a research pathway towards embodied active acoustic intelligence, empowering AI systems to construct an internal "intuitive physics" engine through sound.

Paperid: 858, https://arxiv.org/pdf/2506.13658.pdf

Abstract:
Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is often infeasible due to epistemic uncertainty, cost, or time constraints, resulting in models that fail to accurately describe the behavior of the system. On the other hand, data-driven machine learning models such as variational autoencoders are not guaranteed to identify a parsimonious representation. As a result, they can suffer from poor generalization performance and reconstruction accuracy in the regime of limited and noisy data. We propose a physics-informed variational autoencoder architecture that combines the interpretability of physics-based models with the flexibility of data-driven models. To promote disentanglement of the known physics and confounding influences, the latent space is partitioned into physically meaningful variables that parametrize a physics-based model, and data-driven variables that capture variability in the domain and class of the physical system. The encoder is coupled with a decoder that integrates physics-based and data-driven components, and constrained by an adversarial training objective that prevents the data-driven components from overriding the known physics, ensuring that the physics-grounded latent variables remain interpretable. We demonstrate that the model is able to disentangle features of the input signal and separate the known physics from confounding influences using supervision in the form of class and domain observables. The model is evaluated on a series of synthetic case studies relevant to engineering structures, demonstrating the feasibility of the proposed approach.

Paperid: 859, https://arxiv.org/pdf/2506.04742.pdf

Abstract:
Neural networks have been used to solve optimal control problems, typically by training neural networks using a combined loss function that considers data, differential equation residuals, and objective costs. We show that including cost functions in the training process is unnecessary, advocating for a simpler architecture and streamlined approach by decoupling the optimal control problem from the training process. Thus, our work shows that a simple neural operator architecture, such as DeepONet, coupled with an unconstrained optimization routine, can solve multiple optimal control problems with a single physics-informed training phase and a subsequent optimization phase. We achieve this by adding a penalty term based on the differential equation residual to the cost function and computing gradients with respect to the control using automatic differentiation through the trained neural operator within an iterative optimization routine. Our results show acceptable accuracy for practical applications and potential computational savings for more complex and higher-dimensional problems.

Paperid: 860, https://arxiv.org/pdf/2506.04375.pdf

Abstract:
From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared to standard forward and inverse problems in the physics-informed machine learning literature. In particular, neural network discretizations of solutions to eigenvalue problems have seen only a handful of studies. Owing to their nonlinearity, neural network discretizations prevent the conversion of the continuous eigenvalue differential equation into a standard discrete eigenvalue problem. In this setting, eigenvalue analysis requires more specialized techniques. Using a neural network discretization of the eigenfunction, we show that a variational form of the eigenvalue problem called the "Rayleigh quotient" in tandem with a Gram-Schmidt orthogonalization procedure is a particularly simple and robust approach to find the eigenvalues and their corresponding eigenfunctions. This method is shown to be useful for finding sets of harmonic functions on irregular domains, parametric and nonlinear eigenproblems, and high-dimensional eigenanalysis. We also discuss the utility of harmonic functions as a spectral basis for approximating solutions to partial differential equations. Through various examples from engineering mechanics, the combination of the Rayleigh quotient objective, Gram-Schmidt procedure, and the neural network discretization of the eigenfunction is shown to offer unique advantages for handling continuous eigenvalue problems.

Paperid: 861, https://arxiv.org/pdf/2506.01445.pdf

Abstract:
Sonar imaging is fundamental to underwater exploration, with critical applications in defense, navigation, and marine research. Shadow regions, in particular, provide essential cues for object detection and classification, yet existing studies primarily focus on highlight-based analysis, leaving shadow-based classification underexplored. To bridge this gap, we propose a Context-adaptive sonar image classification framework that leverages advanced image processing techniques to extract and integrate discriminative shadow and highlight features. Our framework introduces a novel shadow-specific classifier and adaptive shadow segmentation, enabling effective classification based on the dominant region. This approach ensures optimal feature representation, improving robustness against noise and occlusions. In addition, we introduce a Region-aware denoising model that enhances sonar image quality by preserving critical structural details while suppressing noise. This model incorporates an explainability-driven optimization strategy, ensuring that denoising is guided by feature importance, thereby improving interpretability and classification reliability. Furthermore, we present S3Simulator+, an extended dataset incorporating naval mine scenarios with physics-informed noise specifically tailored for the underwater sonar domain, fostering the development of robust AI models. By combining novel classification strategies with an enhanced dataset, our work addresses key challenges in sonar image analysis, contributing to the advancement of autonomous underwater perception.

Paperid: 862, https://arxiv.org/pdf/2506.00471.pdf

Abstract:
Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from slow convergence due to the complexity of of the wavefield solution. To address these challenges, we introduce a latent diffusion-based strategy for rapid and effective PINN initialization. First, we train multiple PINNs to represent frequency-domain scattered wavefields for various velocity models, then flatten each trained network's parameters into a one-dimensional vector, creating a comprehensive parameter dataset. Next, we employ an autoencoder to learn latent representations of these parameter vectors, capturing essential patterns across diverse PINN's parameters. We then train a conditional diffusion model to store the distribution of these latent vectors, with the corresponding velocity models serving as conditions. Once trained, this diffusion model can generate latent vectors corresponding to new velocity models, which are subsequently decoded by the autoencoder into complete PINN parameters. Experimental results indicate that our method significantly accelerates training and maintains high accuracy across in-distribution and out-of-distribution velocity scenarios.

Paperid: 863, https://arxiv.org/pdf/2505.23354.pdf

Abstract:
The local structure of a protein strongly impacts its function and interactions with other molecules. Therefore, a concise, informative representation of a local protein environment is essential for modeling and designing proteins and biomolecular interactions. However, these environments' extensive structural and chemical variability makes them challenging to model, and such representations remain under-explored. In this work, we propose a novel representation for a local protein environment derived from the intermediate features of atomistic foundation models (AFMs). We demonstrate that this embedding effectively captures both local structure (e.g., secondary motifs), and chemical features (e.g., amino-acid identity and protonation state). We further show that the AFM-derived representation space exhibits meaningful structure, enabling the construction of data-driven priors over the distribution of biomolecular environments. Finally, in the context of biomolecular NMR spectroscopy, we demonstrate that the proposed representations enable a first-of-its-kind physics-informed chemical shift predictor that achieves state-of-the-art accuracy. Our results demonstrate the surprising effectiveness of atomistic foundation models and their emergent representations for protein modeling beyond traditional molecular simulations. We believe this will open new lines of work in constructing effective functional representations for protein environments.

Paperid: 864, https://arxiv.org/pdf/2505.22761.pdf

Abstract:
Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to gain wider popularity. Through this survey, we present a comprehensive overview of PINNs approaches exploring various aspects related to their architecture, variants, areas of application, real-world use cases, challenges, and so on. Even though existing surveys can be identified, they fail to provide a comprehensive view as they primarily focus on either different application scenarios or limit their study to a superficial level. This survey attempts to bridge the gap in the existing literature by presenting a detailed analysis of all these factors combined with recent advancements and state-of-the-art research in PINNs. Additionally, we discuss prevalent challenges in PINNs implementation and present some of the future research directions as well. The overall contributions of the survey can be summarised into three sections: A detailed overview of PINNs architecture and variants, a performance analysis of PINNs on different equations and application domains highlighting their features. Finally, we present a detailed discussion of current issues and future research directions.

Paperid: 865, https://arxiv.org/pdf/2505.19320.pdf

Abstract:
Recent advances in generative AI offer promising solutions for synthetic data generation but often rely on large datasets for effective training. To address this limitation, we propose a novel generative model that learns from limited data by incorporating physical constraints to enhance performance. Specifically, we extend the VAE architecture by incorporating physical models in the generative process, enabling it to capture underlying dynamics more effectively. While physical models provide valuable insights, they struggle to capture complex temporal dependencies present in real-world data. To bridge this gap, we introduce a discrepancy term to account for unmodeled dynamics, represented within a latent Gaussian Process VAE (GPVAE). Furthermore, we apply regularization to ensure the generated data aligns closely with observed data, enhancing both the diversity and accuracy of the synthetic samples. The proposed method is applied to indoor temperature data, achieving state-of-the-art performance. Additionally, we demonstrate that PIGPVAE can produce realistic samples beyond the observed distribution, highlighting its robustness and usefulness under distribution shifts.

Paperid: 866, https://arxiv.org/pdf/2505.17308.pdf

Abstract:
Physics-informed neural networks (PINNs) have proven an effective tool for solving differential equations, in particular when considering non-standard or ill-posed settings. When inferring solutions and parameters of the differential equation from data, uncertainty estimates are preferable to point estimates, as they give an idea about the accuracy of the solution. In this work, we consider the inverse problem and employ repulsive ensembles of PINNs (RE-PINN) for obtaining such estimates. The repulsion is implemented by adding a particular repulsive term to the loss function, which has the property that the ensemble predictions correspond to the true Bayesian posterior in the limit of infinite ensemble members. Where possible, we compare the ensemble predictions to Monte Carlo baselines. Whereas the standard ensemble tends to collapse to maximum-a-posteriori solutions, the repulsive ensemble produces significantly more accurate uncertainty estimates and exhibits higher sample diversity.

Paperid: 867, https://arxiv.org/pdf/2505.14595.pdf

Abstract:
Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the characteristics of the solution fields and their time-dependent dynamics. Although high-fidelity numerical solvers generate the training datasets, they have thus far been excluded from the training process, causing the learned latent dynamics to drift away from the discretized governing physics. This mismatch often limits generalization and forecasting capabilities. In this work, we propose Physics-informed ROM ($Î¦$-ROM) by incorporating differentiable PDE solvers into the training procedure. Specifically, the latent space dynamics and its dependence on PDE parameters are shaped directly by the governing physics encoded in the solver, ensuring a strong correspondence between the full and reduced systems. Our model outperforms state-of-the-art data-driven ROMs and other physics-informed strategies by accurately generalizing to new dynamics arising from unseen parameters, enabling long-term forecasting beyond the training horizon, maintaining continuity in both time and space, and reducing the data cost. Furthermore, $Î¦$-ROM learns to recover and forecast the solution fields even when trained or evaluated with sparse and irregular observations of the fields, providing a flexible framework for field reconstruction and data assimilation. We demonstrate the framework's robustness across different PDE solvers and highlight its broad applicability by providing an open-source JAX implementation readily extensible to other PDE systems and differentiable solvers.

Paperid: 868, https://arxiv.org/pdf/2505.12389.pdf

Abstract:
The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the finite element method (FEM), typically rely on mesh-based approaches to obtain approximate solutions. However, these methods often require complex and computationally intensive techniques to overcome the limitations of approximation, leading to significant increases in computational cost. The objective of this study is to develop a series of novel numerical methods based on physics-informed neural networks (PINN) for solving the Saint-Venant torsion equations. Utilizing the expressive power and the automatic differentiation capability of neural networks, the PINN can solve partial differential equations (PDEs) along with boundary conditions without the need for intricate computational techniques. First, a PINN solver was developed to compute the torsional constant for bars with arbitrary cross-sectional geometries. This was followed by the development of a solver capable of handling cases with sharp geometric transitions; variable-scaling PINN (VS-PINN). Finally, a parametric PINN was constructed to address the limitations of conventional single-instance PINN. The results from all three solvers showed good agreement with reference solutions, demonstrating their accuracy and robustness. Each solver can be selectively utilized depending on the specific requirements of torsional behavior analysis.

Paperid: 869, https://arxiv.org/pdf/2505.11638.pdf

Abstract:
Natural Gradient Descent (NGD) has emerged as a promising optimization algorithm for training neural network-based solvers for partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs). However, its practical use is often limited by the high computational cost of solving linear systems involving the Gramian matrix. While matrix-free NGD methods based on the conjugate gradient (CG) method avoid explicit matrix inversion, the ill-conditioning of the Gramian significantly slows the convergence of CG. In this work, we extend matrix-free NGD to broader classes of problems than previously considered and propose the use of Randomized NystrÃ¶m preconditioning to accelerate convergence of the inner CG solver. The resulting algorithm demonstrates substantial performance improvements over existing NGD-based methods on a range of PDE problems discretized using neural networks.

Paperid: 870, https://arxiv.org/pdf/2505.04875.pdf

Abstract:
One use case of ``physics-informed neural networks'' (PINNs) is solution reconstruction, which aims to estimate the full-field state of a physical system from sparse measurements. Parameterized governing equations of the system are used in tandem with the measurements to regularize the regression problem. However, in real-world solution reconstruction problems, the parameterized governing equation may be inconsistent with the physical phenomena that give rise to the measurement data. We show that due to assuming consistency between the true and parameterized physics, PINNs-based approaches may fail to satisfy three basic criteria of interpretability, robustness, and data consistency. As we argue, these criteria ensure that (i) the quality of the reconstruction can be assessed, (ii) the reconstruction does not depend strongly on the choice of physics loss, and (iii) that in certain situations, the physics parameters can be uniquely recovered. In the context of elasticity and heat transfer, we demonstrate how standard formulations of the physics loss and techniques for constraining the solution to respect the measurement data lead to different ``constraint forces" -- which we define as additional source terms arising from the constraints -- and that these constraint forces can significantly influence the reconstructed solution. To avoid the potentially substantial influence of the choice of physics loss and method of constraint enforcement on the reconstructed solution, we propose the ``explicit constraint force method'' (ECFM) to gain control of the source term introduced by the constraint. We then show that by satisfying the criteria of interpretability, robustness, and data consistency, this approach leads to more predictable and customizable reconstructions from noisy measurement data, even when the parameterization of the missing physics is inconsistent with the measured system.

Paperid: 871, https://arxiv.org/pdf/2505.03783.pdf

Abstract:
Accurate modeling of closure terms is a critical challenge in engineering and scientific research, particularly when data is sparse (scarse or incomplete), making widely applicable models difficult to develop. This study proposes a novel approach for constructing closure models in such challenging scenarios. We introduce a Series-Parallel Multi-Network Architecture that integrates Physics-Informed Neural Networks (PINNs) to incorporate physical constraints and heterogeneous data from multiple initial and boundary conditions, while employing dedicated subnetworks to independently model unknown closure terms, enhancing generalizability across diverse problems. These closure models are integrated into an accurate Partial Differential Equation (PDE) solver, enabling robust solutions to complex predictive simulations in engineering applications.

Paperid: 872, https://arxiv.org/pdf/2504.08341.pdf

Abstract:
We present a deep learning approach for computing multi-phase solutions to the semiclassical limit of the SchrÃ¶dinger equation. Traditional methods require deriving a multi-phase ansatz to close the moment system of the Liouville equation, a process that is often computationally intensive and impractical. Our method offers an efficient alternative by introducing a novel two-stage neural network framework to close the $2N\times 2N$ moment system, where $N$ represents the number of phases in the solution ansatz. In the first stage, we train neural networks to learn the mapping between higher-order moments and lower-order moments (along with their derivatives). The second stage incorporates physics-informed neural networks (PINNs), where we substitute the learned higher-order moments to systematically close the system. We provide theoretical guarantees for the convergence of both the loss functions and the neural network approximations. Numerical experiments demonstrate the effectiveness of our method for one- and two-dimensional problems with various phase numbers $N$ in the multi-phase solutions. The results confirm the accuracy and computational efficiency of the proposed approach compared to conventional techniques.

Paperid: 873, https://arxiv.org/pdf/2504.00910.pdf

Abstract:
Despite considerable scientific advances in numerical simulation, efficiently solving PDEs remains a complex and often expensive problem. Physics-informed Neural Networks (PINN) have emerged as an efficient way to learn surrogate solvers by embedding the PDE in the loss function and minimizing its residuals using automatic differentiation at so-called collocation points. Originally uniformly sampled, the choice of the latter has been the subject of recent advances leading to adaptive sampling refinements for PINNs. In this paper, leveraging a new quadrature method for approximating definite integrals, we introduce a provably accurate sampling method for collocation points based on the Hessian of the PDE residuals. Comparative experiments conducted on a set of 1D and 2D PDEs demonstrate the benefits of our method.

Paperid: 874, https://arxiv.org/pdf/2503.23729.pdf

Abstract:
Evolution equations, including both ordinary differential equations (ODEs) and partial differential equations (PDEs), play a pivotal role in modeling dynamic systems. However, achieving accurate long-time integration for these equations remains a significant challenge. While physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDEs, they often suffer from temporal error accumulation, which limits their effectiveness in capturing long-time behaviors. To alleviate this issue, we propose integral regularization PINNs (IR-PINNs), a novel approach that enhances temporal accuracy by incorporating an integral-based residual term into the loss function. This method divides the entire time interval into smaller sub-intervals and enforces constraints over these sub-intervals, thereby improving the resolution and correlation of temporal dynamics. Furthermore, IR-PINNs leverage adaptive sampling to dynamically refine the distribution of collocation points based on the evolving solution, ensuring higher accuracy in regions with sharp gradients or rapid variations. Numerical experiments on benchmark problems demonstrate that IR-PINNs outperform original PINNs and other state-of-the-art methods in capturing long-time behaviors, offering a robust and accurate solution for evolution equations.

Paperid: 875, https://arxiv.org/pdf/2503.17379.pdf

Abstract:
Solving partial differential equations (PDEs) with discontinuous solutions , such as shock waves in multiphase viscous flow in porous media , is critical for a wide range of scientific and engineering applications, as they represent sudden changes in physical quantities. Physics-Informed Neural Networks (PINNs), an approach proposed for solving PDEs, encounter significant challenges when applied to such systems. Accurately solving PDEs with discontinuities using PINNs requires specialized techniques to ensure effective solution accuracy and numerical stability. A benchmarking study was conducted on two multiphase flow problems in porous media: the classic Buckley-Leverett (BL) problem and a fully coupled system of equations involving shock waves but with varying levels of solution complexity. The findings show that PM and LM approaches can provide accurate solutions for the BL problem by effectively addressing the infinite gradients associated with shock occurrences. In contrast, AM methods failed to effectively resolve the shock waves. When applied to fully coupled PDEs (with more complex loss landscape), the generalization error in the solutions quickly increased, highlighting the need for ongoing innovation. This study provides a comprehensive review of existing techniques for managing PDE discontinuities using PINNs, offering information on their strengths and limitations. The results underscore the necessity for further research to improve PINNs ability to handle complex discontinuities, particularly in more challenging problems with complex loss landscapes. This includes problems involving higher dimensions or multiphysics systems, where current methods often struggle to maintain accuracy and efficiency.

Paperid: 876, https://arxiv.org/pdf/2502.15058.pdf

Abstract:
What if our clothes could capture our body motion accurately? This paper introduces Flexible Inertial Poser (FIP), a novel motion-capturing system using daily garments with two elbow-attached flex sensors and four Inertial Measurement Units (IMUs). To address the inevitable sensor displacements in loose wearables which degrade joint tracking accuracy significantly, we identify the distinct characteristics of the flex and inertial sensor displacements and develop a Displacement Latent Diffusion Model and a Physics-informed Calibrator to compensate for sensor displacements based on such observations, resulting in a substantial improvement in motion capture accuracy. We also introduce a Pose Fusion Predictor to enhance multimodal sensor fusion. Extensive experiments demonstrate that our method achieves robust performance across varying body shapes and motions, significantly outperforming SOTA IMU approaches with a 19.5% improvement in angular error, a 26.4% improvement in elbow angular error, and a 30.1% improvement in positional error. FIP opens up opportunities for ubiquitous human-computer interactions and diverse interactive applications such as Metaverse, rehabilitation, and fitness analysis.

Paperid: 877, https://arxiv.org/pdf/2502.00897.pdf

Abstract:
Physics-informed neural networks (PINNs) face significant challenges in modeling multi-frequency wavefields in complex velocity models due to their slow convergence, difficulty in representing high-frequency details, and lack of generalization to varying frequencies and velocity scenarios. To address these issues, we propose Meta-LRPINN, a novel framework that combines low-rank parameterization using singular value decomposition (SVD) with meta-learning and frequency embedding. Specifically, we decompose the weights of PINN's hidden layers using SVD and introduce an innovative frequency embedding hypernetwork (FEH) that links input frequencies with the singular values, enabling efficient and frequency-adaptive wavefield representation. Meta-learning is employed to provide robust initialization, improving optimization stability and reducing training time. Additionally, we implement adaptive rank reduction and FEH pruning during the meta-testing phase to further enhance efficiency. Numerical experiments, which are presented on multi-frequency scattered wavefields for different velocity models, demonstrate that Meta-LRPINN achieves much fast convergence speed and much high accuracy compared to baseline methods such as Meta-PINN and vanilla PINN. Also, the proposed framework shows strong generalization to out-of-distribution frequencies while maintaining computational efficiency. These results highlight the potential of our Meta-LRPINN for scalable and adaptable seismic wavefield modeling.

Paperid: 878, https://arxiv.org/pdf/2501.12914.pdf

Abstract:
Counterfactuals are a concept inherited from the field of logic and in general attain to the existence of causal relations between sentences or events. In particular, this concept has been introduced also in the context of interpretability in artificial intelligence, where counterfactuals refer to the minimum change to the feature values that changes the prediction of a classification model. The artificial intelligence framework of counterfactuals is mostly focused on machine learning approaches, typically neglecting the physics of the variables that determine a change in class. However, a theoretical formulation of counterfactuals in a control system framework - i.e., able to account for the mechanisms underlying a change in class - is lacking. To fill this gap, in this work we propose an original control system, physics-informed, theoretical foundation for counterfactuals, by means of the formulation of an optimal control problem. We apply the proposed methodology to a general glucose-insulin regulation model and results appear promising and pave the way to the possible integration with artificial intelligence techniques, with the aim of feeding machine learning models with the physics knowledge acquired through the system framework.

Paperid: 879, https://arxiv.org/pdf/2501.08430.pdf

Abstract:
The assimilation and prediction of phase-resolved surface gravity waves are critical challenges in ocean science and engineering. Potential flow theory (PFT) has been widely employed to develop wave models and numerical techniques for wave prediction. However, traditional wave prediction methods are often limited. For example, most simplified wave models have a limited ability to capture strong wave nonlinearity, while fully nonlinear PFT solvers often fail to meet the speed requirements of engineering applications. This computational inefficiency also hinders the development of effective data assimilation techniques, which are required to reconstruct spatial wave information from sparse measurements to initialize the wave prediction. To address these challenges, we propose a novel solver method that leverages physics-informed neural networks (PINNs) that parameterize PFT solutions as neural networks. This provides a computationally inexpensive way to assimilate and predict wave data. The proposed PINN framework is validated through comparisons with analytical linear PFT solutions and experimental data collected in a laboratory wave flume. The results demonstrate that our approach accurately captures and predicts irregular, nonlinear, and dispersive wave surface dynamics. Moreover, the PINN can infer the fully nonlinear velocity potential throughout the entire fluid volume solely from surface elevation measurements, enabling the calculation of fluid velocities that are difficult to measure experimentally.

Paperid: 880, https://arxiv.org/pdf/2501.07765.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems.

Paperid: 881, https://arxiv.org/pdf/2412.13695.pdf

Abstract:
'A trustworthy representation of uncertainty is desirable and should be considered as a key feature of any machine learning method' (Huellermeier and Waegeman, 2021). This conclusion of Huellermeier et al. underpins the importance of calibrated uncertainties. Since AI-based algorithms are heavily impacted by dataset shifts, the automotive industry needs to safeguard its system against all possible contingencies. One important but often neglected dataset shift is caused by optical aberrations induced by the windshield. For the verification of the perception system performance, requirements on the AI performance need to be translated into optical metrics by a bijective mapping. Given this bijective mapping it is evident that the optical system characteristics add additional information about the magnitude of the dataset shift. As a consequence, we propose to incorporate a physical inductive bias into the neural network calibration architecture to enhance the robustness and the trustworthiness of the AI target application, which we demonstrate by using a semantic segmentation task as an example. By utilizing the Zernike coefficient vector of the optical system as a physical prior we can significantly reduce the mean expected calibration error in case of optical aberrations. As a result, we pave the way for a trustworthy uncertainty representation and for a holistic verification strategy of the perception chain.

Paperid: 882, https://arxiv.org/pdf/2412.13200.pdf

Abstract:
In this work, we address the challenges posed by the high nonlinearity of the Butler-Volmer (BV) equation in forward and inverse simulations of the pseudo-two-dimensional (P2D) model using the physics-informed neural network (PINN) framework. The BV equation presents significant challenges for PINNs, primarily due to the hyperbolic sine term, which renders the Hessian of the PINN loss function highly ill-conditioned. To address this issue, we introduce a bypassing term that improves numerical stability by substantially reducing the condition number of the Hessian matrix. Furthermore, the small magnitude of the ionic flux $ j $ often leads to a common failure mode where PINNs converge to incorrect solutions. We demonstrate that incorporating a secondary conservation law for the solid-phase potential $ Ï$ effectively prevents such convergence issues and ensures solution accuracy. The proposed methods prove effective for solving both forward and inverse problems involving the BV equation. Specifically, we achieve precise parameter estimation in inverse scenarios and reliable solution predictions for forward simulations.

Paperid: 883, https://arxiv.org/pdf/2412.10782.pdf

Abstract:
In the recent years, Physics Informed Neural Networks (PINNs) have received strong interest as a method to solve PDE driven systems, in particular for data assimilation purpose. This method is still in its infancy, with many shortcomings and failures that remain not properly understood. In this paper we propose a natural gradient approach to PINNs which contributes to speed-up and improve the accuracy of the training. Based on an in depth analysis of the differential geometric structures of the problem, we come up with two distinct contributions: (i) a new natural gradient algorithm that scales as $\min(P^2S, S^2P)$, where $P$ is the number of parameters, and $S$ the batch size; (ii) a mathematically principled reformulation of the PINNs problem that allows the extension of natural gradient to it, with proved connections to Green's function theory.

Paperid: 884, https://arxiv.org/pdf/2412.09022.pdf

Abstract:
This paper explores the application of physics-informed neural networks (PINNs) to tackle forward problems in 3D contact mechanics, focusing on small deformation elasticity. We utilize a mixed-variable formulation, enhanced with output transformations, to enforce Dirichlet and Neumann boundary conditions as hard constraints. The inherent inequality constraints in contact mechanics, particularly the Karush-Kuhn-Tucker (KKT) conditions, are addressed as soft constraints by integrating them into the network's loss function. To enforce the KKT conditions, we leverage the nonlinear complementarity problem (NCP) approach, specifically using the Fischer-Burmeister function, which is known for its advantageous properties in optimization. We investigate two benchmark examples of PINNs in 3D contact mechanics: a single contact patch test and the Hertzian contact problem.

Paperid: 885, https://arxiv.org/pdf/2412.08650.pdf

Abstract:
Maxwell's equations are the fundamental equations for understanding electric and magnetic field interactions and play a crucial role in designing and optimizing sensor systems like capacitive touch sensors, which are widely prevalent in automotive switches and smartphones. Ensuring robust functionality and stability of the sensors in dynamic environments necessitates profound domain expertise and computationally intensive multi-physics simulations. This paper introduces a novel approach using a Physics-Informed Neural Network (PINN) based surrogate model to accelerate the design process. The PINN model solves the governing electrostatic equations describing the interaction between a finger and a capacitive sensor. Inputs include spatial coordinates from a 3D domain encompassing the finger, sensor, and PCB, along with finger distances. By incorporating the electrostatic equations directly into the neural network's loss function, the model captures the underlying physics. The learned model thus serves as a surrogate sensor model on which inference can be carried out in seconds for different experimental setups without the need to run simulations. Efficacy results evaluated on unseen test cases demonstrate the significant potential of PINNs in accelerating the development and design optimization of capacitive touch sensors.

Paperid: 886, https://arxiv.org/pdf/2412.07514.pdf

Abstract:
Vector-borne diseases continue to pose a significant health threat globally with more than 3 billion people at risk each year. Despite some limitations, mechanistic dynamic models are a popular approach to representing biological processes using ordinary differential equations where the parameters describe the different development and survival rates. Recent advances in population modelling have seen the combination of these mechanistic models with machine learning. One approach is physics-informed neural networks (PINNs) whereby the machine learning framework embeds physical, biological, or chemical laws into neural networks trained on observed or measured data. This enables forward simulations, predicting system behaviour from given parameters and inputs, and inverse modelling, improving parameterisation of existing parameters and estimating unknown or latent variables. In this paper, we focus on improving the parameterisation of biological processes in mechanistic models using PINNs to determine inverse parameters. In comparing mechanistic and PINN models, our experiments offer important insights into the strengths and weaknesses of both approaches but demonstrated that the PINN approach generally outperforms the dynamic model. For a deeper understanding of the performance of PINN models, a final validation was used to investigate how modifications to PINN architectures affect the performance of the framework. By varying only a single component at a time and keeping all other factors constant, we are able to observe the effect of each change.

Paperid: 887, https://arxiv.org/pdf/2412.01954.pdf

Abstract:
Design exploration or optimization using computational fluid dynamics (CFD) is commonly used in the industry. Geometric variation is a key component of such design problems, especially in turbulent flow scenarios, which involves running costly simulations at every design iteration. While parametric RANS-PINN type approaches have been proven to make effective turbulent surrogates, as a means of predicting unknown Reynolds number flows for a given geometry at near real-time, geometry aware physics informed surrogates with the ability to predict varying geometries are a relatively less studied topic. A novel geometry aware parametric PINN surrogate model has been created, which can predict flow fields for NACA 4 digit airfoils in turbulent conditions, for unseen shapes as well as inlet flow conditions. A local+global approach for embedding has been proposed, where known global design parameters for an airfoil as well as local SDF values can be used as inputs to the model along with velocity inlet/Reynolds number ($\mathcal{R}_e$) to predict the flow fields. A RANS formulation of the Navier-Stokes equations with a 2-equation k-epsilon turbulence model has been used for the PDE losses, in addition to limited CFD data from 8 different NACA airfoils for training. The models have then been validated with unknown NACA airfoils at unseen Reynolds numbers.

Paperid: 888, https://arxiv.org/pdf/2411.18459.pdf

Abstract:
Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what is being learned by physics-informed DeepONets by assessing the universality of the extracted basis functions and demonstrating their potential toward model reduction with spectral methods. Results provide clarity about measuring the performance of a physics-informed DeepONet through the decays of singular values and expansion coefficients. In addition, we propose a transfer learning approach for improving training for physics-informed DeepONets between parameters of the same PDE as well as across different, but related, PDEs where these models struggle to train well. This approach results in significant error reduction and learned basis functions that are more effective in representing the solution of a PDE.

Paperid: 889, https://arxiv.org/pdf/2411.15919.pdf

Abstract:
We present a new method for enhancing symbolic regression for differential equations via dimensional analysis, specifically Ipsen's and Buckingham pi methods. Since symbolic regression often suffers from high computational costs and overfitting, non-dimensionalizing datasets reduces the number of input variables, simplifies the search space, and ensures that derived equations are physically meaningful. As our main contribution, we integrate Ipsen's method of dimensional analysis with Universal Physics-Informed Neural Networks. We also combine dimensional analysis with the AI Feynman symbolic regression algorithm to show that dimensional analysis significantly improves the accuracy of the recovered equation. The results demonstrate that transforming data into a dimensionless form significantly decreases computation time and improves accuracy of the recovered hidden term. For algebraic equations, using the Buckingham pi theorem reduced complexity, allowing the AI Feynman model to converge faster with fewer data points and lower error rates. For differential equations, Ipsen's method was combined with Universal Physics-Informed Neural Networks (UPINNs) to identify hidden terms more effectively. These findings suggest that integrating dimensional analysis with symbolic regression can significantly lower computational costs, enhance model interpretability, and increase accuracy, providing a robust framework for automated discovery of governing equations in complex systems when data is limited.

Paperid: 890, https://arxiv.org/pdf/2411.06447.pdf

Abstract:
Biophysical model fitting plays a key role in obtaining quantitative parameters from physiological signals and images. However, the model complexity for molecular magnetic resonance imaging (MRI) often translates into excessive computation time, which makes clinical use impractical. Here, we present a generic computational approach for solving the parameter extraction inverse problem posed by ordinary differential equation (ODE) modeling coupled with experimental measurement of the system dynamics. This is achieved by formulating a numerical ODE solver to function as a step-wise analytical one, thereby making it compatible with automatic differentiation-based optimization. This enables efficient gradient-based model fitting, and provides a new approach to parameter quantification based on self-supervised learning from a single data observation. The neural-network-based train-by-fit pipeline was used to quantify semisolid magnetization transfer (MT) and chemical exchange saturation transfer (CEST) amide proton exchange parameters in the human brain, in an in-vivo molecular MRI study (n = 4). The entire pipeline of the first whole brain quantification was completed in 18.3 $\pm$ 8.3 minutes. Reusing the single-subject-trained network for inference in new subjects took 1.0 $\pm$ 0.2 s, to provide results in agreement with literature values and scan-specific fit results.

Paperid: 891, https://arxiv.org/pdf/2410.20801.pdf

Abstract:
We propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the workflow in forward and inverse modeling of a synthetic problem of flow in fractured porous media, we applied it to a real experimental dataset in which brine is injected at a constant pressure drop into a CO2 saturated naturally fractured shale core plug. The exact spatial positions of natural fractures and the dynamic in-situ distribution of fluids were imaged using a CT-scan setup. To model the targeted system, we followed a domain decomposition approach for matrix and fractures and a multi-network architecture for the separate calculation of water saturation and pressure. The flow equations in the matrix, fractures and interplay between them were solved during training. Prior to fully-coupled simulations, we proposed pre-training the model. This aided in a more efficient and successful training of the coupled system. Both for the synthetic and experimental inverse problems, we determined flow parameters within the matrix and the fractures. Multiple random initializations of network and system parameters were performed to assess the uncertainty and uniqueness of the results. The results confirmed the precision of the inverse calculated parameters in retrieving the main flow characteristics of the system. The consideration of multiscale matrix-fracture impacts is commonly overlooked in existing workflows. Accounting for them led to several orders of magnitude variations in the calculated flow properties compared to not accounting for them. To the best of our knowledge, the proposed PINNs-based workflow is the first to offer a reliable and computationally efficient solution for inverse modeling of multiphase flow in fractured porous media, achieved through history-matching noisy and multi-fidelity experimental measurements.

Paperid: 892, https://arxiv.org/pdf/2410.18917.pdf

Abstract:
Computational fluid dynamics (CFD) solvers employing two-equation eddy viscosity models are the industry standard for simulating turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) formulation. While these methods are computationally less expensive than direct numerical simulations, they can still incur significant computational costs to achieve the desired accuracy. In this context, physics-informed neural networks (PINNs) offer a promising approach for developing parametric surrogate models that leverage both existing, but limited CFD solutions and the governing differential equations to predict simulation outcomes in a computationally efficient, differentiable, and near real-time manner. In this work, we build upon the previously proposed RANS-PINN framework, which only focused on predicting flow over a cylinder. To investigate the efficacy of RANS-PINN as a viable approach to building parametric surrogate models, we investigate its accuracy in predicting relevant turbulent flow variables for both internal and external flows. To ensure training convergence with a more complex loss function, we adopt a novel sampling approach that exploits the domain geometry to ensure a proper balance among the contributions from various regions within the solution domain. The effectiveness of this framework is then demonstrated for two scenarios that represent a broad class of internal and external flow problems.

Paperid: 893, https://arxiv.org/pdf/2410.16173.pdf

Abstract:
At the forefront of control techniques is Model Predictive Control (MPC). While MPCs are effective, their requisite to recompute an optimal control given a new state leads to sparse response to the system and may make their implementation infeasible in small systems with low computational resources. To address these limitations in stability control, this research presents a small deterministic Physics-Informed MPC Surrogate model (PI-MPCS). PI-MPCS was developed to approximate the control by an MPC while encouraging stability and robustness through the integration of the system dynamics and the formation of a Lyapunov stability profile. Empirical results are presented on the task of 2D quadcopter landing. They demonstrate a rapid and precise MPC approximation on a non-linear system along with an estimated two times speed up on the computational requirements when compared against an MPC. PI-MPCS, in addition, displays a level of stable control for in- and out-of-distribution states as encouraged by the discrete dynamics residual and Lyapunov stability loss functions. PI-MPCS is meant to serve as a surrogate to MPC on situations in which the computational resources are limited.

Paperid: 894, https://arxiv.org/pdf/2410.00288.pdf

Abstract:
Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its succeeding variants are well established models for stock volatility forecasting. More recently, deep learning models have gained popularity in volatility prediction as they demonstrated promising accuracy in certain time series prediction tasks. Inspired by Physics-Informed Neural Networks (PINN), we constructed a new, hybrid Deep Learning model that combines the strengths of GARCH with the flexibility of a Long Short-Term Memory (LSTM) Deep Neural Network (DNN), thus capturing and forecasting market volatility more accurately than either class of models are capable of on their own. We refer to this novel model as a GARCH-Informed Neural Network (GINN). When compared to other time series models, GINN showed superior out-of-sample prediction performance in terms of the Coefficient of Determination ($R^2$), Mean Squared Error (MSE), and Mean Absolute Error (MAE).

Paperid: 895, https://arxiv.org/pdf/2409.19081.pdf

Abstract:
Computer simulation of "virtual interventions" may inform optimal valve repair for a given patient prior to intervention. However, the paucity of noninvasive methods to determine in vivo mechanical parameters of valves limits the accuracy of computer prediction and their clinical application. To address this, we propose ADEPT: A noninvasive method for Determining Elastic Parameters of valve Tissue. In this work, we demonstrated its application to the tricuspid valve of a child. We first tracked valve displacements from open to closed frames within a 3D echocardiogram time sequence using image registration. Physics-informed neural networks were subsequently applied to estimate the nonlinear mechanical properties from first principles and reference displacements. The simulated model using these patient-specific parameters closely aligned with the reference image segmentation, achieving a mean symmetric distance of less than 1 mm. Our approach doubled the accuracy of the simulated model compared to the generic parameters reported in the literature.

Paperid: 896, https://arxiv.org/pdf/2409.04708.pdf

Abstract:
Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly and time-consuming, especially when dealing with systems governed by complex physical laws which necessitates computationally intensive numerical methods such as finite element or finite volume techniques. On the other hand, surrogate-based methods offer an efficient alternative for computing reliability by approximating the underlying model from limited data. Neural operators have recently emerged as effective surrogates for modelling physical systems governed by partial differential equations. These operators can learn solutions to PDEs for varying inputs and parameters. Here, we investigate the efficacy of the recently developed physics-informed wavelet neural operator in solving reliability analysis problems. In particular, we investigate the possibility of using physics-informed operator for solving high-dimensional reliability analysis problems, while bypassing the need for any simulation. Through four numerical examples, we illustrate that physics-informed operator can seamlessly solve high-dimensional reliability analysis problems with reasonable accuracy, while eliminating the need for running expensive simulations.

Paperid: 897, https://arxiv.org/pdf/2409.03160.pdf

Abstract:
This paper proposes a novel learning-based framework for autonomous driving based on the concept of maximal safety probability. Efficient learning requires rewards that are informative of desirable/undesirable states, but such rewards are challenging to design manually due to the difficulty of differentiating better states among many safe states. On the other hand, learning policies that maximize safety probability does not require laborious reward shaping but is numerically challenging because the algorithms must optimize policies based on binary rewards sparse in time. Here, we show that physics-informed reinforcement learning can efficiently learn this form of maximally safe policy. Unlike existing drift control methods, our approach does not require a specific reference trajectory or complex reward shaping, and can learn safe behaviors only from sparse binary rewards. This is enabled by the use of the physics loss that plays an analogous role to reward shaping. The effectiveness of the proposed approach is demonstrated through lane keeping in a normal cornering scenario and safe drifting in a high-speed racing scenario.

Paperid: 898, https://arxiv.org/pdf/2601.21234.pdf

Abstract:
Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however, most methods require \emph{explicit governing equations} during training, which are often only partially known due to complex and nonlinear dynamics. We introduce \textbf{PHDME}, a port-Hamiltonian diffusion framework designed for \emph{sparse observations} and \emph{incomplete physics}. PHDME leverages port-Hamiltonian structural prior but does not require full knowledge of the closed-form governing equations. Our approach first trains a Gaussian process distributed Port-Hamiltonian system (GP-dPHS) on limited observations to capture an energy-based representation of the dynamics. The GP-dPHS is then used to generate a physically consistent artificial dataset for diffusion training, and to inform the diffusion model with a structured physics residual loss. After training, the diffusion model acts as an amortized sampler and forecaster for fast trajectory generation. Finally, we apply split conformal calibration to provide uncertainty statements for the generated predictions. Experiments on PDE benchmarks and a real-world spring system show improved accuracy and physical consistency under data scarcity.

Paperid: 899, https://arxiv.org/pdf/2601.19297.pdf

Abstract:
We propose a method for estimating the magnitude distribution of an acoustic field from spatially sparse magnitude measurements. Such a method is useful when phase measurements are unreliable or inaccessible. Physics-informed neural networks (PINNs) have shown promise for sound field estimation by incorporating constraints derived from governing partial differential equations (PDEs) into neural networks. However, they do not extend to settings where phase measurements are unavailable, as the loss function based on the governing PDE relies on phase information. To remedy this, we propose a phase-retrieval-based PINN for magnitude field estimation. By representing the magnitude and phase distributions with separate networks, the PDE loss can be computed based on the reconstructed complex amplitude. We demonstrate the effectiveness of our phase-retrieval-based PINN through experimental evaluation.

Paperid: 900, https://arxiv.org/pdf/2601.14235.pdf

Authors:LSST Dark Energy Science Collaboration, Eric Aubourg, Camille Avestruz, Matthew R. Becker, Biswajit Biswas, Rahul Biswas, Boris Bolliet, Adam S. Bolton, Clecio R. Bom, Raphaël Bonnet-Guerrini, Alexandre Boucaud, Jean-Eric Campagne, Chihway Chang, Aleksandra Ćiprijanović, Johann Cohen-Tanugi, Michael W. Coughlin, John Franklin Crenshaw, Juan C. Cuevas-Tello, Juan de Vicente, Seth W. Digel, Steven Dillmann, Mariano Javier de León Dominguez Romero, Alex Drlica-Wagner, Sydney Erickson, Alexander T. Gagliano, Christos Georgiou, Aritra Ghosh, Matthew Grayling, Kirill A. Grishin, Alan Heavens, Lindsay R. House, Mustapha Ishak, Wassim Kabalan, Arun Kannawadi, François Lanusse, C. Danielle Leonard, Pierre-François Léget, Michelle Lochner, Yao-Yuan Mao, Peter Melchior, Grant Merz, Martin Millon, Anais Möller, Gautham Narayan, Yuuki Omori, Hiranya Peiris, Laurence Perreault-Levasseur, Andrés A. Plazas Malagón, Nesar Ramachandra, Benjamin Remy, Cécile Roucelle, Jaime Ruiz-Zapatero, Stefan Schuldt, Ignacio Sevilla-Noarbe, Ved G. Shah, Tjitske Starkenburg, Stephen Thorp, Laura Toribio San Cipriano, Tilman Tröster, Roberto Trotta, Padma Venkatraman, Amanda Wasserman, Tim White, Justine Zeghal, Tianqing Zhang, Yuanyuan Zhang

Abstract:
The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.

Paperid: 901, https://arxiv.org/pdf/2601.10690.pdf

Abstract:
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle with stochastic dynamics and fail to quantify prediction uncertainty, limiting their utility in robust decision-making contexts. To address these challenges, we introduce a data-driven framework for learning continuous-time stochastic ROMs that generalize across parameter spaces and forcing conditions. Our approach, based on amortized stochastic variational inference, leverages a reparametrization trick for Markov Gaussian processes to eliminate the need for computationally expensive forward solvers during training. This enables us to jointly learn a probabilistic autoencoder and stochastic differential equations governing the latent dynamics, at a computational cost that is independent of the dataset size and system stiffness. Additionally, our approach offers the flexibility of incorporating physics-informed priors if available. Numerical studies are presented for three challenging test problems, where we demonstrate excellent generalization to unseen parameter combinations and forcings, and significant efficiency gains compared to existing approaches.

Paperid: 902, https://arxiv.org/pdf/2601.08709.pdf

Abstract:
A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the domain-decomposition-inspired additive architecture of FBPINNs, in which local neural networks are defined on subdomains, thereby localizing the network representation. Parallel, subdomain-local quasi-Newton corrections are then constructed on the corresponding local parts of the architecture. A key feature is a novel nonlinear multi-preconditioning mechanism, in which subdomain corrections are optimally combined through the solution of a low-dimensional subspace minimization problem. Numerical experiments indicate that MP-LBFGS can improve convergence speed, as well as model accuracy over standard LBFGS while incurring lower communication overhead.

Paperid: 903, https://arxiv.org/pdf/2601.05889.pdf

Abstract:
In the analysis of complex physical systems, the objective often extends beyond merely computing a numerical solution to capturing the precise crossover between different regimes and extracting parameters containing meaningful information. However, standard numerical solvers and conventional deep learning approaches, such as Physics-Informed Neural Networks (PINNs), typically operate as black boxes that output solution fields without disentangling the solution into its interpretable constituent parts. In this work, we propose GlueNN, a physics-informed learning framework that decomposes the global solution into interpretable, patchwise analytic components. Rather than approximating the solution directly, GlueNN promotes the integration constants of local asymptotic expansions to learnable, scale-dependent coefficient functions. By constraining these coefficients with the differential equation, the network effectively performs regime transition, smoothly interpolating between asymptotic limits without requiring ad hoc boundary matching. We demonstrate that this coefficient-centric approach reproduces accurate global solutions in various examples and thus directly extracts physical information that is not explicitly available through standard numerical integration.

Paperid: 904, https://arxiv.org/pdf/2601.02088.pdf

Abstract:
Orthognathic surgery repositions jaw bones to restore occlusion and enhance facial aesthetics. Accurate simulation of postoperative facial morphology is essential for preoperative planning. However, traditional biomechanical models are computationally expensive, while geometric deep learning approaches often lack interpretability. In this study, we develop and validate a physics-informed geometric deep learning framework named PhysSFI-Net for precise prediction of soft tissue deformation following orthognathic surgery. PhysSFI-Net consists of three components: a hierarchical graph module with craniofacial and surgical plan encoders combined with attention mechanisms to extract skeletal-facial interaction features; a Long Short-Term Memory (LSTM)-based sequential predictor for incremental soft tissue deformation; and a biomechanics-inspired module for high-resolution facial surface reconstruction. Model performance was assessed using point cloud shape error (Hausdorff distance), surface deviation error, and landmark localization error (Euclidean distances of craniomaxillofacial landmarks) between predicted facial shapes and corresponding ground truths. A total of 135 patients who underwent combined orthodontic and orthognathic treatment were included for model training and validation. Quantitative analysis demonstrated that PhysSFI-Net achieved a point cloud shape error of 1.070 +/- 0.088 mm, a surface deviation error of 1.296 +/- 0.349 mm, and a landmark localization error of 2.445 +/- 1.326 mm. Comparative experiments indicated that PhysSFI-Net outperformed the state-of-the-art method ACMT-Net in prediction accuracy. In conclusion, PhysSFI-Net enables interpretable, high-resolution prediction of postoperative facial morphology with superior accuracy, showing strong potential for clinical application in orthognathic surgical planning and simulation.

Paperid: 905, https://arxiv.org/pdf/2512.23761.pdf

Abstract:
Advances in data acquisition and computational methods have accelerated the use of differential equation based modelling for complex systems. Such systems are often described by coupled (or more) variables, yet governing equation is typically available for one variable, while the remaining variable can be accessed only through data. This mismatch between known physics and observed data poses a fundamental challenge for existing physics-informed machine learning approaches, which generally assume either complete knowledge of the governing equations or full data availability across all variables. In this paper, we introduce MUSIC (Multitask Learning Under Sparse and Incomplete Constraints), a sparsity induced multitask neural network framework that integrates partial physical constraints with data-driven learning to recover full-dimensional solutions of coupled systems when physics-constrained and data-informed variables are mutually exclusive. MUSIC employs mesh-free (random) sampling of training data and sparsity regularization, yielding highly compressed models with improved training and evaluation efficiency. We demonstrate that MUSIC accurately learns solutions (shock wave solutions, discontinuous solutions, pattern formation solutions) to complex coupled systems under data-scarce and noisy conditions, consistently outperforming non-sparse formulations. These results highlight MUSIC as a flexible and effective approach for modeling partially observed systems with incomplete physical knowledge.

Paperid: 906, https://arxiv.org/pdf/2512.23726.pdf

Abstract:
The 3D fast silent multi-parametric mapping sequence with zero echo time (MuPa-ZTE) is a novel quantitative MRI (qMRI) acquisition that enables nearly silent scanning by using a 3D phyllotaxis sampling scheme. MuPa-ZTE improves patient comfort and motion robustness, and generates quantitative maps of T1, T2, and proton density using the acquired weighted image series. In this work, we propose a diffusion model-based qMRI mapping method that leverages both a deep generative model and physics-based data consistency to further improve the mapping performance. Furthermore, our method enables additional acquisition acceleration, allowing high-quality qMRI mapping from a fourfold-accelerated MuPa-ZTE scan (approximately 1 minute). Specifically, we trained a denoising diffusion probabilistic model (DDPM) to map MuPa-ZTE image series to qMRI maps, and we incorporated the MuPa-ZTE forward signal model as an explicit data consistency (DC) constraint during inference. We compared our mapping method against a baseline dictionary matching approach and a purely data-driven diffusion model. The diffusion models were trained entirely on synthetic data generated from digital brain phantoms, eliminating the need for large real-scan datasets. We evaluated on synthetic data, a NISM/ISMRM phantom, healthy volunteers, and a patient with brain metastases. The results demonstrated that our method produces 3D qMRI maps with high accuracy, reduced noise and better preservation of structural details. Notably, it generalised well to real scans despite training on synthetic data alone. The combination of the MuPa-ZTE acquisition and our physics-informed diffusion model is termed q3-MuPa, a quick, quiet, and quantitative multi-parametric mapping framework, and our findings highlight its strong clinical potential.

Paperid: 907, https://arxiv.org/pdf/2512.23054.pdf

Abstract:
Millimeter-wave (mmWave) radar enables privacy-preserving, illumination-invariant Human Pose Estimation (HPE). However, current mmWave-based HPE systems face a signal-noise dilemma: Heatmaps retain human reflections but embed environmental clutter, while Point Clouds (PC) suppress noise through aggressive thresholding but discard informative human reflections, limiting robustness across environments and radar configurations. To address this intrinsic bottleneck, we introduce Person Parametric Physics-informed Representation (PPPR), a physics-informed parametric intermediate representation that replaces purely signal-level encodings with human-centric parameterization. PPPR models each human joint as a Gaussian primitive encoding both kinematic properties, which include position, velocity, orientation, and electromagnetic properties, which include scattering intensity and Doppler signature. These parameters enable optimization through a dual-constraint process: kinematic objectives enforce biomechanical consistency to suppress spatial artifacts, while electromagnetic objectives ensure adherence to mmWave propagation physics, decoupling input representations from non-human noise. Experiments across three mmWave-based HPE datasets with four HPE models demonstrate that replacing conventional inputs with PPPR consistently yields substantial accuracy gains. Furthermore, cross-scenes and cross-datasets experiments confirm PPPR's noise decoupling capability: models trained with PPPR maintain stable performance across diverse furniture arrangements and different radar chipsets, demonstrating its promising generalization capability in the challenging cross-dataset settings. Code will be released upon publication.

Paperid: 908, https://arxiv.org/pdf/2512.17612.pdf

Abstract:
High-resolution (HR) quantitative MRI (qMRI) relaxometry provides objective tissue characterization but remains clinically underutilized due to lengthy acquisition times. We propose a physics-informed, self-supervised framework for qMRI super-resolution that uses routinely acquired HR weighted MRI (wMRI) scans as guidance, thus, removing the necessity for HR qMRI ground truth during training. We formulate super-resolution as Bayesian maximum a posteriori inference, minimizing two discrepancies: (1) between HR images synthesized from super-resolved qMRI maps and acquired wMRI guides via forward signal models, and (2) between acquired LR qMRI and downsampled predictions. This physics-informed objective allows the models to learn from clinical wMRI without HR qMRI supervision. To validate the concept, we generate training data by synthesizing wMRI guides from HR qMRI using signal equations, then degrading qMRI resolution via k-space truncation. A deep neural network learns the super-resolution mapping. Ablation experiments demonstrate that T1-weighted images primarily enhance T1 maps, T2-weighted images improve T2 maps, and combined guidance optimally enhances all parameters simultaneously. Validation on independently acquired in-vivo data from a different qMRI sequence confirms cross-qMRI sequence generalizability. Models trained on synthetic data can produce super-resolved maps from a 1-minute acquisition with quality comparable to a 5-minute reference scan, leveraging the scanner-independent nature of relaxometry parameters. By decoupling training from HR qMRI requirement, our framework enables fast qMRI acquisitions enhanced via routine clinical images, offering a practical pathway for integrating quantitative relaxometry into clinical workflows with acceptable additional scan time.

Paperid: 909, https://arxiv.org/pdf/2512.15086.pdf

Abstract:
Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal fields for new initial conditions or forcing functions. Existing architectures such as DeepONet and the Fourier Neural Operator (FNO) show strong empirical performance but often require large training datasets, lack explicit physical structure, and may suffer from instability in their trunk-network features, where mode imbalance or collapse can hinder accurate operator approximation. Motivated by the stability and locality of classical partition-of-unity (PoU) methods, we investigate PoU-based regularization techniques for operator learning and develop a revised formulation of the existing POU--PI--DeepONet framework. The resulting \emph{P}hysics-\emph{i}nformed \emph{P}artition \emph{P}enalty Deep Operator Network (PIP$^{2}$ Net) introduces a simplified and more principled partition penalty that improved the coordinated trunk outputs that leads to more expressiveness without sacrificing the flexibility of DeepONet. We evaluate PIP$^{2}$ Net on three nonlinear PDEs: the viscous Burgers equation, the Allen--Cahn equation, and a diffusion--reaction system. The results show that it consistently outperforms DeepONet, PI-DeepONet, and POU-DeepONet in prediction accuracy and robustness.

Paperid: 910, https://arxiv.org/pdf/2512.10611.pdf

Abstract:
Data center (DC) infrastructure serves as the backbone to support the escalating demand for computing capacity. Traditional design methodologies that blend human expertise with specialized simulation tools scale poorly with the increasing system complexity. Recent studies adopt generative artificial intelligence to design plausible human-centric indoor layouts. However, they do not consider the underlying physics, making them unsuitable for the DC design that sets quantifiable operational objectives and strict physical constraints. To bridge the gap, we propose Phythesis, a novel framework that synergizes large language models (LLMs) and physics-guided evolutionary optimization to automate simulation-ready (SimReady) scene synthesis for energy-efficient DC design. Phythesis employs an iterative bi-level optimization architecture, where (i) the LLM-driven optimization level generates physically plausible three-dimensional layouts and self-criticizes them to refine the scene topology, and (ii) the physics-informed optimization level identifies the optimal asset parameters and selects the best asset combination. Experiments on three generation scales show that Phythesis achieves 57.3% generation success rate increase and 11.5% power usage effectiveness (PUE) improvement, compared with the vanilla LLM-based solution.

Paperid: 911, https://arxiv.org/pdf/2512.04183.pdf

Abstract:
This paper introduces a direct comparative study of Physics-Informed Neural Networks (PINNs) and Long Short-Term Memory (LSTM) networks for adaptive steam temperature control in Heat Recovery Steam Generators (HRSGs), particularly under valve leakage faults. Maintaining precise steam temperature in HRSGs is critical for efficiency and safety, yet traditional control strategies struggle with nonlinear, fault-induced dynamics. Both architectures are designed to adaptively tune the gains of a PI-plus-feedforward control law in real-time. The LSTM controller, a purely data-driven approach, was trained offline on historical operational data, while the PINN controller integrates fundamental thermodynamic laws directly into its online learning process through a physics-based loss function. Their performance was evaluated using a model validated with data from a combined cycle power plant, under normal load changes and a challenging valve leakage fault scenario. Results demonstrate that while the LSTM controller offers significant improvement over conventional methods, its performance degrades under the unseen fault. The PINN controller consistently delivered superior robustness and performance, achieving a 54\% reduction in integral absolute error compared to the LSTM under fault conditions. This study concludes that embedding physical knowledge into data-driven control is essential for developing reliable, fault-tolerant autonomous control systems in complex industrial applications.

Paperid: 912, https://arxiv.org/pdf/2512.03846.pdf

Abstract:
This paper presents a novel fault-tolerant control framework for steam temperature regulation in Heat Recovery Steam Generators (HRSGs) subject to actuator faults. Addressing the critical challenge of valve degradation in superheater spray attemperators, we propose a synergistic architecture comprising three components: (1) a Sliding Mode Observer (SMO) for estimation of unmeasured thermal states, (2) a Physics-Informed Neural Network (PINN) for estimating multiplicative actuator faults using physical laws as constraints, and (3) a one-sided Sliding Mode Controller (SMC) that adapts to the estimated faults while minimizing excessive actuation. The key innovation lies in the framework of closed-loop physics-awareness, where the PINN continuously informs both the observer and controller about fault severity while preserving thermodynamic consistency. Rigorous uniform ultimate boundedness (UUB) is established via Lyapunov analysis under practical assumptions. Validated on real HRSG operational data, the framework demonstrates effective fault adaptation, reduced temperature overshoot, and maintains steam temperature within 1°C of the setpoint under valve effectiveness loss. This work bridges control theory and physics-guided machine learning to deliver a practically deployable solution for power plant resilience, with extensions applicable to thermal systems subject to multiplicative faults.

Paperid: 913, https://arxiv.org/pdf/2512.03196.pdf

Abstract:
Diffusion MRI (dMRI) enables non-invasive assessment of prostate microstructure but conventional metrics such as the Apparent Diffusion Coefficient in multiparametric MRI lack specificity to underlying histology. Integrating dMRI with the compartment-based biophysical VERDICT (Vascular, Extracellular, and Restricted Diffusion for Cytometry in Tumours) framework offers richer microstructural insights, though clinical gradient systems (40-80 mT/m) suffer from poor signal-to-noise ratio (SNR) at stronger diffusion weightings due to prolonged echo times. Ultra-strong gradients (up to 300 mT/m) can mitigate these limitations by improving SNR and contrast-to-noise ratios (CNR) but their adoption has until recently been limited to research environments due to challenges with peripheral nerve stimulation thresholds and gradient non-uniformity. This study investigates whether physics-informed self-supervised VERDICT (ssVERDICT) fitting applied to ultra-strong gradients enhances prostate cancer characterization relative to current clinical acquisitions. We developed enhanced ssVERDICT fitting approaches using dense multilayer perceptron (Dense MLP) and convolutional U-Net architectures, benchmarking them against non-linear least-squares (NLLS) fitting and Diffusion Kurtosis Imaging across clinical- to ultra-strong gradient systems. Dense ssVERDICT at ultra-strong gradient notably outperformed NLLS VERDICT, boosting median CNR by 47%, cutting inter-patient Coefficient of Variation by 52%, and reducing pooled f_ic variation by 50%. Overall, it delivered the highest CNR, the most stable parameter estimates, and the clearest tumour-normal contrast compared with conventional methods and clinical gradient systems. These findings highlight the potential of advanced gradient systems and deep learning-based modelling to improve non-invasive prostate cancer characterization and reduce unnecessary biopsies.

Paperid: 914, https://arxiv.org/pdf/2512.00990.pdf

Abstract:
Faults and operational disturbances in Heat Recovery Steam Generators (HRSGs), such as valve leakage, present significant challenges, disrupting steam temperature regulation and potentially causing efficiency losses, safety risks, and unit shutdowns. Traditional PI controllers often struggle due to inherent system delays, nonlinear dynamics, and static gain limitations. This paper introduces a fault-tolerant temperature control framework by integrating a PI plus feedforward control strategy with Physics-Informed Neural Networks (PINNs). The feedforward component anticipates disturbances, preemptively adjusting control actions, while the PINN adaptively tunes control gains in real-time, embedding thermodynamic constraints to manage varying operating conditions and valve leakage faults. A Lyapunov-based stability analysis confirms the asymptotic convergence of temperature tracking errors under bounded leakage conditions. Simulation results using operational data from the Pareh-Sar combined cycle power plant demonstrate significantly improved response times, reduced temperature deviations, enhanced fault resilience, and smooth gain adjustments. The proposed adaptive, data-driven methodology shows strong potential for industrial deployment, ensuring reliable operation, autonomous fault recovery, and enhanced performance in HRSG systems.

Paperid: 915, https://arxiv.org/pdf/2511.22836.pdf

Abstract:
Serving as an essential prerequisite for modern power system operation, robust state estimation (RSE) could effectively resist noises and outliers in measurements. The emerging neural network (NN) based end-to-end (E2E) learning framework enables real-time application of RSE but cannot strictly enforce the physical constraints involved, potentially yielding solutions that are statistically accurate yet physically inconsistent. To bridge this gap, this work proposes a novel E2E learning based RSE framework, where the RSE problem is innovatively constructed as an explicit differentiable layer of NN for the first time, ensuring physics alignments with rigors. Also, the measurement weights are treated as learnable parameters of NN to enhance estimation robustness. A hybrid loss function is formulated to pursue accurate and physically consistent solutions. To realize the proposed NN structure, the original non-convex RSE problem is specially relaxed. Extensive numerical simulations have been carried out to demonstrate that the proposed framework can significantly improve the SE performance while fulfilling physical consistency on six testing systems, in comparisons to the classical E2E learning based approach and the physics-informed neural network (PINN) approach.

Paperid: 916, https://arxiv.org/pdf/2511.16195.pdf

Abstract:
Model Predictive Control evolved as the state of the art paradigm for safety critical control tasks. Control-as-Inference approaches thereof model the constrained optimization problem as a probabilistic inference problem. The constraints have to be implemented into the inference model. A recently introduced physics-informed Gaussian Process method uses Control-as-Inference with a Gaussian likelihood for state constraint modeling, but lacks guarantees of open-loop constraint satisfaction. We mitigate the lack of guarantees via an additional sampling step using Hamiltonian Monte Carlo sampling in order to obtain safe rollouts of the open-loop dynamics which are then used to obtain an approximation of the truncated normal distribution which has full probability mass in the safe area. We provide formal guarantees of constraint satisfaction while maintaining the ODE structure of the Gaussian Process on a discretized grid. Moreover, we show that we are able to perform optimization of a quadratic cost function by closed form Gaussian Process computations only and introduce the Matérn kernel into the inference model.

Paperid: 917, https://arxiv.org/pdf/2511.16093.pdf

Abstract:
Accurate and efficient thermal dynamics models of permanent magnet synchronous motors are vital to efficient thermal management strategies. Physics-informed methods combine model-based and data-driven methods, offering greater flexibility than model-based methods and superior explainability compared to data-driven methods. Nonetheless, there are still challenges in balancing real-time performance, estimation accuracy, and explainability. This paper presents a hardware-efficient complex neural dynamics model achieved through the linear decoupling, diagonalization, and reparameterization of the state-space model, introducing a novel paradigm for the physics-informed method that offers high explainability and accuracy in electric motor temperature estimation tasks. We validate this physics-informed method on an NVIDIA A800 GPU using the JAX machine learning framework, parallel prefix sum algorithm, and Compute Unified Device Architecture (CUDA) platform. We demonstrate its superior estimation accuracy and parallelizable hardware acceleration capabilities through experimental evaluation on a real electric motor.

Paperid: 918, https://arxiv.org/pdf/2511.15182.pdf

Abstract:
Efficient and sustainable maritime transport increasingly depends on reliable forecasting and adaptive routing, yet operational adoption remains difficult due to forecast latencies and the need for human judgment in rapid decision-making under changing ocean conditions. We introduce SWR-Viz, an AI-assisted visual analytics framework that combines a physics-informed Fourier Neural Operator wave forecast model with SIMROUTE-based routing and interactive emissions analytics. The framework generates near-term forecasts directly from current conditions, supports data assimilation with sparse observations, and enables rapid exploration of what-if routing scenarios. We evaluate the forecast models and SWR-Viz framework along key shipping corridors in the Japan Coast and Gulf of Mexico, showing both improved forecast stability and realistic routing outcomes comparable to ground-truth reanalysis wave products. Expert feedback highlights the usability of SWR-Viz, its ability to isolate voyage segments with high emission reduction potential, and its value as a practical decision-support system. More broadly, this work illustrates how lightweight AI forecasting can be integrated with interactive visual analytics to support human-centered decision-making in complex geospatial and environmental domains.

Paperid: 919, https://arxiv.org/pdf/2511.14925.pdf

Abstract:
Nonlinear physical phenomena often show complex multiscale interactions; motivated by the principles of multiscale modeling in scientific computing, we propose PAS-Net, a physics-informed Adaptive-Scale Deep Operator Network for learning solution operators of nonlinear and singularly perturbed evolution PDEs with small parameters and localized features. Specifically, PAS-Net augments the trunk input in the physics informed Deep Operator Network (PI-DeepONet) with a prescribed (or learnable) locally rescaled coordinate transformation centered at reference points. This addition introduces a multiscale feature embedding that acts as an architecture-independent preconditioner which improves the representation of localized, stiff, and multiscale dynamics. From an optimization perspective, the adaptive-scale embedding in PAS-Net modifies the geometry of the Neural Tangent Kernel (NTK) associated with the neural network by increasing its smallest eigenvalue, which in turn improves spectral conditioning and accelerates gradient-based convergence. We further show that this adaptive-scale mechanism explicitly accelerates neural network training in approximating functions with steep transitions and strong asymptotic behavior, and we provide a rigorous proof of this function-approximation result within the finite-dimensional NTK matrix framework. We test the proposed PAS-Net on three different problems: (i) the one-dimensional viscous Burgers equation, (ii) a nonlinear diffusion-reaction system with sharp spatial gradients, and (iii) a two-dimensional eikonal equation. The numerical results show that PAS-Net consistently achieves higher accuracy and faster convergence than the standard DeepONet and PI-DeepONet models under a similar training cost.

Paperid: 920, https://arxiv.org/pdf/2511.14348.pdf

Abstract:
Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, despite their foundational role, the hidden irreversibility implied by the Second Law of Thermodynamics is often neglected during training, leading to unphysical solutions or even training failures in conventional PINNs. In this paper, we identify this critical gap and introduce a simple, generalized, yet robust irreversibility-regularized strategy that enforces hidden physical laws as soft constraints during training. This approach ensures that the learned solutions consistently respect the intrinsic one-way nature of irreversible physical processes. Across a wide range of benchmarks spanning traveling wave propagation, steady combustion, ice melting, corrosion evolution, and crack propagation, we demonstrate that our regularization scheme reduces predictive errors by more than an order of magnitude, while requiring only minimal modification to existing PINN frameworks. We believe that the proposed framework is broadly applicable to a wide class of PDE-governed physical systems and will have significant impact within the scientific machine learning community.

Paperid: 921, https://arxiv.org/pdf/2511.12512.pdf

Abstract:
Physics-informed learning for PDEs is surging across scientific computing and industrial simulation, yet prevailing methods face spectral bias, residual-data imbalance, and weak extrapolation. We introduce a representation-level spectral remodeling xLSTM-PINN that combines gated-memory multiscale feature extraction with adaptive residual-data weighting to curb spectral bias and strengthen extrapolation. Across four benchmarks, we integrate gated cross-scale memory, a staged frequency curriculum, and adaptive residual reweighting, and verify with analytic references and extrapolation tests, achieving markedly lower spectral error and RMSE and a broader stable learning-rate window. Frequency-domain benchmarks show raised high-frequency kernel weights and a right-shifted resolvable bandwidth, shorter high-k error decay and time-to-threshold, and narrower error bands with lower MSE, RMSE, MAE, and MaxAE. Compared with the baseline PINN, we reduce MSE, RMSE, MAE, and MaxAE across all four benchmarks and deliver cleaner boundary transitions with attenuated high-frequency ripples in both frequency and field maps. This work suppresses spectral bias, widens the resolvable band and shortens the high-k time-to-threshold under the same budget, and without altering AD or physics losses improves accuracy, reproducibility, and transferability.

Paperid: 922, https://arxiv.org/pdf/2511.10878.pdf

Abstract:
Time-efficient estimation of muscle activations and forces across multi-joint systems is critical for clinical assessment and assistive device control. However, conventional approaches are computationally expensive and lack a high-quality labeled dataset for multi-joint applications. To address these challenges, we propose a physics-informed deep learning framework that estimates muscle activations and forces directly from kinematics. The framework employs a novel Multi-Joint Cross-Attention (MJCA) module with Bidirectional Gated Recurrent Unit (BiGRU) layers to capture inter-joint coordination, enabling each joint to adaptively integrate motion information from others. By embedding multi-joint dynamics, inter-joint coupling, and external force interactions into the loss function, our Physics-Informed MJCA-BiGRU (PI-MJCA-BiGRU) delivers physiologically consistent predictions without labeled data while enabling time-efficient inference. Experimental validation on two datasets demonstrates that PI-MJCA-BiGRU achieves performance comparable to conventional supervised methods without requiring ground-truth labels, while the MJCA module significantly enhances inter-joint coordination modeling compared to other baseline architectures.

Paperid: 923, https://arxiv.org/pdf/2511.08831.pdf

Abstract:
In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems -- especially in aerospace -- this region cannot be determined a priori and is often challenging to compute. One of the most common methods for computing the stability region is to identify a Lyapunov function. A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive, which provides a sufficient condition for stability and characterizes an estimated stability region. However, existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations. In this work, we present a new physics-informed machine learning method of characterizing an estimated stability region by inferring a Lyapunov function from system trajectory data that treats the dynamical system as a black box and does not require explicit knowledge of the system governing equations. In our presented Lyapunov function Inference method (LyapInf), we propose a quadratic form for the unknown Lyapunov function and fit the unknown quadratic operator to system trajectory data by minimizing the average residual of the Zubov equation, a first-order partial differential equation whose solution yields a Lyapunov function. The inferred quadratic Lyapunov function can then characterize an ellipsoidal estimate of the stability region. Numerical results on benchmark examples demonstrate that our physics-informed stability analysis method successfully characterizes a near-maximal ellipsoid of the system stability region associated with the inferred Lyapunov function without requiring knowledge of the system governing equations.

Paperid: 924, https://arxiv.org/pdf/2511.06614.pdf

Abstract:
Spiking neural networks (SNNs) offer biologically inspired computation but remain underexplored for continuous regression tasks in scientific machine learning. In this work, we introduce and systematically evaluate Quadratic Integrate-and-Fire (QIF) neurons as an alternative to the conventional Leaky Integrate-and-Fire (LIF) model in both directly trained SNNs and ANN-to-SNN conversion frameworks. The QIF neuron exhibits smooth and differentiable spiking dynamics, enabling gradient-based training and stable optimization within architectures such as multilayer perceptrons (MLPs), Deep Operator Networks (DeepONets), and Physics-Informed Neural Networks (PINNs). Across benchmarks on function approximation, operator learning, and partial differential equation (PDE) solving, QIF-based networks yield smoother, more accurate, and more stable predictions than their LIF counterparts, which suffer from discontinuous time-step responses and jagged activation surfaces. These results position the QIF neuron as a computational bridge between spiking and continuous-valued deep learning, advancing the integration of neuroscience-inspired dynamics into physics-informed and operator-learning frameworks.

Paperid: 925, https://arxiv.org/pdf/2511.05879.pdf

Abstract:
Green hydrogen production via polymer electrolyte membrane (PEM) water electrolysis is pivotal for energy transition, yet hydrogen crossover through membranes threatens safety and economic viability-approaching explosive limits (4 mol% H$_2$ in O$_2$) while reducing Faradaic efficiency by 2.5%. Current physics-based models require extensive calibration and computational resources that preclude real-time implementation, while purely data-driven approaches fail to extrapolate beyond training conditions-critical for dynamic electrolyzer operation. Here we present the first application of physics-informed neural networks (PINNs) for hydrogen crossover prediction, integrating mass conservation, Fick's diffusion law, and Henry's solubility law within a compact architecture (17,793 parameters). Validated across six membranes under industrially relevant conditions (0.05-5.0 A/cm$^2$, 1-200 bar, 25-85°C), our PINN achieves exceptional accuracy (R$^2$ = 99.84%, RMSE = 0.0348%) with sub-millisecond inference times suitable for real-time control. Remarkably, the model maintains R$^2$ > 86% when predicting crossover at pressures 2.5x beyond training range-substantially outperforming pure neural networks (R$^2$ = 43.4%). The hardware-agnostic deployment, from desktop CPUs to edge devices (Raspberry Pi 4), enables distributed safety monitoring essential for gigawatt-scale installations. By bridging physical rigor and computational efficiency, this work establishes a new paradigm for real-time electrolyzer monitoring, accelerating deployment of safe, efficient green hydrogen infrastructure crucial for net-zero emissions targets.

Paperid: 926, https://arxiv.org/pdf/2511.04490.pdf

Abstract:
Training physics informed neural networks PINNs for hyperbolic conservation laws near the inviscid limit presents considerable difficulties because strong form residuals become ill posed at shock discontinuities, while small viscosity regularization introduces narrow boundary layers that exacerbate spectral bias. To address these issues this paper proposes a novel two stage adaptive lifting PINN, a lifting based framework designed to mitigate such challenges without requiring a priori knowledge of the interface geometry. The key idea is to augment the physical coordinates by introducing a learned auxiliary field generated through r adaptive coordinate transformations. Theoretically we first derive an a posteriori L2 error estimate to quantify how training difficulty depends on viscosity. Secondly we provide a statistical interpretation revealing that embedded sampling induces variance reduction analogous to importance sampling. Finally we perform an NTK and gradient flow analysis, demonstrating that input augmentation improves conditioning and accelerates residual decay. Supported by these insights our numerical experiments show accelerated and more stable convergence as well as accurate reconstructions near discontinuities.

Paperid: 927, https://arxiv.org/pdf/2510.25648.pdf

Abstract:
Estimating subsurface dielectric properties is essential for applications ranging from environmental surveys of soils to nondestructive evaluation of concrete in infrastructure. Conventional wave inversion methods typically assume few discrete homogeneous layers and require dense measurements or strong prior knowledge of material boundaries, limiting scalability and accuracy in realistic settings where properties vary continuously. We present a physics informed machine learning framework that reconstructs subsurface permittivity as a fully neural, continuous function of depth, trained to satisfy both measurement data and Maxwells equations. We validate the framework with both simulations and custom built radar experiments on multilayered natural materials. Results show close agreement with in-situ permittivity measurements (R^2=0.93), with sensitivity to even subtle variations (Delta eps_r=2). Parametric analysis reveals that accurate profiles can be recovered with as few as three strategically placed sensors in two layer systems. This approach reframes subsurface inversion from boundary-driven to continuous property estimation, enabling accurate characterization of smooth permittivity variations and advancing electromagnetic imaging using low cost radar systems.

Paperid: 928, https://arxiv.org/pdf/2510.23999.pdf

Abstract:
We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs) which allows for sampling based on an arbitrary problem-specific heuristic which may depend on the network and its gradients. In particular we focus our analysis on the Allen-Cahn equations, attempting to accurately resolve the characteristic interfacial regions using a PINN without any post-hoc resampling. In experiments, we show the effectiveness of these methods over residual-adaptive frameworks.

Paperid: 929, https://arxiv.org/pdf/2510.22848.pdf

Abstract:
Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

Paperid: 930, https://arxiv.org/pdf/2510.21262.pdf

Abstract:
Recent advances in Scientific Machine Learning have shown that second-order methods can enhance the training of Physics-Informed Neural Networks (PINNs), making them a suitable alternative to traditional numerical methods for Partial Differential Equations (PDEs). However, second-order methods induce large memory requirements, making them scale poorly with the model size. In this paper, we define a local Mixture of Experts (MoE) combining the parameter-efficiency of ensemble models and sparse coding to enable the use of second-order training. Our model -- \textsc{PINN Balls} -- also features a fully learnable domain decomposition structure, achieved through the use of Adversarial Adaptive Sampling (AAS), which adapts the DD to the PDE and its domain. \textsc{PINN Balls} achieves better accuracy than the state-of-the-art in scientific machine learning, while maintaining invaluable scalability properties and drawing from a sound theoretical background.

Paperid: 931, https://arxiv.org/pdf/2510.21018.pdf

Abstract:
Fatigue behaviors of metal components by laser fusion suffer from scattering due to random geometrical defects (e.g., porosity, lack of fusion). Monitoring fatigue crack initiation and growth is critical, especially for laser-fused components with significant inherent fatigue scattering. Conventional statistics-based curve-fitting fatigue models have difficulty incorporating significant scattering in their fatigue life due to the random geometrical defects. A scattering-informed predictive method is needed for laser-fused materials' crack size and growth. Current data-driven machine learning could circumvent the issue of deterministic modeling, but results in a black-box function that lacks interpretability. To address these challenges, this study explores a novel nondimensionalized physics-informed machine learning (PIML) model to predict fatigue crack growth of laser-fused SS-316L by integrating fatigue laws and constraints with small data to ensure a realistic and interpretable prediction. Resonance process signature data were leveraged with Paris's law to train the PIML model without experimental crack growth data. The results show that Paris's law constants can be learned with good similarity to comparable data from the literature, and the crack growth rate can be predicted to compute crack sizes.

Paperid: 932, https://arxiv.org/pdf/2510.13677.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) embed the partial differential equations (PDEs) governing the system under study directly into the training of Neural Networks, ensuring solutions that respect physical laws. While effective for single-system problems, standard PINNs scale poorly to datasets containing many realizations of the same underlying physics with varying parameters. To address this limitation, we present a complementary approach by including auxiliary physically-redundant information in loss (APRIL), i.e. augment the standard supervised output-target loss with auxiliary terms which exploit exact physical redundancy relations among outputs. We mathematically demonstrate that these terms preserve the true physical minimum while reshaping the loss landscape, improving convergence toward physically consistent solutions. As a proof-of-concept, we benchmark APRIL on a fully-connected neural network for gravitational wave (GW) parameter estimation (PE). We use simulated, noise-free compact binary coalescence (CBC) signals, focusing on inspiral-frequency waveforms to recover the chirp mass $\mathcal{M}$, the total mass $M_\mathrm{tot}$, and symmetric mass ratio $η$ of the binary. In this controlled setting, we show that APRIL achieves up to an order-of-magnitude improvement in test accuracy, especially for parameters that are otherwise difficult to learn. This method provides physically consistent learning for large multi-system datasets and is well suited for future GW analyses involving realistic noise and broader parameter ranges.

Paperid: 933, https://arxiv.org/pdf/2510.13461.pdf

Abstract:
Accurate prediction of vehicle collision dynamics is crucial for advanced safety systems and post-impact control applications, yet existing methods face inherent trade-offs among computational efficiency, prediction accuracy, and data requirements. This paper proposes a dual Physics-Informed Neural Network framework addressing these challenges through two complementary networks. The first network integrates Gaussian Mixture Models with PINN architecture to learn impact force distributions from finite element analysis data while enforcing momentum conservation and energy consistency constraints. The second network employs an adaptive PINN with dynamic constraint weighting to predict post-collision vehicle dynamics, featuring an adaptive physics guard layer that prevents unrealistic predictions whil e preserving data-driven learning capabilities. The framework incorporates uncertainty quantification through time-varying parameters and enables rapid adaptation via fine-tuning strategies. Validation demonstrates significant improvements: the impact force model achieves relative errors below 15.0% for force prediction on finite element analysis (FEA) datasets, while the vehicle dynamics model reduces average trajectory prediction error by 63.6% compared to traditional four-degree-of-freedom models in scaled vehicle experiments. The integrated system maintains millisecond-level computational efficiency suitable for real-time applications while providing probabilistic confidence bounds essential for safety-critical control. Comprehensive validation through FEA simulation, dynamic modeling, and scaled vehicle experiments confirms the framework's effectiveness for Precision Immobilization Technique scenarios and general collision dynamics prediction.

Paperid: 934, https://arxiv.org/pdf/2508.17687.pdf

Abstract:
Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis remains limited, especially regarding convergence guarantees. This work develops a general optimisation framework for energy minimisation problems arising from linear self-adjoint elliptic PDEs, formulated over nonlinear but analytically tractable approximation spaces. The framework accommodates a natural split between linear and nonlinear parameters and supports hybrid optimisation strategies: linear variables are updated via linear solves or steepest descent, while nonlinear variables are handled using constrained projected descent. We establish both local and global convergence of the resulting algorithm under modular structural assumptions on the discrete energy functional, including differentiability, boundedness, regularity, and directional convexity. These assumptions are stated in an abstract form, allowing the framework to apply to a broad class of nonlinear approximation manifolds. In a companion paper [Magueresse, Badia (2025, arXiv:2508.17705)], we introduce a concrete instance of such a space based on overlapping free-knot tensor-product B-splines, which satisfies the required assumptions and enables geometrically adaptive solvers with rigorous convergence guarantees.

Paperid: 935, https://arxiv.org/pdf/2508.10126.pdf

Abstract:
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors. Specifically, we use the $\star_{\boldsymbol{M}}$-product framework for tensor decompositions which we demonstrate offers excellent compression compared to matrix-based methods and can be implemented in a computationally efficient manner. We show how the proposed approach is connected to the traditional DMD and physics-informed DMD frameworks. We give a computational framework for computing the tensor-based DMD and detail the computational costs. We also give a randomized algorithm that enables efficient $\star_{\boldsymbol{M}}$-DMD computations in the streaming setting. The numerical results show that the proposed method achieves equal or better accuracy for the same storage compared to the standard DMD on these examples and is more efficient to compute.

Paperid: 936, https://arxiv.org/pdf/2508.08935.pdf

Abstract:
Physics-informed neural networks (PINNs) have attracted considerable attention for their ability to integrate partial differential equation priors into deep learning frameworks; however, they often exhibit limited predictive accuracy when applied to complex problems. To address this issue, we propose LNN-PINN, a physics-informed neural network framework that incorporates a liquid residual gating architecture while preserving the original physics modeling and optimization pipeline to improve predictive accuracy. The method introduces a lightweight gating mechanism solely within the hidden-layer mapping, keeping the sampling strategy, loss composition, and hyperparameter settings unchanged to ensure that improvements arise purely from architectural refinement. Across four benchmark problems, LNN-PINN consistently reduced RMSE and MAE under identical training conditions, with absolute error plots further confirming its accuracy gains. Moreover, the framework demonstrates strong adaptability and stability across varying dimensions, boundary conditions, and operator characteristics. In summary, LNN-PINN offers a concise and effective architectural enhancement for improving the predictive accuracy of physics-informed neural networks in complex scientific and engineering problems.

Paperid: 937, https://arxiv.org/pdf/2508.08114.pdf

Abstract:
Microwave Tomography (MWT) aims to reconstruct the dielectric properties of tissues from measured scattered electromagnetic fields. This inverse problem is highly nonlinear and ill-posed, posing significant challenges for conventional optimization-based methods, which, despite being grounded in physical models, often fail to recover fine structural details. Recent deep learning strategies, including end-to-end and post-processing networks, have improved reconstruction quality but typically require large paired training datasets and may struggle to generalize. To overcome these limitations, we propose a physics-informed hybrid framework that integrates diffusion models as learned regularization within a data-consistency-driven variational scheme. Specifically, we introduce Single-Step Diffusion Regularization (SSD-Reg), a novel approach that embeds diffusion priors into the iterative reconstruction process, enabling the recovery of complex anatomical structures without the need for paired data. SSD-Reg maintains fidelity to both the governing physics and learned structural distributions, improving accuracy, stability, and robustness. Extensive experiments demonstrate that SSD-Reg, implemented as a Plug-and-Play (PnP) module, provides a flexible and effective solution for tackling the ill-posedness inherent in functional image reconstruction.

Paperid: 938, https://arxiv.org/pdf/2508.07994.pdf

Abstract:
Rigorous error estimation is a fundamental topic in numerical analysis. With the increasing use of physics-informed neural networks (PINNs) for solving partial differential equations, several approaches have been developed to quantify the associated prediction error. In this work, we build upon a semigroup-based framework previously introduced by the authors for estimating the PINN error. While this estimator has so far been limited to academic examples - due to the need to compute quantities related to input-to-state stability - we extend its applicability to a significantly broader class of problems. This is accomplished by modifying the error bound and proposing numerical strategies to approximate the required stability parameters. The extended framework enables the certification of PINN predictions in more realistic scenarios, as demonstrated by a numerical study of Stokes flow around a cylinder.

Paperid: 939, https://arxiv.org/pdf/2508.06634.pdf

Abstract:
Driven by recent advances in sensing and computing, deep reinforcement learning (DRL) technologies have shown great potential for addressing distribution system restoration (DSR) under uncertainty. However, their data-intensive nature and reliance on the Markov Decision Process (MDP) assumption limit their ability to handle scenarios that require long-term temporal dependencies or few-shot and zero-shot decision making. Emerging Decision Transformers (DTs), which leverage causal transformers for sequence modeling in DRL tasks, offer a promising alternative. However, their reliance on return-to-go (RTG) cloning and limited generalization capacity restricts their effectiveness in dynamic power system environments. To address these challenges, we introduce an innovative Dual-Head Physics-informed Graph Decision Transformer (DH-PGDT) that integrates physical modeling, structural reasoning, and subgoal-based guidance to enable scalable and robust DSR even in zero-shot or few-shot scenarios. DH-PGDT features a dual-head physics-informed causal transformer architecture comprising Guidance Head, which generates subgoal representations, and Action Head, which uses these subgoals to generate actions independently of RTG. It also incorporates an operational constraint-aware graph reasoning module that encodes power system topology and operational constraints to generate a confidence-weighted action vector for refining DT trajectories. This design effectively improves generalization and enables robust adaptation to unseen scenarios. While this work focuses on DSR, the underlying computing model of the proposed PGDT is broadly applicable to sequential decision making across various power system operations and other complex engineering domains.

Paperid: 940, https://arxiv.org/pdf/2508.03965.pdf

Abstract:
This paper introduces BubbleONet, an operator learning model designed to map pressure profiles from an input function space to corresponding bubble radius responses. BubbleONet is built upon the physics-informed deep operator network (PI-DeepONet) framework, leveraging DeepONet's powerful universal approximation capabilities for operator learning alongside the robust physical fidelity provided by the physics-informed neural networks. To mitigate the inherent spectral bias in deep learning, BubbleONet integrates the Rowdy adaptive activation function, enabling improved representation of high-frequency features. The model is evaluated across various scenarios, including: (1) Rayleigh-Plesset equation based bubble dynamics with a single initial radius, (2) Keller-Miksis equation based bubble dynamics with a single initial radius, and (3) Keller-Miksis equation based bubble dynamics with multiple initial radii. Moreover, the performance of single-step versus two-step training techniques for BubbleONet is investigated. The results demonstrate that BubbleONet serves as a promising surrogate model for simulating bubble dynamics, offering a computationally efficient alternative to traditional numerical solvers.

Paperid: 941, https://arxiv.org/pdf/2508.01463.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful class of mesh-free numerical methods for solving partial differential equations (PDEs), particularly those involving complex geometries. In this work, we present an innovative Extended Interface Physics-Informed Neural Network (XI-PINN) framework specifically designed to solve parabolic moving interface problems. The proposed approach incorporates a level set function to characterize the interface, which can be obtained either directly or through a neural network solution. We conduct a rigorous a priori error analysis for the XI-PINN method, providing error bounds for the approximation. Leveraging the Neural Tangent Kernel (NTK) theory, we further demonstrate that XI-PINN achieves a faster training convergence rate compared to conventional PINN approaches. The method's versatility is further demonstrated by its application to the Oseen equations. We perform comprehensive numerical experiments to validate the efficacy, accuracy, and robustness of the proposed framework.

Paperid: 942, https://arxiv.org/pdf/2508.00918.pdf

Abstract:
Recent developments in AI techniques for space applications mirror the success achieved in terrestrial applications. Machine learning, which excels in data rich environments, is particularly well suited to space-based computer vision applications, such as space optical attitude sensing. Of these sensors, digital sun sensors (DSS) are one of the most common and important sensors for spacecraft attitude determination. The main challenge in using the DSS for attitude estimation are sensor errors, which limit the overall achievable estimation accuracy. However, the traditional sun sensor calibration process is costly, slow, labor-intensive and inefficient. These limitations motivate the use of AI techniques to enable more accurate and efficient DSS calibration. The objective of this work is to develop an end-to-end predictive calibration methodology for digital sun sensors to solve 2-axis state estimates utilizing a sparse submanifold convolutional neural network (SSCNN). We find that the proposed framework can achieve state-of-the-art performance on synthetic data with a mean accuracy of 0.005Â° for the two sun angle estimates. Furthermore, the model is highly capable of implicitly learning complex noise patterns and handling mixed noise types, thereby greatly improving the model robustness and accuracy to real-world applications. The main contributions of this work are: (1) the first application (to our knowledge) of a CNN regression model to the problem of DSS predictive calibration, (2) the introduction of a fused end-to-end training approach for DSS calibration, (3) the creation of a publicly available physics-informed synthetic dataset and simulation for DSS training images, and (4) the evaluation of the performance of the deep learning approach for various mask configurations.

Paperid: 943, https://arxiv.org/pdf/2507.22959.pdf

Abstract:
The field of scientific machine learning, which originally utilized multilayer perceptrons (MLPs), is increasingly adopting Kolmogorov-Arnold Networks (KANs) for data encoding. This shift is driven by the limitations of MLPs, including poor interpretability, fixed activation functions, and difficulty capturing localized or high-frequency features. KANs address these issues with enhanced interpretability and flexibility, enabling more efficient modeling of complex nonlinear interactions and effectively overcoming the constraints associated with conventional MLP architectures. This review categorizes recent progress in KAN-based models across three distinct perspectives: (i) data-driven learning, (ii) physics-informed modeling, and (iii) deep operator learning. Each perspective is examined through the lens of architectural design, training strategies, application efficacy, and comparative evaluation against MLP-based counterparts. By benchmarking KANs against MLPs, we highlight consistent improvements in accuracy, convergence, and spectral representation, clarifying KANs' advantages in capturing complex dynamics while learning more effectively. Finally, this review identifies critical challenges and open research questions in KAN development, particularly regarding computational efficiency, theoretical guarantees, hyperparameter tuning, and algorithm complexity. We also outline future research directions aimed at improving the robustness, scalability, and physical consistency of KAN-based frameworks.

Paperid: 944, https://arxiv.org/pdf/2507.18346.pdf

Abstract:
HyperDeepONets were introduced in Lee, Cho and Hwang [ICLR, 2023] as an alternative architecture for operator learning, in which a hypernetwork generates the weights for the trunk net of a DeepONet. While this improves expressivity, it incurs high memory and computational costs due to the large number of output parameters required. In this work we introduce, in the physics-informed machine learning setting, a variation, PI-LoRA-HyperDeepONets, which leverage low-rank adaptation (LoRA) to reduce complexity by decomposing the hypernetwork's output layer weight matrix into two smaller low-rank matrices. This reduces the number of trainable parameters while introducing an extra regularization of the trunk networks' weights. Through extensive experiments on both ordinary and partial differential equations we show that PI-LoRA-HyperDeepONets achieve up to 70\% reduction in parameters and consistently outperform regular HyperDeepONets in terms of predictive accuracy and generalization.

Paperid: 945, https://arxiv.org/pdf/2507.15678.pdf

Abstract:
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data, common methods often ignore this underlying geometric fabric. Physics-informed neural networks, for instance, can violate fundamental physical principles, leading to predictions that are unstable over long periods, particularly for high-dimensional and chaotic systems. Here, we introduce \textit{Geometric Hamiltonian Neural Networks (GeoHNN)}, a framework that learns dynamics by explicitly encoding the geometric priors inherent to physical laws. Our approach enforces two fundamental structures: the Riemannian geometry of inertia, by parameterizing inertia matrices in their natural mathematical space of symmetric positive-definite matrices, and the symplectic geometry of phase space, using a constrained autoencoder to ensure the preservation of phase space volume in a reduced latent space. We demonstrate through experiments on systems ranging from coupled oscillators to high-dimensional deformable objects that GeoHNN significantly outperforms existing models. It achieves superior long-term stability, accuracy, and energy conservation, confirming that embedding the geometry of physics is not just a theoretical appeal but a practical necessity for creating robust and generalizable models of the physical world.

Paperid: 946, https://arxiv.org/pdf/2507.14341.pdf

Abstract:
We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such systems, only a few variables contribute nonlinearly to the dynamics, while the majority influence the equations linearly. MENO exploits this property by decomposing the system into two components: the low-dimensional nonlinear part is modeled using conventional neural operators, while the linear time-varying subsystem is integrated using a novel neural matrix exponential formulation. This approach combines the exact solution of linear time-invariant systems with learnable, time-dependent graph-based corrections applied to the linear operators. Unlike black-box or soft-constrained physics-informed (PI) models, MENO embeds the governing equations directly into its architecture, ensuring physical consistency (e.g., steady states), improved robustness, and more efficient training. We validate MENO on three complex thermochemical systems: the POLLU atmospheric chemistry model, an oxygen mixture in thermochemical nonequilibrium, and a collisional-radiative argon plasma in one- and two-dimensional shock-tube simulations. MENO achieves relative errors below 2% in trained zero-dimensional settings and maintains good accuracy in extrapolatory multidimensional regimes. It also delivers substantial computational speedups, achieving up to 4 800$\times$ on GPU and 185$\times$ on CPU compared to standard implicit ODE solvers. Although intrusive by design, MENO's physics-based architecture enables superior generalization and reliability, offering a scalable path for real-time simulation of stiff reactive systems.

Paperid: 947, https://arxiv.org/pdf/2507.11962.pdf

Abstract:
Training deep neural networks for scientific computing remains computationally expensive due to the slow formation of diverse feature representations in early training stages. Recent studies identify a staircase phenomenon in training dynamics, where loss decreases are closely correlated with increases in $\varepsilon$-rank, reflecting the effective number of linearly independent neuron functions. Motivated by this observation, this work proposes a structured first-layer initialization (SFLI) pre-training method to enhance the diversity of neural features at initialization by constructing $\varepsilon$-linearly independent neurons in the input layer. We present systematic initialization schemes compatible with various activation functions and integrate the strategy into multiple neural architectures, including modified multi-layer perceptrons and physics-informed residual adaptive networks. Extensive numerical experiments on function approximation and PDE benchmarks, demonstrate that SFLI significantly improves the initial $\varepsilon$-rank, accelerates convergence, mitigates spectral bias, and enhances prediction accuracy. With the help of SILP, we only need to add one line of code to conventional existing algorithms.

Paperid: 948, https://arxiv.org/pdf/2507.08124.pdf

Abstract:
Traditional physics-informed neural networks (PINNs) do not guarantee strict constraint satisfaction. This is problematic in engineering systems where minor violations of governing laws can degrade the reliability and consistency of model predictions. In this work, we introduce KKT-Hardnet, a neural network architecture that enforces linear and nonlinear equality and inequality constraints up to machine precision. It leverages a differentiable projection onto the feasible region by solving Karush-Kuhn-Tucker (KKT) conditions of a distance minimization problem. Furthermore, we reformulate the nonlinear KKT conditions via a log-exponential transformation to construct a sparse system with linear and exponential terms. We apply KKT-Hardnet to nonconvex pooling problem and a real-world chemical process simulation. Compared to multilayer perceptrons and PINNs, KKT-Hardnet achieves strict constraint satisfaction. It also circumvents the need to balance data and physics residuals in PINN training. This enables the integration of domain knowledge into machine learning towards reliable hybrid modeling of complex systems.

Paperid: 949, https://arxiv.org/pdf/2507.06752.pdf

Abstract:
Machine learning has emerged as a transformative tool for solving differential equations (DEs), yet prevailing methodologies remain constrained by dual limitations: data-driven methods demand costly labeled datasets while model-driven techniques face efficiency-accuracy trade-offs. We present the Mathematical Artificial Data (MAD) framework, a new paradigm that integrates physical laws with data-driven learning to facilitate large-scale operator discovery. By exploiting DEs' intrinsic mathematical structure to generate physics-embedded analytical solutions and associated synthetic data, MAD fundamentally eliminates dependence on experimental or simulated training data. This enables computationally efficient operator learning across multi-parameter systems while maintaining mathematical rigor. Through numerical demonstrations spanning 2D parametric problems where both the boundary values and source term are functions, we showcase MAD's generalizability and superior efficiency/accuracy across various DE scenarios. This physics-embedded-data-driven framework and its capacity to handle complex parameter spaces gives it the potential to become a universal paradigm for physics-informed machine intelligence in scientific computing.

Paperid: 950, https://arxiv.org/pdf/2507.03521.pdf

Abstract:
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical techniques such as finite elements and finite differences. In this paper, we introduce a new class of Physics-Informed Neural Networks (PINNs) trained using discontinuous Galerkin finite element methods. Unlike standard collocation-based PINNs that rely on pointwise gradient evaluations and Monte Carlo quadrature, our approach computes the loss functional using finite element interpolation and integration. This avoids costly pointwise derivative computations, particularly advantageous for elliptic PDEs requiring second-order derivatives, and inherits key stability and accuracy benefits from the finite element framework. We present a convergence analysis based on variational arguments and support our theoretical findings with numerical experiments that demonstrate improved efficiency and robustness.

Paperid: 951, https://arxiv.org/pdf/2507.01841.pdf

Abstract:
In this paper, we propose SubLoRA, a rank determination method for Low-Rank Adaptation (LoRA) based on submodular function maximization. In contrast to prior approaches, such as AdaLoRA, that rely on first-order (linearized) approximations of the loss function, SubLoRA utilizes second-order information to capture the potentially complex loss landscape by incorporating the Hessian matrix. We show that the linearization becomes inaccurate and ill-conditioned when the LoRA parameters have been well optimized, motivating the need for a more reliable and nuanced second-order formulation. To this end, we reformulate the rank determination problem as a combinatorial optimization problem with a quadratic objective. However, solving this problem exactly is NP-hard in general. To overcome the computational challenge, we introduce a submodular function maximization framework and devise a greedy algorithm with approximation guarantees. We derive a sufficient and necessary condition under which the rank-determination objective becomes submodular, and construct a closed-form projection of the Hessian matrix that satisfies this condition while maintaining computational efficiency. Our method combines solid theoretical foundations, second-order accuracy, and practical computational efficiency. We further extend SubLoRA to a joint optimization setting, alternating between LoRA parameter updates and rank determination under a rank budget constraint. Extensive experiments on fine-tuning physics-informed neural networks (PINNs) for solving partial differential equations (PDEs) demonstrate the effectiveness of our approach. Results show that SubLoRA outperforms existing methods in both rank determination and joint training performance.

Paperid: 952, https://arxiv.org/pdf/2506.23024.pdf

Abstract:
Physics-informed neural networks (PINNs) offer a flexible way to solve partial differential equations (PDEs) with machine learning, yet they still fall well short of the machine-precision accuracy many scientific tasks demand. In this work, we investigate whether the precision ceiling comes from the ill-conditioning of the PDEs or from the typical multi-layer perceptron (MLP) architecture. We introduce the Barycentric Weight Layer (BWLer), which models the PDE solution through barycentric polynomial interpolation. A BWLer can be added on top of an existing MLP (a BWLer-hat) or replace it completely (explicit BWLer), cleanly separating how we represent the solution from how we take derivatives for the PDE loss. Using BWLer, we identify fundamental precision limitations within the MLP: on a simple 1-D interpolation task, even MLPs with O(1e5) parameters stall around 1e-8 RMSE -- about eight orders above float64 machine precision -- before any PDE terms are added. In PDE learning, adding a BWLer lifts this ceiling and exposes a tradeoff between achievable accuracy and the conditioning of the PDE loss. For linear PDEs we fully characterize this tradeoff with an explicit error decomposition and navigate it during training with spectral derivatives and preconditioning. Across five benchmark PDEs, adding a BWLer on top of an MLP improves RMSE by up to 30x for convection, 10x for reaction, and 1800x for wave equations while remaining compatible with first-order optimizers. Replacing the MLP entirely lets an explicit BWLer reach near-machine-precision on convection, reaction, and wave problems (up to 10 billion times better than prior results) and match the performance of standard PINNs on stiff Burgers' and irregular-geometry Poisson problems. Together, these findings point to a practical path for combining the flexibility of PINNs with the precision of classical spectral solvers.

Paperid: 953, https://arxiv.org/pdf/2506.20696.pdf

Abstract:
Elucidating the biomechanical behavior of the myocardium is crucial for understanding cardiac physiology, but cannot be directly inferred from clinical imaging and typically requires finite element (FE) simulations. However, conventional FE methods are computationally expensive and often fail to reproduce observed cardiac motions. We propose IMC-PINN-FE, a physics-informed neural network (PINN) framework that integrates imaged motion consistency (IMC) with FE modeling for patient-specific left ventricular (LV) biomechanics. Cardiac motion is first estimated from MRI or echocardiography using either a pre-trained attention-based network or an unsupervised cyclic-regularized network, followed by extraction of motion modes. IMC-PINN-FE then rapidly estimates myocardial stiffness and active tension by fitting clinical pressure measurements, accelerating computation from hours to seconds compared to traditional inverse FE. Based on these parameters, it performs FE modeling across the cardiac cycle at 75x speedup. Through motion constraints, it matches imaged displacements more accurately, improving average Dice from 0.849 to 0.927, while preserving realistic pressure-volume behavior. IMC-PINN-FE advances previous PINN-FE models by introducing back-computation of material properties and better motion fidelity. Using motion from a single subject to reconstruct shape modes also avoids the need for large datasets and improves patient specificity. IMC-PINN-FE offers a robust and efficient approach for rapid, personalized, and image-consistent cardiac biomechanical modeling.

Paperid: 954, https://arxiv.org/pdf/2506.17994.pdf

Abstract:
Accurate inverse dynamics models are essential tools for controlling industrial robots. Recent research combines neural network regression with inverse dynamics formulations of the Newton-Euler and the Euler-Lagrange equations of motion, resulting in so-called Newtonian neural networks and Lagrangian neural networks, respectively. These physics-informed models seek to identify unknowns in the analytical equations from data. Despite their potential, current literature lacks guidance on choosing between Lagrangian and Newtonian networks. In this study, we show that when motor torques are estimated instead of directly measuring joint torques, Lagrangian networks prove less effective compared to Newtonian networks as they do not explicitly model dissipative torques. The performance of these models is compared to neural network regression on data of a MABI MAX 100 industrial robot.

Paperid: 955, https://arxiv.org/pdf/2506.17345.pdf

Abstract:
The prediction of crystal properties is essential for understanding structure-property relationships and accelerating the discovery of functional materials. However, conventional approaches relying on experimental measurements or density functional theory (DFT) calculations are often resource-intensive, limiting their scalability. Machine learning (ML) models offer a promising alternative by learning complex structure-property relationships from data, enabling faster predictions. Yet, existing ML models often rely on labeled data, adopt representations that poorly capture essential structural characteristics, and lack integration with physical principles--factors that limit their generalizability and interpretability. Here, we introduce CLOUD (Crystal Language mOdel for Unified and Differentiable materials modeling), a transformer-based framework trained on a novel Symmetry-Consistent Ordered Parameter Encoding (SCOPE) that encodes crystal symmetry, Wyckoff positions, and composition in a compact, coordinate-free string representation. Pre-trained on over six million crystal structures, CLOUD is fine-tuned on multiple downstream tasks and achieves competitive performance in predicting a wide range of material properties, demonstrating strong scaling performance. Furthermore, as proof of concept of differentiable materials modeling, CLOUD is applied to predict the phonon internal energy and heat capacity, which integrates the Debye model to preserve thermodynamic consistency. The CLOUD-DEBYE framework enforces thermodynamic consistency and enables temperature-dependent property prediction without requiring additional data. These results demonstrate the potential of CLOUD as a scalable and physics-informed foundation model for crystalline materials, unifying symmetry-consistent representations with physically grounded learning for property prediction and materials discovery.

Paperid: 956, https://arxiv.org/pdf/2506.11281.pdf

Abstract:
High-quality power flow datasets are essential for training machine learning models in power systems. However, security and privacy concerns restrict access to real-world data, making statistically accurate and physically consistent synthetic datasets a viable alternative. We develop a diffusion model for generating synthetic power flow datasets from real-world power grids that both replicate the statistical properties of the real-world data and ensure AC power flow feasibility. To enforce the constraints, we incorporate gradient guidance based on the power flow constraints to steer diffusion sampling toward feasible samples. For computational efficiency, we further leverage insights from the fast decoupled power flow method and propose a variable decoupling strategy for the training and sampling of the diffusion model. These solutions lead to a physics-informed diffusion model, generating power flow datasets that outperform those from the standard diffusion in terms of feasibility and statistical similarity, as shown in experiments across IEEE benchmark systems.

Paperid: 957, https://arxiv.org/pdf/2506.09721.pdf

Abstract:
Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping from the parameters to the PDE solution. Two prominent methods for this are Data-driven Non-Intrusive Reduced Order Models (DROMs) and Parametrised Physics Informed Neural Networks (PPINNs). However, their accuracy tends to degrade as the number of geometric parameters increases. To address this, we propose adopting Generative Models to create new geometries, effectively reducing the number of parameters, and improving the performance of DROMs and PPINNs. The first section briefly reviews the general theory of Generative Models and provides some examples, whereas the second focusses on their application to geometries with fixed or variable points, emphasising their integration with DROMs and PPINNs. DROMs trained on geometries generated by these models demonstrate enhanced accuracy due to reduced parameter dimensionality. For PPINNs, we introduce a methodology that leverages Generative Models to reduce the parameter dimensions and improve convergence. This approach is tested on a Poisson equation defined over deformed Stanford Bunny domains.

Paperid: 958, https://arxiv.org/pdf/2506.07958.pdf

Abstract:
Physics-informed Kolmogorov-Arnold Networks (PIKANs), and in particular their Chebyshev-based variants (cPIKANs), have recently emerged as promising models for solving partial differential equations (PDEs). However, their training dynamics and convergence behavior remain largely unexplored both theoretically and numerically. In this work, we aim to advance the theoretical understanding of cPIKANs by analyzing them using Neural Tangent Kernel (NTK) theory. Our objective is to discern the evolution of kernel structure throughout gradient-based training and its subsequent impact on learning efficiency. We first derive the NTK of standard cKANs in a supervised setting, and then extend the analysis to the physics-informed context. We analyze the spectral properties of NTK matrices, specifically their eigenvalue distributions and spectral bias, for four representative PDEs: the steady-state Helmholtz equation, transient diffusion and Allen-Cahn equations, and forced vibrations governed by the Euler-Bernoulli beam equation. We also conduct an investigation into the impact of various optimization strategies, e.g., first-order, second-order, and hybrid approaches, on the evolution of the NTK and the resulting learning dynamics. Results indicate a tractable behavior for NTK in the context of cPIKANs, which exposes learning dynamics that standard physics-informed neural networks (PINNs) cannot capture. Spectral trends also reveal when domain decomposition improves training, directly linking kernel behavior to convergence rates under different setups. To the best of our knowledge, this is the first systematic NTK study of cPIKANs, providing theoretical insight that clarifies and predicts their empirical performance.

Paperid: 959, https://arxiv.org/pdf/2506.03173.pdf

Abstract:
Physical intelligence -- anticipating and shaping the world from partial, multisensory observations -- is critical for next-generation world models. We propose FOLIAGE, a physics-informed multimodal world model for unbounded accretive surface growth. In its Action-Perception loop, a unified context encoder maps images, mesh connectivity, and point clouds to a shared latent state. A physics-aware predictor, conditioned on physical control actions, advances this latent state in time to align with the target latent of the surface, yielding a Modality-Agnostic Growth Embedding (MAGE) that interfaces with critic heads for downstream objectives. FOLIAGE's Accretive Graph Network (AGN) captures dynamic connectivity through Age Positional Encoding and Energy-Gated Message-Passing. Geometry-Correspondence Fusion and Cross-Patch Masking enhance MAGE's expressiveness, while Hierarchical Pooling balances global context with local dynamics. We create SURF-GARDEN, a world model learning platform comprising a Counterfactual Physics Simulator, a Multimodal Correspondence Extractor, and Evolution Tracing, which generates 7,200 diverse surface-growth sequences. SURF-BENCH, our physical-intelligence evaluation suite, evaluates six core tasks -- topology recognition, inverse material estimation, growth-stage classification, latent roll-out, cross-modal retrieval, and dense correspondence -- and four stress tests -- sensor dropout, zero-shot modality transfer, long-horizon prediction, and physics ablation -- to probe resilience. FOLIAGE outperforms specialized baselines while remaining robust across dynamic environments, establishing a new world-model based, multimodal pathway to physical intelligence.

Paperid: 960, https://arxiv.org/pdf/2506.00858.pdf

Abstract:
Data-driven soft sensors have been widely applied in complex industrial processes. However, the interpretable spatio-temporal features extraction by soft sensors remains a challenge. In this light, this work introduces a novel method termed spatio-temporal consistent and interpretable model (STCIM). First, temporal and spatial features are captured and aligned by a far topological spatio-temporal consistency extraction block. Then, the features are mapped into an interpretable latent space for further prediction by explicitly giving physical meanings to latent variables. The efficacy of the proposed STCIM is demonstrated through the modeling of two generated datasets and a real-life dataset of coal-fired power plants. The corresponding experiments show: 1) The generalization of STCIM outperforms other methods, especially in different operation situations. 2) The far topological spatio-temporal consistency is vital for feature alignment. 3) The hyper-parameters of physics-informed interpretable latent space loss decide the performance of STCIM.

Paperid: 961, https://arxiv.org/pdf/2505.21842.pdf

Abstract:
We propose a physics-informed neural networks (PINNs) framework to solve the infinite-horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations (PDEs), they can be employed to learn the value function of the infinite-horizon optimal control problem via solving the associated steady-state Hamilton-Jacobi-Bellman (HJB) equation. However, an issue here is that the steady-state HJB equation generally yields multiple solutions; hence if PINNs are directly employed to it, they may end up approximating a solution that is different from the optimal value function of the problem. We tackle this by instead applying PINNs to a finite-horizon variant of the steady-state HJB that has a unique solution, and which uniformly approximates the optimal value function as the horizon increases. An algorithm to verify if the chosen horizon is large enough is also given, as well as a method to extend it -- with reduced computations and robustness to approximation errors -- in case it is not. Unlike many existing methods, the proposed technique works well with non-polynomial basis functions, does not require prior knowledge of a stabilizing controller, and does not perform iterative policy evaluations. Simulations are performed, which verify and clarify theoretical findings.

Paperid: 962, https://arxiv.org/pdf/2505.14252.pdf

Abstract:
In this work, we explore the integration of Sequence Encoding for Online Parameter Identification with Physics-Informed Neural Networks to create a model that, once trained, can be utilized for real time applications with variable parameters, boundary conditions, and initial conditions. Recently, the combination of PINNs with Sparse Regression has emerged as a method for performing dynamical system identification through supervised learning and sparse regression optimization, while also solving the dynamics using PINNs. However, this approach can be limited by variations in parameters or boundary and initial conditions, requiring retraining of the model whenever changes occur. In this work, we introduce an architecture that employs Deep Sets or Sequence Encoders to encode dynamic parameters, boundary conditions, and initial conditions, using these encoded features as inputs for the PINN, enabling the model to adapt to changes in parameters, BCs, and ICs. We apply this approach to three different problems. First, we analyze the Rossler ODE system, demonstrating the robustness of the model with respect to noise and its ability to generalize. Next, we explore the model's capability in a 2D Navier-Stokes PDE problem involving flow past a cylinder with a parametric sinusoidal inlet velocity function, showing that the model can encode pressure data from a few points to identify the inlet velocity profile and utilize physics to compute velocity and pressure throughout the domain. Finally, we address a 1D heat monitoring problem using real data from the heating of glass fiber and thermoplastic composite plates.

Paperid: 963, https://arxiv.org/pdf/2505.10919.pdf

Abstract:
Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems are computationally prohibitive. To address this, we present a novel physics-informed spatio-temporal surrogate model for Rayleigh-BÃ©nard convection (RBC), a canonical example of convective fluid flow. Our approach combines convolutional neural networks for spatial feature extraction with an innovative recurrent architecture inspired by large language models, comprising a context builder and a sequence generator to capture temporal dynamics. Inference is penalized with respect to the governing partial differential equations to ensure physical interpretability. Given the sensitivity of turbulent convection to initial conditions, we quantify uncertainty using a conformal prediction framework. This model replicates key features of RBC dynamics while significantly reducing computational cost, offering a scalable alternative to DNS for long-term simulations.

Paperid: 964, https://arxiv.org/pdf/2505.09899.pdf

Abstract:
Cancer remains a leading cause of death worldwide, necessitating personalized treatment approaches to improve outcomes. Theranostics, combining molecular-level imaging with targeted therapy, offers potential for precision oncology but requires optimized, patient-specific care plans. This paper investigates state-of-the-art data-driven decision support applications with a reinforcement learning focus in precision oncology. We review current applications, training environments, state-space representation, performance evaluation criteria, and measurement of risk and reward, highlighting key challenges. We propose a framework integrating data-driven modeling with reinforcement learning-based decision support to optimize radiopharmaceutical therapy dosing, addressing identified challenges and setting directions for future research. The framework leverages Neural Ordinary Differential Equations and Physics-Informed Neural Networks to enhance Physiologically Based Pharmacokinetic models while applying reinforcement learning algorithms to iteratively refine treatment policies based on patient-specific data.

Paperid: 965, https://arxiv.org/pdf/2505.01078.pdf

Abstract:
Backward stochastic differential equation (BSDE)-based deep learning methods provide an alternative to Physics-Informed Neural Networks (PINNs) for solving high-dimensional partial differential equations (PDEs), offering algorithmic advantages in settings such as stochastic optimal control, where the PDEs of interest are tied to an underlying dynamical system. However, existing BSDE-based solvers have empirically been shown to underperform relative to PINNs in the literature. In this paper, we identify the root cause of this performance gap as a discretization bias introduced by the standard Euler-Maruyama (EM) integration scheme applied to short-horizon self-consistency BSDE losses, which shifts the optimization landscape off target. We find that this bias cannot be satisfactorily addressed through finer step sizes or longer self-consistency horizons. To properly handle this issue, we propose a Stratonovich-based BSDE formulation, which we implement with stochastic Heun integration. We show that our proposed approach completely eliminates the bias issues faced by EM integration. Furthermore, our empirical results show that our Heun-based BSDE method consistently outperforms EM-based variants and achieves competitive results with PINNs across multiple high-dimensional benchmarks. Our findings highlight the critical role of integration schemes in BSDE-based PDE solvers, an algorithmic detail that has received little attention thus far in the literature.

Paperid: 966, https://arxiv.org/pdf/2504.20019.pdf

Abstract:
Physics-informed neural networks (PINNs) integrate physical laws with data-driven models to improve generalization and sample efficiency. This work introduces an open-source implementation of the Physics-Informed Neural Network with Control (PINC) framework, designed to model the dynamics of an underwater vehicle. Using initial states, control actions, and time inputs, PINC extends PINNs to enable physically consistent transitions beyond the training domain. Various PINC configurations are tested, including differing loss functions, gradient-weighting schemes, and hyperparameters. Validation on a simulated underwater vehicle demonstrates more accurate long-horizon predictions compared to a non-physics-informed baseline

Paperid: 967, https://arxiv.org/pdf/2504.17210.pdf

Abstract:
Many data-driven modules in smart grid rely on access to high-quality power flow data; however, real-world data are often limited due to privacy and operational constraints. This paper presents a physics-informed generative framework based on Denoising Diffusion Probabilistic Models (DDPMs) for synthesizing feasible power flow data. By incorporating auxiliary training and physics-informed loss functions, the proposed method ensures that the generated data exhibit both statistical fidelity and adherence to power system feasibility. We evaluate the approach on the IEEE 14-bus and 30-bus benchmark systems, demonstrating its ability to capture key distributional properties and generalize to out-of-distribution scenarios. Comparative results show that the proposed model outperforms three baseline models in terms of feasibility, diversity, and accuracy of statistical features. This work highlights the potential of integrating generative modelling into data-driven power system applications.

Paperid: 968, https://arxiv.org/pdf/2504.16447.pdf

Abstract:
Severe accidents (SAs) in nuclear power plants have been analyzed using thermal-hydraulic (TH) system codes such as MELCOR and MAAP. These codes efficiently simulate the progression of SAs, while they still have inherent limitations due to their inconsistent finite difference schemes. The use of empirical schemes incorporating both implicit and explicit formulations inherently induces unidirectional coupling in multi-physics analyses. The objective of this study is to develop a novel numerical method for TH system codes using physics-informed neural network (PINN). They have shown strength in solving multi-physics due to the innate feature of neural networks-automatic differentiation. We propose a node-assigned PINN (NA-PINN) that is suitable for the control volume approach-based system codes. NA-PINN addresses the issue of spatial governing equation variation by assigning an individual network to each nodalization of the system code, such that spatial information is excluded from both the input and output domains, and each subnetwork learns to approximate a purely temporal solution. In this phase, we evaluated the accuracy of the PINN methods for the hydrodynamic module. In the 6 water tank simulation, PINN and NA-PINN showed maximum absolute errors of 1.678 and 0.007, respectively. It should be noted that only NA-PINN demonstrated acceptable accuracy. To the best of the authors' knowledge, this is the first study to successfully implement a system code using PINN. Our future work involves extending NA-PINN to a multi-physics solver and developing it in a surrogate manner.

Paperid: 969, https://arxiv.org/pdf/2504.10539.pdf

Abstract:
This paper presents an improved approach for preserving sharp interfaces in multiphase Lattice Boltzmann Method (LBM) simulations using Physics-Informed Neural Networks (PINNs). Interface diffusion is a common challenge in multiphase LBM, leading to reduced accuracy in simulating phenomena where interfacial dynamics are critical. We propose a coupled PINN-LBM framework that maintains interface sharpness while preserving the physical accuracy of the simulation. Our approach is validated through droplet simulations, with quantitative metrics measuring interface width, maximum gradient, phase separation, effective interface width, and interface energy. The enhanced visualization techniques employed in this work clearly demonstrate the superior performance of PINN-LBM over standard LBM for multiphase simulations, particularly in maintaining well-defined interfaces throughout the simulation. We provide a comprehensive analysis of the results, showcasing how the neural network integration effectively counteracts numerical diffusion, while maintaining physical consistency with the underlying fluid dynamics.

Paperid: 970, https://arxiv.org/pdf/2504.08484.pdf

Abstract:
We show that data that is not sufficiently informative to allow for system re-identification can still provide meaningful information when combined with external or physical knowledge of the system, such as bounded system matrix norms. We then illustrate how this information can be leveraged for safety and energy minimization problems and to enhance predictions in unmodelled dynamics. This preliminary work outlines key ideas toward using limited data for effective control by integrating physical knowledge of the system and exploiting interpolation conditions.

Paperid: 971, https://arxiv.org/pdf/2504.02283.pdf

Abstract:
In this paper, we demonstrate the possibility of performing automatic Technology Computer-Aided-Design (TCAD) parameter calibration using machine learning, verified with experimental data. The machine only needs to be trained by TCAD data. Schottky Barrier Diode (SBD) fabricated with emerging ultra-wide-bandgap material, Gallium Oxide (Ga$_2$O$_3$), is measured and its current-voltage (IV) is used for Ga$_2$O$_3$ Philips Unified Mobility (PhuMob) model parameters, effective anode workfunction, and ambient temperature extraction (7 parameters). A machine comprised of an autoencoder (AE) and a neural network (NN) (AE-NN) is used. Ga$_2$O$_3$ PhuMob parameters are extracted from the noisy experimental curves. TCAD simulation with the extracted parameters shows that the quality of the parameters is as good as an expert's calibration at the pre-turned-on regime but not in the on-state regime. By using a simple physics-informed neural network (PINN) (AE-PINN), the machine performs as well as the human expert in all regimes.

Paperid: 972, https://arxiv.org/pdf/2503.22396.pdf

Abstract:
This paper presents a novel physical parameter estimation framework for on-site model characterization, using a two-phase modelling strategy with Physics-Informed Neural Networks (PINNs) and transfer learning (TL). In the first phase, a PINN is trained using only the physical principles of the single particle model (SPM) equations. In the second phase, the majority of the PINN parameters are frozen, while critical electrochemical parameters are set as trainable and adjusted using real-world voltage profile data. The proposed approach significantly reduces computational costs, making it suitable for real-time implementation on Battery Management Systems (BMS). Additionally, as the initial phase does not require field data, the model is easy to deploy with minimal setup requirements. With the proposed methodology, we have been able to effectively estimate relevant electrochemical parameters with operating data. This has been proved estimating diffusivities and active material volume fractions with charge data in different degradation conditions. The methodology is experimentally validated in a Raspberry Pi device using data from a standard charge profile with a 3.89\% relative accuracy estimating the active material volume fractions of a NMC cell with 82.09\% of its nominal capacity.

Paperid: 973, https://arxiv.org/pdf/2503.16310.pdf

Abstract:
This paper presents a rigorous evaluation of Real-to-Sim parameter estimation approaches for fabric manipulation in robotics. The study systematically assesses three state-of-the-art approaches, namely two differential pipelines and a data-driven approach. We also devise a novel physics-informed neural network approach for physics parameter estimation. These approaches are interfaced with two simulations across multiple Real-to-Sim scenarios (lifting, wind blowing, and stretching) for five different fabric types and evaluated on three unseen scenarios (folding, fling, and shaking). We found that the simulation engines and the choice of Real-to-Sim approaches significantly impact fabric manipulation performance in our evaluation scenarios. Moreover, PINN observes superior performance in quasi-static tasks but shows limitations in dynamic scenarios.

Paperid: 974, https://arxiv.org/pdf/2503.14913.pdf

Abstract:
In this paper, we propose a hybrid method that combines finite element method (FEM) and physics-informed neural network (PINN) for solving linear elliptic problems. This method contains three steps: (1) train a PINN and obtain an approximate solution $u_Î¸$; (2) enrich the finite element space with $u_Î¸$; (3) obtain the final solution by FEM in the enriched space. In the second step, the enriched space is constructed by addition $v + u_Î¸$ or multiplication $v \cdot u_Î¸$, where $v$ belongs to the standard finite element space. We conduct the convergence analysis for the proposed method. Compared to the standard FEM, the same convergence order is obtained and higher accuracy can be achieved when solution derivatives are well approximated in PINN. Numerical examples from one dimension to three dimensions verify these theoretical results. For some examples, the accuracy of the proposed method can be reduced by a couple of orders of magnitude compared to the standard FEM.

Paperid: 975, https://arxiv.org/pdf/2503.07528.pdf

Abstract:
The precision, stability, and performance of lightweight high-strength steel structures in heavy machinery is affected by their highly nonlinear dynamics. This, in turn, makes control more difficult, simulation more computationally intensive, and achieving real-time autonomy, using standard approaches, impossible. Machine learning through data-driven, physics-informed and physics-inspired networks, however, promises more computationally efficient and accurate solutions to nonlinear dynamic problems. This study proposes a novel framework that has been developed to estimate real-time structural deflection in hydraulically actuated three-dimensional systems. It is based on SLIDE, a machine-learning-based method to estimate dynamic responses of mechanical systems subjected to forced excitations.~Further, an algorithm is introduced for the data acquisition from a hydraulically actuated system using randomized initial configurations and hydraulic pressures.~The new framework was tested on a hydraulically actuated flexible boom with various sensor combinations and lifting various payloads. The neural network was successfully trained in less time using standard parameters from PyTorch, ADAM optimizer, the various sensor inputs, and minimal output data. The SLIDE-trained neural network accelerated deflection estimation solutions by a factor of $10^7$ in reference to flexible multibody simulation batches and provided reasonable accuracy. These results support the studies goal of providing robust, real-time solutions for control, robotic manipulators, structural health monitoring, and automation problems.

Paperid: 976, https://arxiv.org/pdf/2503.05009.pdf

Abstract:
Quantum computing leverages qubits, exploiting superposition and entanglement to solve problems intractable for classical computers, offering significant computational advantages. Quantum machine learning (QML), which integrates quantum computing with machine learning, holds immense potential across various fields but remains largely unexplored in geosciences. However, its progress is hindered by the limitations of current NISQ hardware. To address these challenges, hybrid quantum neural networks (HQNNs) have emerged, combining quantum layers within classical neural networks to leverage the strengths of both paradigms. To the best of our knowledge, this study presents the first application of QML to subsurface imaging through the development of hybrid quantum physics-informed neural networks (HQ-PINNs) for seismic inversion. We apply the HQ-PINN framework to invert pre-stack and post-stack seismic datasets, estimating P- and S-impedances. The proposed HQ-PINN architecture follows an encoder-decoder structure, where the encoder (HQNN), processes seismic data to estimate elastic parameters, while the decoder utilizes these parameters to generate the corresponding seismic data based on geophysical relationships. The HQ-PINN model is trained by minimizing the misfit between the input and predicted seismic data generated by the decoder. We systematically evaluate various quantum layer configurations, differentiation methods, and quantum device simulators on the inversion performance, and demonstrate real-world applicability through the individual and simultaneous inversion cases of the Sleipner dataset. The HQ-PINN framework consistently and efficiently estimated accurate subsurface impedances across the synthetic and field case studies, establishing the feasibility of leveraging QML for seismic inversion, thereby paving the way for broader applications of quantum computing in geosciences.

Paperid: 977, https://arxiv.org/pdf/2502.17585.pdf

Abstract:
This review explores the integration of deep learning (DL) with full-waveform inversion (FWI) for enhanced seismic imaging and subsurface characterization. It covers FWI and DL fundamentals, geophysical applications (velocity estimation, deconvolution, tomography), and challenges (model complexity, data quality). The review also outlines future research directions, including hybrid, generative, and physics-informed models for improved accuracy, efficiency, and reliability in subsurface property estimation. The synergy between DL and FWI has the potential to transform geophysics, providing new insights into Earth's subsurface.

Paperid: 978, https://arxiv.org/pdf/2502.15755.pdf

Abstract:
Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors mitigate these issues by penalizing deviations from known physical laws, as in physics-informed neural networks, or by designing architectures that automatically satisfy specific invariants. However, penalization approaches do not guarantee compliance with physical constraints for unseen inputs, and invariant-based methods lack flexibility and generality. We propose a novel physics-consistent machine learning method that directly enforces compliance with physical principles by projecting model outputs onto the manifold defined by these laws. This procedure ensures that predictions inherently adhere to the chosen physical constraints, improving reliability and interpretability. Our method is demonstrated on two systems: a spring-mass system and a low-temperature reactive plasma. Compared to purely data-driven models, our approach significantly reduces errors in physical law compliance, enhances predictive accuracy of physical quantities, and outperforms alternatives when working with simpler models or limited datasets. The proposed projection-based technique is versatile and can function independently or in conjunction with existing physics-informed neural networks, offering a powerful, general, and scalable solution for developing fast and reliable surrogate models of complex physical systems, particularly in resource-constrained scenarios.

Paperid: 979, https://arxiv.org/pdf/2502.12177.pdf

Abstract:
Solving differential equations is a critical challenge across a host of domains. While many software packages efficiently solve these equations using classical numerical approaches, there has been less effort in developing a library for researchers interested in solving such systems using neural networks. With PyTorch as its backend, NeuroDiffEq is a software library that exploits neural networks to solve differential equations. In this paper, we highlight the latest features of the NeuroDiffEq library since its debut. We show that NeuroDiffEq can solve complex boundary value problems in arbitrary dimensions, tackle boundary conditions at infinity, and maintain flexibility for dynamic injection at runtime.

Paperid: 980, https://arxiv.org/pdf/2502.11942.pdf

Abstract:
Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and strongly coupled solutions. In this work, we present a novel Sharp-PINN framework to tackle complex phase field corrosion problems. Instead of minimizing all governing PDE residuals simultaneously, the Sharp-PINNs introduce a staggered training scheme that alternately minimizes the residuals of Allen-Cahn and Cahn-Hilliard equations, which govern the corrosion system. To further enhance its efficiency and accuracy, we design an advanced neural network architecture that integrates random Fourier features as coordinate embeddings, employs a modified multi-layer perceptron as the primary backbone, and enforces hard constraints in the output layer. This framework is benchmarked through simulations of corrosion problems with multiple pits, where the staggered training scheme and network architecture significantly improve both the efficiency and accuracy of PINNs. Moreover, in three-dimensional cases, our approach is 5-10 times faster than traditional finite element methods while maintaining competitive accuracy, demonstrating its potential for real-world engineering applications in corrosion prediction.

Paperid: 981, https://arxiv.org/pdf/2502.09025.pdf

Abstract:
This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft constraints in loss functions and enforcing boundary conditions via collocation points, our framework integrates physical principles, such as the governing equations and constraints, directly into the neural network architecture. This approach eliminates the dependency on problem-specific retraining for new boundary value problems, ensuring adaptability and consistency. By embedding constitutive behavior into the network's foundational design, our method represents a significant step toward unifying material modeling with machine learning for computational fracture mechanics. Specifically, a feedforward neural network is designed to embed physical laws within its architecture, ensuring thermodynamic consistency. Building on this foundation, synthetic datasets generated from finite element-based phase-field simulations are employed to train the proposed framework, focusing on capturing the homogeneous responses of brittle and ductile fractures. Detailed analyses are performed on the stored elastic energy and the dissipated work due to plasticity and fracture, demonstrating the capability of the framework to predict essential fracture features. The proposed physics-based machine learning framework overcomes the shortcomings of classical machine learning models, which rely heavily on large datasets and lack guarantees of physical principles. By leveraging its physics-integrated design, the physics-based machine learning framework demonstrates exceptional performance in predicting key properties of brittle and ductile fractures with limited training data.

Paperid: 982, https://arxiv.org/pdf/2502.07129.pdf

Abstract:
In the field of systems biology, differential equations are commonly used to model biological systems, but solving them for large-scale and complex systems can be computationally expensive. Recently, the integration of machine learning and mathematical modeling has offered new opportunities for scientific discoveries in biology and health. The emerging physics-informed neural network (PINN) has been proposed as a solution to this problem. However, PINN can be computationally expensive and unreliable for complex biological systems. To address these issues, we propose the Fourier-enhanced Neural Networks for systems biology (SB-FNN). SB-FNN uses an embedded Fourier neural network with an adaptive activation function and a cyclic penalty function to optimize the prediction of biological dynamics, particularly for biological systems that exhibit oscillatory patterns. Experimental results demonstrate that SB-FNN achieves better performance and is more efficient than PINN for handling complex biological models. Experimental results on cellular and population models demonstrate that SB-FNN outperforms PINN in both accuracy and efficiency, making it a promising alternative approach for handling complex biological models. The proposed method achieved better performance on six biological models and is expected to replace PINN as the most advanced method in systems biology.

Paperid: 983, https://arxiv.org/pdf/2502.07093.pdf

Abstract:
Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this work, we derive such estimates for the inverse of a nonlinear map defined on a manifold that captures both unknown parameters and the nonlinear physical processes they influence. Our analysis is based on finite-dimensional, learnable representations of the manifold and provides Lipschitz stability estimates on the manifold-based subspaces, for a class of inverse maps associated with parameter dependent linear compact operators. Such operators model scattered and far-field data that can be used to detect structures such as cracks. We apply our theoretical ML manifold framework to inverse Helmholtz problems in unbounded regions exterior to cracks, addressing the scattered-field data-driven inverse problem while ensuring injectivity conditions on the manifold, a requirement for the Lipschitz stability. Our method accurately recovers crack-defining parameters without requiring prior knowledge of inputs such as incident wave types or external forces on the crack. Numerical experiments using NN approximations confirm the accuracy, efficiency, and robustness of the proposed approach.

Paperid: 984, https://arxiv.org/pdf/2501.12116.pdf

Abstract:
Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to facilitate the solution of nonlinear multiscale differential equations and, especially, inverse problems using Physics-Informed Neural Networks (PINNs). This framework is based on what is called \textit{multi-head} (MH) training, which involves training the network to learn a general space of all solutions for a given set of equations with certain variability, rather than learning a specific solution of the system. This setup is used with a second novel technique that we call Unimodular Regularization (UR) of the latent space of solutions. We show that the multi-head approach, combined with Unimodular Regularization, significantly improves the efficiency of PINNs by facilitating the transfer learning process thereby enabling the finding of solutions for nonlinear, coupled, and multiscale differential equations.

Paperid: 985, https://arxiv.org/pdf/2501.08501.pdf

Abstract:
Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. Additionally, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

Paperid: 986, https://arxiv.org/pdf/2501.02762.pdf

Abstract:
Partial Differential Equations (PDEs) are integral to modeling many scientific and engineering problems. Physics-informed Neural Networks (PINNs) have emerged as promising tools for solving PDEs by embedding governing equations into the neural network loss function. However, when dealing with PDEs characterized by strong oscillatory dynamics over large computational domains, PINNs based on Multilayer Perceptrons (MLPs) often exhibit poor convergence and reduced accuracy. To address these challenges, this paper introduces Scaled-cPIKAN, a physics-informed architecture rooted in Kolmogorov-Arnold Networks (KANs). Scaled-cPIKAN integrates Chebyshev polynomial representations with a domain scaling approach that transforms spatial variables in PDEs into the standardized domain $[-1,1]^d$, as intrinsically required by Chebyshev polynomials. By combining the flexibility of Chebyshev-based KANs (cKANs) with the physics-driven principles of PINNs, and the spatial domain transformation, Scaled-cPIKAN enables efficient representation of oscillatory dynamics across extended spatial domains while improving computational performance. We demonstrate Scaled-cPIKAN efficacy using four benchmark problems: the diffusion equation, the Helmholtz equation, the Allen-Cahn equation, as well as both forward and inverse formulations of the reaction-diffusion equation (with and without noisy data). Our results show that Scaled-cPIKAN significantly outperforms existing methods in all test cases. In particular, it achieves several orders of magnitude higher accuracy and faster convergence rate, making it a highly efficient tool for approximating PDE solutions that feature oscillatory behavior over large spatial domains.

Paperid: 987, https://arxiv.org/pdf/2412.18362.pdf

Abstract:
Nonlinear structural analyses in engineering often require extensive finite element simulations, limiting their applicability in design optimization, uncertainty quantification, and real-time control. Conventional deep learning surrogates, such as convolutional neural networks (CNNs), physics-informed neural networks (PINNs), and fourier neural operators (FNOs), face challenges with complex non-parametric three-dimensional (3D) geometries, directionally varying loads, and high-fidelity predictions on unstructured meshes. This work presents Point-DeepONet, an operator-learning-based surrogate that integrates PointNet into the DeepONet framework. By directly processing non-parametric point clouds and incorporating signed distance functions (SDF) for geometric context, Point-DeepONet accurately predicts three-dimensional displacement and von Mises stress fields without mesh parameterization or retraining. Trained using only about 5,000 nodes (2.5% of the original 200,000-node mesh), Point-DeepONet can still predict the entire mesh at high fidelity, achieving a coefficient of determination reaching 0.987 for displacement and 0.923 for von Mises stress under a horizontal load case. Compared to nonlinear finite element analyses that require about 19.32 minutes per case, Point-DeepONet provides predictions in mere seconds-approximately 400 times faster-while maintaining excellent scalability and accuracy with increasing dataset sizes. These findings highlight the potential of Point-DeepONet to enable rapid, high-fidelity structural analyses, ultimately supporting more effective design exploration and informed decision-making in complex engineering workflows.

Paperid: 988, https://arxiv.org/pdf/2412.17001.pdf

Abstract:
Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizing Physics-Informed Neural Networks (PINNs) to solve the nonlinear energy supply-demand (ESD) system. We design a neural network with four outputs, where each output approximates a function that corresponds to one of the unknown functions in the nonlinear system of differential equations describing the four-dimensional ESD problem. The neural network model is then trained and the parameters are identified, optimized to achieve a more accurate solution. The solutions obtained from the neural network for this problem are equivalent when we compare and evaluate them against the Runge-Kutta numerical method of order 4/5 (RK45). However, the method utilizing neural networks is considered a modern and promising approach, as it effectively exploits the superior computational power of advanced computer systems, especially in solving complex problems. Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. In other words, neural networks are not only trained to approximate the solution functions for the nonlinear ESD system but can also represent the complex dynamic relationships between the system's components. However, this approach requires significant time and computational power due to the need for model training.

Paperid: 989, https://arxiv.org/pdf/2412.16644.pdf

Abstract:
Traditional numerical methods, such as the finite element method and finite volume method, adress partial differential equations (PDEs) by discretizing them into algebraic equations and solving these iteratively. However, this process is often computationally expensive and time-consuming. An alternative approach involves transforming PDEs into integral equations and solving them using Green's functions, which provide analytical solutions. Nevertheless, deriving Green's functions analytically is a challenging and non-trivial task, particularly for complex systems. In this study, we introduce a novel framework, termed GreensONet, which is constructed based on the strucutre of deep operator networks (DeepONet) to learn embedded Green's functions and solve PDEs via Green's integral formulation. Specifically, the Trunk Net within GreensONet is designed to approximate the unknown Green's functions of the system, while the Branch Net are utilized to approximate the auxiliary gradients of the Green's function. These outputs are subsequently employed to perform surface integrals and volume integrals, incorporating user-defined boundary conditions and source terms, respectively. The effectiveness of the proposed framework is demonstrated on three types of PDEs in bounded domains: 3D heat conduction equations, reaction-diffusion equations, and Stokes equations. Comparative results in these cases demonstrate that GreenONet's accuracy and generalization ability surpass those of existing methods, including Physics-Informed Neural Networks (PINN), DeepONet, Physics-Informed DeepONet (PI-DeepONet), and Fourier Neural Operators (FNO).

Paperid: 990, https://arxiv.org/pdf/2412.09775.pdf

Authors:Talon Chandler, Ivan E. Ivanov, Gabriel Sturm, Sheng Xiao, Xiang Zhao, Alexander Hillsley, Allyson Quinn Ryan, Ziwen Liu, Sricharan Reddy Varra, Ilan Theodoro, Eduardo Hirata-Miyasaki, Deepika Sundarraman, Amitabh Verma, Madhurya Sekhar, Chad Liu, Soorya Pradeep, See-Chi Lee, Shannon N. Rhoads, Maria Clara Zanellati, Sarah Cohen, Carolina Arias, Manuel D. Leonetti, Adrian Jacobo, Keir Balla, Loïc A. Royer, Shalin B. Mehta

Abstract:
Correlative computational microscopy can accelerate imaging and modeling of cellular dynamics by relaxing trade-offs inherent to dynamic imaging. Existing computational microscopy frameworks are either specialized or overly generic, limiting use to fixed configurations or domain experts. We introduce WaveOrder, a generalist wave-optical framework for imaging the architectural order of biomolecules. WaveOrder reconstructs diverse specimen properties from multi-channel acquisitions, with or without fluorescence. It provides a unified representation of linear optical properties and differentiable physics-based image formation models spanning widefield, confocal, light-sheet, and oblique label-free geometries. WaveOrder uses physics-informed ML to auto-tune model parameters and solve blind shift-variant restoration problems. This open-source, PyTorch-based framework enables scalable quantitative imaging across scales from organelles to adult zebrafish, and improves restoration of cellular structures in high-throughput experiments. We validate WaveOrder on diverse imaging applications, demonstrating its ability to recover biomolecular structure beyond the limits of existing approaches.

Paperid: 991, https://arxiv.org/pdf/2412.06158.pdf

Abstract:
In this paper, we study the neural tangent kernel (NTK) for general partial differential equations (PDEs) based on physics-informed neural networks (PINNs). As we all know, the training of an artificial neural network can be converted to the evolution of NTK. We analyze the initialization of NTK and the convergence conditions of NTK during training for general PDEs. The theoretical results show that the homogeneity of differential operators plays a crucial role for the convergence of NTK. Moreover, based on the PINNs, we validate the convergence conditions of NTK using the initial value problems of the sine-Gordon equation and the initial-boundary value problem of the KdV equation.

Paperid: 992, https://arxiv.org/pdf/2412.05233.pdf

Abstract:
This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for modeling latent dynamics over time with a decoder that reconstructs PDE solutions from the corresponding latent states. We introduce a physics-informed learning objective for CNF-ROM, which includes two key components. First, the framework uses coordinate-based neural networks to calculate and minimize PDE residuals by computing spatial derivatives via automatic differentiation and applying the chain rule for time derivatives. Second, exact initial and boundary conditions (IC/BC) are imposed using approximate distance functions (ADFs) [Sukumar and Srivastava, CMAME, 2022]. However, ADFs introduce a trade-off as their second- or higher-order derivatives become unstable at the joining points of boundaries. To address this, we introduce an auxiliary network inspired by [Gladstone et al., NeurIPS ML4PS workshop, 2022]. Our method is validated through parameter extrapolation and interpolation, temporal extrapolation, and comparisons with analytical solutions.

Paperid: 993, https://arxiv.org/pdf/2412.04502.pdf

Abstract:
We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.

Paperid: 994, https://arxiv.org/pdf/2412.04213.pdf

Abstract:
Computational biomechanical analysis plays a pivotal role in understanding and improving human movements and physical functions. Although physics-based modeling methods can interpret the dynamic interaction between the neural drive to muscle dynamics and joint kinematics, they suffer from high computational latency. In recent years, data-driven methods have emerged as a promising alternative due to their fast execution speed, but label information is still required during training, which is not easy to acquire in practice. To tackle these issues, this paper presents a novel physics-informed deep learning method to predict muscle forces without any label information during model training. In addition, the proposed method could also identify personalized muscle-tendon parameters. To achieve this, the Hill muscle model-based forward dynamics is embedded into the deep neural network as the additional loss to further regulate the behavior of the deep neural network. Experimental validations on the wrist joint from six healthy subjects are performed, and a fully connected neural network (FNN) is selected to implement the proposed method. The predicted results of muscle forces show comparable or even lower root mean square error (RMSE) and higher coefficient of determination compared with baseline methods, which have to use the labeled surface electromyography (sEMG) signals, and it can also identify muscle-tendon parameters accurately, demonstrating the effectiveness of the proposed physics-informed deep learning method.

Paperid: 995, https://arxiv.org/pdf/2412.03949.pdf

Abstract:
Virtual models of human gait, or digital twins, offer a promising solution for studying mobility without the need for labor-intensive data collection. However, challenges such as the sim-to-real gap and limited adaptability to diverse walking conditions persist. To address these, we developed and validated a framework to create a skeletal humanoid agent capable of adapting to varying walking speeds while maintaining biomechanically realistic motions. The framework combines a synthetic data generator, which produces biomechanically plausible gait kinematics from open-source biomechanics data, and a training system that uses adversarial imitation learning to train the agent's walking policy. We conducted comprehensive analyses comparing the agent's kinematics, synthetic data, and the original biomechanics dataset. The agent achieved a root mean square error of 5.24 +- 0.09 degrees at varying speeds compared to ground-truth kinematics data, demonstrating its adaptability. This work represents a significant step toward developing a digital twin of human locomotion, with potential applications in biomechanics research, exoskeleton design, and rehabilitation.

Paperid: 996, https://arxiv.org/pdf/2411.11801.pdf

Abstract:
Machine learning for scientific discovery is increasingly becoming popular because of its ability to extract and recognize the nonlinear characteristics from the data. The black-box nature of deep learning methods poses difficulties in interpreting the identified model. There is a dire need to interpret the machine learning models to develop a physical understanding of dynamic systems. An interpretable form of neural network called Kolmogorov-Arnold networks (KAN) or Multiplicative KAN (MultKAN) offers critical features that help recognize the nonlinearities in the governing ordinary/partial differential equations (ODE/PDE) of various dynamic systems and find their equation structures. In this study, an equation discovery framework is proposed that includes i) sequentially regularized derivatives for denoising (SRDD) algorithm to denoise the measure data to obtain accurate derivatives, ii) KAN to identify the equation structure and suggest relevant nonlinear functions that are used to create a small overcomplete library of functions, and iii) physics-informed spline fitting (PISF) algorithm to filter the excess functions from the library and converge to the correct equation. The framework was tested on the forced Duffing oscillator, Van der Pol oscillator (stiff ODE), Burger's equation, and Bouc-Wen model (coupled ODE). The proposed method converged to the true equation for the first three systems. It provided an approximate model for the Bouc-Wen model that could acceptably capture the hysteresis response. Using KAN maintains low complexity, which helps the user interpret the results throughout the process and avoid the black-box-type nature of machine learning methods.

Paperid: 997, https://arxiv.org/pdf/2411.10048.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as an influential technology, merging the swift and automated capabilities of machine learning with the precision and dependability of simulations grounded in theoretical physics. PINNs are often employed to solve algebraic or differential equations to replace some or even all steps of multi-stage computational workflows, leading to their significant speed-up. However, wide adoption of PINNs is still hindered by reliability issues, particularly at extreme ends of the input parameter ranges. In this study, we demonstrate this in the context of a system of coupled non-linear differential reaction-diffusion and heat transfer equations related to Fischer-Tropsch synthesis, which are solved by a finite-difference method with a PINN used in evaluating their source terms. It is shown that the testing strategies traditionally used to assess the accuracy of neural networks as function approximators can overlook the peculiarities which ultimately cause instabilities of the finite-difference solver. We propose a domain knowledge-based modifications to the PINN architecture ensuring its correct asymptotic behavior. When combined with an improved numerical scheme employed as an initial guess generator, the proposed modifications are shown to recover the overall stability of the simulations, while preserving the speed-up brought by PINN as the workflow component. We discuss the possible applications of the proposed hybrid transport equation solver in context of chemical reactors simulations.

Paperid: 998, https://arxiv.org/pdf/2411.09329.pdf

Abstract:
This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature.

Paperid: 999, https://arxiv.org/pdf/2410.10897.pdf

Abstract:
Multilayer perceptron (MLP) networks are predominantly used to develop data-driven constitutive models for granular materials. They offer a compelling alternative to traditional physics-based constitutive models in predicting nonlinear responses of these materials, e.g., elasto-plasticity, under various loading conditions. To attain the necessary accuracy, MLPs often need to be sufficiently deep or wide, owing to the curse of dimensionality inherent in these problems. To overcome this limitation, we present an elasto-plasticity informed Chebyshev-based Kolmogorov-Arnold network (EPi-cKAN) in this study. This architecture leverages the benefits of KANs and augmented Chebyshev polynomials, as well as integrates physical principles within both the network structure and the loss function. The primary objective of EPi-cKAN is to provide an accurate and generalizable function approximation for non-linear stress-strain relationships, using fewer parameters compared to standard MLPs. To evaluate the efficiency, accuracy, and generalization capabilities of EPi-cKAN in modeling complex elasto-plastic behavior, we initially compare its performance with other cKAN-based models, which include purely data-driven parallel and serial architectures. Furthermore, to differentiate EPi-cKAN's distinct performance, we also compare it against purely data-driven and physics-informed MLP-based methods. Lastly, we test EPi-cKAN's ability to predict blind strain-controlled paths that extend beyond the training data distribution to gauge its generalization and predictive capabilities. Our findings indicate that, even with limited data and fewer parameters compared to other approaches, EPi-cKAN provides superior accuracy in predicting stress components and demonstrates better generalization when used to predict sand elasto-plastic behavior under blind triaxial axisymmetric strain-controlled loading paths.

Paperid: 1000, https://arxiv.org/pdf/2410.10023.pdf

Abstract:
Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true and false functions difficult, which limits the choice of functions. In this study, an equation discovery method has been proposed to tackle these problems. The key elements include a) use of B-splines for data fitting to get analytical derivatives superior to numerical derivatives, b) sequentially regularized derivatives for denoising (SRDD) algorithm, highly effective in removing noise from signal without system information loss, c) uncorrelated component analysis (UCA) algorithm that identifies and eliminates highly correlated functions while retaining the true functions, and d) physics-informed spline fitting (PISF) where the spline fitting is updated gradually while satisfying the governing equation with a dictionary of candidate functions to converge to the correct equation sequentially. The complete framework is built on a unified deep-learning architecture that eases the optimization process. The proposed method is demonstrated to discover various differential equations at various noise levels, including three-dimensional, fourth-order, and stiff equations. The parameter estimation converges accurately to the true values with a small coefficient of variation, suggesting robustness to the noise.

Paperid: 1001, https://arxiv.org/pdf/2410.08041.pdf

Abstract:
Kolmogorov--Arnold Networks (KANs), a recently proposed neural network architecture, have gained significant attention in the deep learning community, due to their potential as a viable alternative to multi-layer perceptrons (MLPs) and their broad applicability to various scientific tasks. Empirical investigations demonstrate that KANs optimized via stochastic gradient descent (SGD) are capable of achieving near-zero training loss in various machine learning (e.g., regression, classification, and time series forecasting, etc.) and scientific tasks (e.g., solving partial differential equations). In this paper, we provide a theoretical explanation for the empirical success by conducting a rigorous convergence analysis of gradient descent (GD) and SGD for two-layer KANs in solving both regression and physics-informed tasks. For regression problems, we establish using the neural tangent kernel perspective that GD achieves global linear convergence of the objective function when the hidden dimension of KANs is sufficiently large. We further extend these results to SGD, demonstrating a similar global convergence in expectation. Additionally, we analyze the global convergence of GD and SGD for physics-informed KANs, which unveils additional challenges due to the more complex loss structure. This is the first work establishing the global convergence guarantees for GD and SGD applied to optimize KANs and physics-informed KANs.

Paperid: 1002, https://arxiv.org/pdf/2410.01990.pdf

Abstract:
This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its limited insight into the structure of inner and outer functions and the large number of unknown variables it introduces. Kolmogorov-Arnold Networks (KANs) leverage KST for function approximation, but they have faced scrutiny due to mixed results compared to traditional multilayer perceptrons (MLPs) and practical limitations imposed by the original KST formulation. To address these issues, we introduce ActNet, a scalable deep learning model that builds on the KST and overcomes many of the drawbacks of Kolmogorov's original formulation. We evaluate ActNet in the context of Physics-Informed Neural Networks (PINNs), a framework well-suited for leveraging KST's strengths in low-dimensional function approximation, particularly for simulating partial differential equations (PDEs). In this challenging setting, where models must learn latent functions without direct measurements, ActNet consistently outperforms KANs across multiple benchmarks and is competitive against the current best MLP-based approaches. These results present ActNet as a promising new direction for KST-based deep learning applications, particularly in scientific computing and PDE simulation tasks.

Paperid: 1003, https://arxiv.org/pdf/2410.01340.pdf

Abstract:
The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based principles and can be derived from corresponding governing equations, often of differential equation form. However, complex system characteristics, such as nonlinearities and energy dissipation mechanisms, often imply that such models are approximative and often imprecise. This challenge is further compounded in SHM, where sensor data is often sparse, making it difficult to fully observe the system's states. To address these issues, this paper explores the use of Physics-Informed Neural Networks (PINNs), a class of physics-enhanced machine learning (PEML) techniques, for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena, even in the presence of uncertainties. This study specifically investigates three key applications of PINNs: state estimation in systems with sparse sensing, joint state-parameter estimation, when both system response and parameters are unknown, and parameter estimation within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors. However, these errors tend to have a more significant impact on parameter estimation, as the optimization process must reconcile discrepancies between the prescribed model and the true system behavior. Despite these challenges, PINNs show promise in dynamical system modeling, offering a robust approach to handling uncertainties.

Paperid: 1004, https://arxiv.org/pdf/2410.00278.pdf

Abstract:
We propose a method utilizing physics-informed neural networks (PINNs) to solve Poisson equations that serve as control variates in the computation of transport coefficients via fluctuation formulas, such as the Green--Kubo and generalized Einstein-like formulas. By leveraging approximate solutions to the Poisson equation constructed through neural networks, our approach significantly reduces the variance of the estimator at hand. We provide an extensive numerical analysis of the estimators and detail a methodology for training neural networks to solve these Poisson equations. The approximate solutions are then incorporated into Monte Carlo simulations as effective control variates, demonstrating the suitability of the method for moderately high-dimensional problems where fully deterministic solutions are computationally infeasible.

Paperid: 1005, https://arxiv.org/pdf/2409.17938.pdf

Abstract:
We consider the subcritical nonlinear SchrÃ¶dinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximation of NLS solutions from the numerical and theoretical point of view in the case of bounded domains. In this paper, we introduce a new PINNs method to treat the case of unbounded domains and show rigorous bounds on the associated approximation error in terms of the energy and Strichartz norms, provided a reasonable integration scheme is available. Applications to traveling waves, breathers and solitons, as well as numerical experiments confirming the validity of the approximation are also presented as well.

Paperid: 1006, https://arxiv.org/pdf/2409.13185.pdf

Abstract:
Solving Singularly Perturbed Differential Equations (SPDEs) presents challenges due to the rapid change of their solutions at the boundary layer. In this manuscript, We propose Asymptotic Physics-Informed Neural Networks (ASPINN), a generalization of Physics-Informed Neural Networks (PINN) and General-Kindred Physics-Informed Neural Networks (GKPINN) approaches. This is a decomposition method based on the idea of asymptotic analysis. Compared to PINN, the ASPINN method has a strong fitting ability for solving SPDEs due to the placement of exponential layers at the boundary layer. Unlike GKPINN, ASPINN lessens the number of fully connected layers, thereby reducing the training cost more effectively. Moreover, ASPINN theoretically approximates the solution at the boundary layer more accurately, which accuracy is also improved compared to GKPINN. We demonstrate the effect of ASPINN by solving diverse classes of SPDEs, which clearly shows that the ASPINN method is promising in boundary layer problems. Furthermore, we introduce Chebyshev Kolmogorov-Arnold Networks (Chebyshev-KAN) instead of MLP, achieving better performance in various experiments.

Paperid: 1007, https://arxiv.org/pdf/2409.10911.pdf

Abstract:
The high-pressure transportation process of pipeline necessitates an accurate hydraulic transient simulation tool to prevent slack line flow and over-pressure, which can endanger pipeline operations. However, current numerical solution methods often face difficulties in balancing computational efficiency and accuracy. Additionally, few studies attempt to reform physics-informed learning architecture for pipeline transient simulation with magnitude different in outputs and imbalanced gradient in loss function. To address these challenges, a Knowledge-Inspired Hierarchical Physics-Informed Neural Network is proposed for hydraulic transient simulation of multi-product pipelines. The proposed model integrates governing equations, boundary conditions, and initial conditions into the training process to ensure consistency with physical laws. Furthermore, magnitude conversion of outputs and equivalent conversion of governing equations are implemented to enhance the training performance of the neural network. To further address the imbalanced gradient of multiple loss terms with fixed weights, a hierarchical training strategy is designed. Numerical simulations demonstrate that the proposed model outperforms state-of-the-art models and can still produce accurate simulation results under complex hydraulic transient conditions, with mean absolute percentage errors reduced by 87.8\% and 92.7 \% in pressure prediction. Thus, the proposed model can conduct accurate and effective hydraulic transient analysis, ensuring the safe operation of pipelines.

Paperid: 1008, https://arxiv.org/pdf/2409.08799.pdf

Abstract:
In this paper, we present two computational methods for performing simulations of pollution propagation described by advection-diffusion equations. The first method employs graph grammars to describe the generation process of the computational mesh used in simulations with the meshless solver of the three-dimensional finite element method. The graph transformation rules express the three-dimensional Rivara longest-edge refinement algorithm. This solver is used for an exemplary application: performing three-dimensional simulations of pollution generation by the coal-burning power plant and its propagation in the city of Longyearbyen, the capital of Spitsbergen. The second computational code is based on the Physics Informed Neural Networks method. It is used to calculate the dissipation of the pollution along the valley in which the city of Longyearbyen is located. We discuss the instantiation and execution of the PINN method using Google Colab implementation. We discuss the benefits and limitations of the PINN implementation.

Paperid: 1009, https://arxiv.org/pdf/2409.04143.pdf

Abstract:
Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use the variational form of the PDE residuals in their loss function. Although hp-VPINNs have shown promise over traditional PINNs, they suffer from higher training times and lack a framework capable of handling complex geometries, which limits their application to more complex PDEs. As such, hp-VPINNs have not been applied in solving the Navier-Stokes equations, amongst other problems in CFD, thus far. FastVPINNs was introduced to address these challenges by incorporating tensor-based loss computations, significantly improving the training efficiency. Moreover, by using the bilinear transformation, the FastVPINNs framework was able to solve PDEs on complex geometries. In the present work, we extend the FastVPINNs framework to vector-valued problems, with a particular focus on solving the incompressible Navier-Stokes equations for two-dimensional forward and inverse problems, including problems such as the lid-driven cavity flow, the Kovasznay flow, and flow past a backward-facing step for Reynolds numbers up to 200. Our results demonstrate a 2x improvement in training time while maintaining the same order of accuracy compared to PINNs algorithms documented in the literature. We further showcase the framework's efficiency in solving inverse problems for the incompressible Navier-Stokes equations by accurately identifying the Reynolds number of the underlying flow. Additionally, the framework's ability to handle complex geometries highlights its potential for broader applications in computational fluid dynamics. This implementation opens new avenues for research on hp-VPINNs, potentially extending their applicability to more complex problems.

Paperid: 1010, https://arxiv.org/pdf/2409.01536.pdf

Abstract:
Compared to purely data-driven methods, a key feature of physics-informed neural networks (PINNs) - a proven powerful tool for solving partial differential equations (PDEs) - is the embedding of PDE constraints into the loss function. The selection and distribution of collocation points for evaluating PDE residuals are critical to the performance of PINNs. Furthermore, the causal training is currently a popular training mode. In this work, we propose the causality-guided adaptive sampling (Causal AS) method for PINNs. Given the characteristics of causal training, we use the weighted PDE residuals as the indicator for the selection of collocation points to focus on areas with larger PDE residuals within the regions being trained. For the hyper-parameter $p$ involved, we develop the temporal alignment driven update (TADU) scheme for its dynamic update beyond simply fixing it as a constant. The collocation points selected at each time will be released before the next adaptive sampling step to avoid the cumulative effects caused by previously chosen collocation points and reduce computational costs. To illustrate the effectiveness of the Causal AS method, we apply it to solve time-dependent equations, including the Allen-Cahn equation, the NLS equation, the KdV equation and the mKdV equation. During the training process, we employe a time-marching technique and strictly impose the periodic boundary conditions by embedding the input coordinates into Fourier expansion to mitigate optimization challenges. Numerical results indicate that the predicted solution achieves an excellent agreement with the ground truth. Compared to a similar work, the causal extension of R3 sampling (Causal R3), our proposed Causal AS method demonstrates a significant advantage in accuracy.

Paperid: 1011, https://arxiv.org/pdf/2601.12971.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs) by embedding governing physical laws into neural network training. In practice, however, their performance is often hindered by limited representational capacity and optimization difficulties caused by competing physical constraints and conflicting gradients. In this work, we study PINN training from a unified architecture-optimization perspective. We first propose a layer-wise dynamic attention mechanism to enhance representational flexibility, resulting in the Layer-wise Dynamic Attention PINN (LDA-PINN). We then reformulate PINN training as a multi-task learning problem and introduce a conflict-resolved gradient update strategy to alleviate gradient interference, leading to the Gradient-Conflict-Resolved PINN (GC-PINN). By integrating these two components, we develop the Architecture-Conflict-Resolved PINN (ACR-PINN), which combines attentive representations with conflict-aware optimization while preserving the standard PINN loss formulation. Extensive experiments on benchmark PDEs, including the Burgers, Helmholtz, Klein-Gordon, and lid-driven cavity flow problems, demonstrate that ACR-PINN achieves faster convergence and significantly lower relative $L_2$ and $L_\infty$ errors than standard PINNs. These results highlight the effectiveness of architecture-optimization co-design for improving the robustness and accuracy of PINN-based solvers.

Paperid: 1012, https://arxiv.org/pdf/2601.11794.pdf

Abstract:
Wildfire monitoring requires high-resolution atmospheric measurements, yet low-cost sensors on Unmanned Aerial Vehicles (UAVs) exhibit baseline drift, cross-sensitivity, and response lag that corrupt concentration estimates. Traditional deep learning denoising approaches demand large datasets impractical to obtain from limited UAV flight campaigns. We present PC$^2$DAE, a physics-informed denoising autoencoder that addresses data scarcity by embedding physical constraints directly into the network architecture. Non-negative concentration estimates are enforced via softplus activations and physically plausible temporal smoothing, ensuring outputs are physically admissible by construction rather than relying on loss function penalties. The architecture employs hierarchical decoder heads for Black Carbon, Gas, and CO$_2$ sensor families, with two variants: PC$^2$DAE-Lean (21k parameters) for edge deployment and PC$^2$DAE-Wide (204k parameters) for offline processing. We evaluate on 7,894 synchronized 1 Hz samples collected from UAV flights during prescribed burns in Saskatchewan, Canada (approximately 2.2 hours of flight data), two orders of magnitude below typical deep learning requirements. PC$^2$DAE-Lean achieves 67.3\% smoothness improvement and 90.7\% high-frequency noise reduction with zero physics violations. Five baselines (LSTM-AE, U-Net, Transformer, CBDAE, DeSpaWN) produce 15--23\% negative outputs. The lean variant outperforms wide (+5.6\% smoothness), suggesting reduced capacity with strong inductive bias prevents overfitting in data-scarce regimes. Training completes in under 65 seconds on consumer hardware.

Paperid: 1013, https://arxiv.org/pdf/2601.07687.pdf

Abstract:
A new wave of work on covariance cleaning and nonlinear shrinkage has delivered asymptotically optimal analytical solutions for large covariance matrices. The same framework has been generalized to empirical cross-covariance matrices, whose singular value decomposition identifies canonical comovement modes between two asset sets, with singular values quantifying the strength of each mode and providing natural targets for shrinkage. Existing analytical cross-covariance cleaners are derived under strong stationarity and large-sample assumptions, and they typically rely on mesoscopic regularity conditions such as bounded spectra; macroscopic common modes (e.g., a global market factor) violate these conditions. When applied to real equity returns, where dependence structures drift over time and global modes are prominent, we find that these theoretically optimal formulas do not translate into robust out-of-sample performance. We address this gap by designing a random-matrix-inspired neural architecture that operates in the empirical singular-vector basis and learns a nonlinear mapping from empirical singular values to their corresponding cleaned values. By construction, the network can recover the analytical solution as a special case, yet it remains flexible enough to adapt to non-stationary dynamics and mode-driven distortions. Trained on a long history of equity returns, the proposed method achieves a more favorable bias-variance trade-off than purely analytical cleaners and delivers systematically lower out-of-sample cross-covariance prediction errors. Our results demonstrate that combining random-matrix theory with machine learning makes asymptotic theories practically effective in realistic time-varying markets.

Paperid: 1014, https://arxiv.org/pdf/2512.23884.pdf

Abstract:
Accurate modeling of scrape-off layer (SOL) and divertor-edge dynamics is vital for designing plasma-facing components in fusion devices. High-fidelity edge fluid/neutral codes such as SOLPS-ITER capture SOL physics with high accuracy, but their computational cost limits broad parameter scans and long transient studies. We present transformer-based, autoregressive surrogates for efficient prediction of 2D, time-dependent plasma edge state fields. Trained on SOLPS-ITER spatiotemporal data, the surrogates forecast electron temperature, electron density, and radiated power over extended horizons. We evaluate model variants trained with increasing autoregressive horizons (1-100 steps) on short- and long-horizon prediction tasks. Longer-horizon training systematically improves rollout stability and mitigates error accumulation, enabling stable predictions over hundreds to thousands of steps and reproducing key dynamical features such as the motion of high-radiation regions. Measured end-to-end wall-clock times show the surrogate is orders of magnitude faster than SOLPS-ITER, enabling rapid parameter exploration. Prediction accuracy degrades when the surrogate enters physical regimes not represented in the training dataset, motivating future work on data enrichment and physics-informed constraints. Overall, this approach provides a fast, accurate surrogate for computationally intensive plasma edge simulations, supporting rapid scenario exploration, control-oriented studies, and progress toward real-time applications in fusion devices.

Paperid: 1015, https://arxiv.org/pdf/2512.22381.pdf

Abstract:
The rapid deployment of electric vehicle charging stations (EVCS) within distribution networks necessitates intelligent and adaptive control to maintain the grid's resilience and reliability. In this work, we propose PHANTOM, a physics-aware adversarial network that is trained and optimized through a multi-agent reinforcement learning model. PHANTOM integrates a physics-informed neural network (PINN) enabled by federated learning (FL) that functions as a digital twin of EVCS-integrated systems, ensuring physically consistent modeling of operational dynamics and constraints. Building on this digital twin, we construct a multi-agent RL environment that utilizes deep Q-networks (DQN) and soft actor-critic (SAC) methods to derive adversarial false data injection (FDI) strategies capable of bypassing conventional detection mechanisms. To examine the broader grid-level consequences, a transmission and distribution (T and D) dual simulation platform is developed, allowing us to capture cascading interactions between EVCS disturbances at the distribution level and the operations of the bulk transmission system. Results demonstrate how learned attack policies disrupt load balancing and induce voltage instabilities that propagate across T and D boundaries. These findings highlight the critical need for physics-aware cybersecurity to ensure the resilience of large-scale vehicle-grid integration.

Paperid: 1016, https://arxiv.org/pdf/2512.21043.pdf

Abstract:
Regulating grasping force to reduce slippage during dynamic object interaction remains a fundamental challenge in robotic manipulation, especially when objects are manipulated by multiple rolling contacts, have unknown properties (such as mass or surface conditions), and when external sensing is unreliable. In contrast, humans can quickly regulate grasping force by touch, even without visual cues. Inspired by this ability, we aim to enable robotic hands to rapidly explore objects and learn tactile-driven grasping force control under motion and limited sensing. We propose a physics-informed energy abstraction that models the object as a virtual energy container. The inconsistency between the fingers' applied power and the object's retained energy provides a physically grounded signal for inferring slip-aware stability. Building on this abstraction, we employ model-based learning and planning to efficiently model energy dynamics from tactile sensing and perform real-time grasping force optimization. Experiments in both simulation and hardware demonstrate that our method can learn grasping force control from scratch within minutes, effectively reduce slippage, and extend grasp duration across diverse motion-object pairs, all without relying on external sensing or prior object knowledge.

Paperid: 1017, https://arxiv.org/pdf/2512.17852.pdf

Abstract:
Raman spectroscopy enables non-destructive, label-free molecular analysis with high specificity, making it a powerful tool for biomedical diagnostics. However, its application to biological tissues is challenged by inherently weak Raman scattering and strong fluorescence background, which significantly degrade signal quality. In this study, we present a simulation-driven denoising framework that combines a statistically grounded noise model with deep learning to enhance Raman spectra acquired under fluorescence-dominated conditions. We comprehensively modeled major noise sources. Based on this model, we generated biologically realistic Raman spectra and used them to train a cascaded deep neural network designed to jointly suppress stochastic detector noise and fluorescence baseline interference. To evaluate the performance of our approach, we simulated human skin spectra derived from real experimental data as a validation case study. Our results demonstrate the potential of physics-informed learning to improve spectral quality and enable faster, more accurate Raman-based tissue analysis.

Paperid: 1018, https://arxiv.org/pdf/2512.16175.pdf

Abstract:
Understanding the magnetic field environment around Mars and its response to upstream solar wind conditions provide key insights into the processes driving atmospheric ion escape. To date, global models of Martian induced magnetosphere have been exclusively physics-based, relying on computationally intensive simulations. For the first time, we develop a data-driven model of the Martian induced magnetospheric magnetic field using Physics-Informed Neural Network (PINN) combined with MAVEN observations and physical laws. Trained under varying solar wind conditions, including B_IMF, P_SW, and θ_cone, the data-driven model accurately reconstructs the three-dimensional magnetic field configuration and its variability in response to upstream solar wind drivers. Based on the PINN results, we identify key dependencies of magnetic field configuration on solar wind parameters, including the hemispheric asymmetries of the draped field line strength in the Mars-Solar-Electric coordinates. These findings demonstrate the capability of PINNs to reconstruct complex magnetic field structures in the Martian induced magnetosphere, thereby offering a promising tool for advancing studies of solar wind-Mars interactions.

Paperid: 1019, https://arxiv.org/pdf/2512.13336.pdf

Abstract:
This work introduces Knowledge-Distilled Physics-Informed Neural Networks (KD-PINN), a framework that transfers the predictive accuracy of a high-capacity teacher model to a compact student through a continuous adaptation of the Kullback-Leibler divergence. In order to confirm its generality for various dynamics and dimensionalities, the framework is evaluated on a representative set of partial differential equations (PDEs). Across the considered benchmarks, the student model achieves inference speedups ranging from x4.8 (Navier-Stokes) to x6.9 (Burgers), while preserving accuracy. Accuracy is improved by on the order of 1% when the model is properly tuned. The distillation process also revealed a regularizing effect. With an average inference latency of 5.3 ms on CPU, the distilled models enter the ultra-low-latency real-time regime defined by sub-10 ms performance. Finally, this study examines how knowledge distillation reduces inference latency in PINNs, to contribute to the development of accurate ultra-low-latency neural PDE solvers.

Paperid: 1020, https://arxiv.org/pdf/2512.12888.pdf

Abstract:
Advancing artificial intelligence for physical sciences requires representations that are both interpretable and compatible with the underlying laws of nature. We introduce METASTRINGS, a symbolic language for photonics that expresses nanostructures as textual sequences encoding materials, geometries, and lattice configurations. Analogous to molecular textual representations in chemistry, METASTRINGS provides a framework connecting human interpretability with computational design by capturing the structural hierarchy of photonic metasurfaces. Building on this representation, we develop Meta-GPT, a foundation transformer model trained on METASTRINGS and finetuned with physics-informed supervised, reinforcement, and chain-of-thought learning. Across various design tasks, the model achieves <3% mean-squared spectral error and maintains >98% syntactic validity, generating diverse metasurface prototypes whose experimentally measured optical responses match their target spectra. These results demonstrate that Meta-GPT can learn the compositional rules of light-matter interactions through METASTRINGS, laying a rigorous foundation for AI-driven photonics and representing an important step toward a metasurface genome project.

Paperid: 1021, https://arxiv.org/pdf/2512.08256.pdf

Abstract:
This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory behavior. Traditional physics-informed neural networks (PINNs) have demonstrated substantial potential in solving differential equations, and their quantum counterparts, quantum-PINNs, exhibit enhanced representational capacity with fewer trainable parameters. However, both approaches face notable challenges in accurately solving multiscale features. Furthermore, their reliance on automatic differentiation for constructing loss functions introduces considerable computational overhead, resulting in longer training times. To overcome these challenges, we developed a wavelet-accelerated physics-informed quantum neural network that eliminates the need for automatic differentiation, significantly reducing computational complexity. The proposed framework incorporates the multiresolution property of wavelets within the quantum neural network architecture, thereby enhancing the network's ability to effectively capture both local and global features of multiscale problems. Numerical experiments demonstrate that our proposed method achieves superior accuracy while requiring less than five percent of the trainable parameters compared to classical wavelet-based PINNs, resulting in faster convergence. Moreover, it offers a speedup of three to five times compared to existing quantum PINNs, highlighting the potential of the proposed approach for efficiently solving challenging multiscale and oscillatory problems.

Paperid: 1022, https://arxiv.org/pdf/2512.07755.pdf

Abstract:
Recent studies have shown the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). In the fields of atmospheric science and environmental monitoring, estimating emission source locations is a central task that further relies on multiple model parameters that dictate velocity profiles and diffusion parameters. Estimating these parameters at the same time as emission sources from scarce data is a difficult task. In this work, we achieve this by leveraging the flexibility and generality of PINNs. We use a weighted adaptive method based on the neural tangent kernels to solve a source inversion problem with parameter estimation on the 2D and 3D advection-diffusion equations with unknown velocity and diffusion coefficients that may vary in space and time. Our proposed weighted adaptive method is presented as an extension of PINNs for forward PDE problems to a highly ill-posed source inversion and parameter estimation problem. The key idea behind our methodology is to attempt the joint recovery of the solution, the sources along with the unknown parameters, thereby using the underlying partial differential equation as a constraint that couples multiple unknown functional parameters, leading to more efficient use of the limited information in the measurements. We present various numerical experiments, using different types of measurements that model practical engineering systems, to show that our proposed method is indeed successful and robust to additional noise in the measurements.

Paperid: 1023, https://arxiv.org/pdf/2512.06268.pdf

Abstract:
Unlike traditional multi-agent coordination frameworks, which assume a fixed number of agents, UAS traffic management (UTM) requires a platform that enables Uncrewed Aerial Systems (UAS) to freely enter or exit constrained low-altitude airspace. Consequently, the number of UAS operating in a given region is time-varying, with vehicles dynamically joining or leaving even in dense, obstacle-laden environments. The primary goal of this paper is to develop a computationally efficient management system that maximizes airspace usability while ensuring safety and efficiency. To achieve this, we first introduce physics-informed methods to structure fixed skyroads across multiple altitude layers of urban airspace, with the directionality of each skyroad designed to guarantee full reachability. We then present a novel Continuous UTM (C-UTM) framework that optimally allocates skyroads to UAS requests while accounting for the time-varying capacity of the airspace. Collectively, the proposed model addresses the key challenges of low-altitude UTM by providing a scalable, safe, and efficient solution for urban airspace usability.

Paperid: 1024, https://arxiv.org/pdf/2512.06134.pdf

Abstract:
Early forecasting of individual cognitive decline in Alzheimer's disease (AD) is central to disease evaluation and management. Despite advances, it is as of yet challenging for existing methodological frameworks to integrate multimodal data for longitudinal personalized forecasting while maintaining interpretability. To address this gap, we present the Neural Koopman Machine (NKM), a new machine learning architecture inspired by dynamical systems and attention mechanisms, designed to forecast multiple cognitive scores simultaneously using multimodal genetic, neuroimaging, proteomic, and demographic data. NKM integrates analytical ($α$) and biological ($β$) knowledge to guide feature grouping and control the hierarchical attention mechanisms to extract relevant patterns. By implementing Fusion Group-Aware Hierarchical Attention within the Koopman operator framework, NKM transforms complex nonlinear trajectories into interpretable linear representations. To demonstrate NKM's efficacy, we applied it to study the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. Our results suggest that NKM consistently outperforms both traditional machine learning methods and deep learning models in forecasting trajectories of cognitive decline. Specifically, NKM (1) forecasts changes of multiple cognitive scores simultaneously, (2) quantifies differential biomarker contributions to predicting distinctive cognitive scores, and (3) identifies brain regions most predictive of cognitive deterioration. Together, NKM advances personalized, interpretable forecasting of future cognitive decline in AD using past multimodal data through an explainable, explicit system and reveals potential multimodal biological underpinnings of AD progression.

Paperid: 1025, https://arxiv.org/pdf/2512.01062.pdf

Abstract:
Precipitation nowcasting, key for early warning of disasters, currently relies on computationally expensive and restrictive methods that limit access to many countries. To overcome this challenge, we propose precipitation nowcasting using satellite imagery with physics constraints for improved accuracy and physical consistency. We use a novel physics-informed dual neural operator (PIANO) structure to enforce the fundamental equation of advection-diffusion during training to predict satellite imagery using a PINN loss. Then, we use a generative model to convert satellite images to radar images, which are used for precipitation nowcasting. Compared to baseline models, our proposed model shows a notable improvement in moderate (4mm/h) precipitation event prediction alongside short-term heavy (8mm/h) precipitation event prediction. It also demonstrates low seasonal variability in predictions, indicating robustness for generalization. This study suggests the potential of the PIANO and serves as a good baseline for physics-informed precipitation nowcasting.

Paperid: 1026, https://arxiv.org/pdf/2511.23449.pdf

Abstract:
Inverse heat problems refer to the estimation of material thermophysical properties given observed or known heat diffusion behaviour. Inverse heat problems have wide-ranging uses, but a critical application lies in quantifying how building facade renovation reduces thermal transmittance, a key determinant of building energy efficiency. However, solving inverse heat problems with non-invasive data collected in situ is error-prone due to environmental variability or deviations from theoretically assumed conditions. Hence, current methods for measuring thermal conductivity are either invasive, require lengthy observation periods, or are sensitive to environmental and experimental conditions. Here, we present a PINN-based iterative framework to estimate the thermal conductivity k of a wall from a set of thermographs; our framework alternates between estimating the forward heat problem with a PINN for a fixed k, and optimizing k by comparing the thermographs and surface temperatures predicted by the PINN, repeating until the estimated k's convergence. Using both environmental data captured by a weather station and data generated from Finite-Volume-Method software simulations, we accurately predict k across different environmental conditions and data collection sampling times, given the temperature profile of the wall at dawn is close to steady state. Although violating the steady-state assumption impacts the accuracy of k's estimation, we show that our proposed framework still only exhibits a maximum MAE of 4.0851. Our work demonstrates the potential of PINN-based methods for reliable estimation of material properties in situ and under realistic conditions, without lengthy measurement campaigns. Given the lack of research on using machine learning, and more specifically on PINNs, for solving in-situ inverse problems, we expect our work to be a starting point for more research on the topic.

Paperid: 1027, https://arxiv.org/pdf/2511.23405.pdf

Abstract:
Underwater object tracking is challenging due to wavelength dependent attenuation and scattering, which severely distort appearance across depths and water conditions. Existing trackers trained on terrestrial data fail to generalize to these physics-driven degradations. We present MANTA, a physics-informed framework integrating representation learning with tracking design for underwater scenarios. We propose a dual-positive contrastive learning strategy coupling temporal consistency with Beer-Lambert augmentations to yield features robust to both temporal and underwater distortions. We further introduce a multi-stage pipeline augmenting motion-based tracking with a physics-informed secondary association algorithm that integrates geometric consistency and appearance similarity for re-identification under occlusion and drift. To complement standard IoU metrics, we propose Center-Scale Consistency (CSC) and Geometric Alignment Score (GAS) to assess geometric fidelity. Experiments on four underwater benchmarks (WebUOT-1M, UOT32, UTB180, UWCOT220) show that MANTA achieves state-of-the-art performance, improving Success AUC by up to 6 percent, while ensuring stable long-term generalized underwater tracking and efficient runtime.

Paperid: 1028, https://arxiv.org/pdf/2511.18515.pdf

Abstract:
Physics-informed neural networks (PINNs) typically minimize average residuals, which can conceal large, localized errors. We propose Residual Risk-Aware Physics-Informed Neural Networks PINNs (RRaPINNs), a single-network framework that optimizes tail-focused objectives using Conditional Value-at-Risk (CVaR), we also introduced a Mean-Excess (ME) surrogate penalty to directly control worst-case PDE residuals. This casts PINN training as risk-sensitive optimization and links it to chance-constrained formulations. The method is effective and simple to implement. Across several partial differential equations (PDEs) such as Burgers, Heat, Korteweg-de-Vries, and Poisson (including a Poisson interface problem with a source jump at x=0.5) equations, RRaPINNs reduce tail residuals while maintaining or improving mean errors compared to vanilla PINNs, Residual-Based Attention and its variant using convolution weighting; the ME surrogate yields smoother optimization than a direct CVaR hinge. The chance constraint reliability level $α$ acts as a transparent knob trading bulk accuracy (lower $α$ ) for stricter tail control (higher $α$ ). We discuss the framework limitations, including memoryless sampling, global-only tail budgeting, and residual-centric risk, and outline remedies via persistent hard-point replay, local risk budgets, and multi-objective risk over BC/IC terms. RRaPINNs offer a practical path to reliability-aware scientific ML for both smooth and discontinuous PDEs.

Paperid: 1029, https://arxiv.org/pdf/2511.16019.pdf

Abstract:
Reconstructing complete traffic flow time-space diagrams from vehicle trajectories offer a comprehensive view on traffic dynamics at arterial intersections. However, obtaining full trajectories across networks is costly, and accurately inferring lane-changing (LC) and car-following behaviors in multi-lane environments remains challenging. This study proposes a generative framework for arterial vehicle trajectory reconstruction that jointly models lane-changing and car-following behaviors through physics-informed multi-task joint learning. The framework consists of a Lane-Change Generative Adversarial Network (LC-GAN) and a Trajectory-GAN. The LC-GAN models stochastic LC behavior from historical trajectories while considering physical conditions of arterial intersections, such as signal control, geometric configuration, and interactions with surrounding vehicles. The Trajectory-GAN then incorporates LC information from the LC-GAN with initial trajectories generated from physics-based car-following models, refining them in a data-driven manner to adapt to dynamic traffic conditions. The proposed framework is designed to reconstruct complete trajectories from only a small subset of connected vehicle (CV) trajectories; for example, even a single observed trajectory per lane, by incorporating partial trajectory information into the generative process. A multi-task joint learning facilitates synergistic interaction between the LC-GAN and Trajectory-GAN, allowing each component to serves as both auxiliary supervision and a physical condition for the other. Validation using two real-world trajectory datasets demonstrates that the framework outperforms conventional benchmark models in reconstructing complete time-space diagrams for multi-lane arterial intersections. This research advances the integration of trajectory-based sensing from CVs with physics-informed deep learning.

Paperid: 1030, https://arxiv.org/pdf/2511.13745.pdf

Abstract:
This study presents a novel deep learning approach aimed at enhancing stochastic Gust Load Alleviation (GLA) specifically for compliant wings. The approach incorporates the concept of smooth wing camber variation, where the camber of the wing's chord is actively adjusted during flight using a control signal to achieve the desired aerodynamic loading. The proposed method employs a deep learning-based model predictive controller designed for probability density shaping. This controller effectively solves the probability density evolution equation through a custom Physics-Informed Neural Network (PINN) and utilizes Automatic Differentiation for Model Predictive Control (MPC) optimization. Comprehensive numerical simulations were conducted on a compliant wing (CW) model, evaluating performance of the proposed approach against stochastic gust profiles. The evaluation involved stochastic aerodynamic loads generated from Band-Limited White Noise (BLWN) and Dryden gust models. The evaluation were conducted for two distinct Compliant Chord Fractions (CCF). The results demonstrate the effectiveness of the proposed probability density shaping model predictive control in alleviating stochastic gust load and reducing wing tip deflection.

Paperid: 1031, https://arxiv.org/pdf/2511.13178.pdf

Abstract:
With the development of digital twins and smart manufacturing systems, there is an urgent need for real-time distortion field prediction to control defects in metal Additive Manufacturing (AM). However, numerical simulation methods suffer from high computational cost, long run-times that prevent real-time use, while conventional Machine learning (ML) models struggle to extract spatiotemporal features for long-horizon prediction and fail to decouple thermo-mechanical fields. This paper proposes a Physics-informed Neural Operator (PINO) to predict z and y-direction distortion for the future 15 s. Our method, Physics-informed Deep Operator Network-Recurrent Neural Network (PIDeepONet-RNN) employs trunk and branch network to process temperature history and encode distortion fields, respectively, enabling decoupling of thermo-mechanical responses. By incorporating the heat conduction equation as a soft constraint, the model ensures physical consistency and suppresses unphysical artifacts, thereby establishing a more physically consistent mapping between the thermal history and distortion. This is important because such a basis function, grounded in physical laws, provides a robust and interpretable foundation for predictions. The proposed models are trained and tested using datasets generated from experimentally validated Finite Element Method (FEM). Evaluation shows that the model achieves high accuracy, low error accumulation, time efficiency. The max absolute errors in the z and y-directions are as low as 0.9733 mm and 0.2049 mm, respectively. The error distribution shows high errors in the molten pool but low gradient norms in the deposited and key areas. The performance of PINO surrogate model highlights its potential for real-time long-horizon physics field prediction in controlling defects.

Paperid: 1032, https://arxiv.org/pdf/2511.11613.pdf

Abstract:
Buried pipelines transporting oil and gas across geohazard-prone regions are exposed to potential ground movement, leading to the risk of significant strain demand and structural failure. Reliability analysis, which determines the probability of failure after accounting for pertinent uncertainties, is essential for ensuring the safety of pipeline systems. However, traditional reliability analysis methods involving computationally intensive numerical models, such as finite element simulations of pipeline subjected to ground movement, have limited applications; this is partly because stochastic sampling approaches require repeated simulations over a large number of samples for the uncertain variables when estimating low probabilities. This study introduces Physics-Informed Neural Network for Reliability Analysis (PINN-RA) for buried pipelines subjected to ground movement, which integrates PINN-based surrogate model with Monte Carlo Simulation (MCS) to achieve efficient reliability assessment. To enable its application under uncertain variables associated with soil properties and ground movement, the PINN-based surrogate model is extended to solve a parametric differential equation system, namely the governing equation of pipelines embedded in soil with different properties. The findings demonstrate that PINN-RA significantly reduces the computational effort required and thus accelerates reliability analysis. By eliminating the need for repetitive numerical evaluations of pipeline subjected to permanent ground movement, the proposed approach provides an efficient and scalable tool for pipeline reliability assessment, enabling rapid decision-making in geohazard-prone regions.

Paperid: 1033, https://arxiv.org/pdf/2511.11228.pdf

Abstract:
In this work, we propose a modified Hybrid Parallel Kolmogorov--Arnold Network and Multilayer Perceptron Physics-Informed Neural Network to overcome the high-frequency and multiscale challenges inherent in Physics-Informed Neural Networks. This proposed model features a trainable weighting parameter to optimize the convex combination of outputs from the Kolmogorov--Arnold Network and the Multilayer Perceptron, thus maximizing the networks' capabilities to capture different frequency components. Furthermore, we adopt an overlapping domain decomposition technique to decompose complex problems into subproblems, which alleviates the challenge of global optimization. Benchmark results demonstrate that our method reduces training costs and improves computational efficiency compared with manual hyperparameter tuning in solving high-frequency multiscale problems.

Paperid: 1034, https://arxiv.org/pdf/2511.07702.pdf

Abstract:
Multidimensional optimization has consistently been a critical challenge in engineering. However, traditional simulation-based optimization methods have long been plagued by significant limitations: they are typically capable of optimizing only a single problem at a time and require substantial computational time for meshing and numerical simulation. This paper introduces a novel framework leveraging cutting-edge Scientific Machine Learning (Sci-ML) methodologies to overcome these inherent drawbacks of conventional approaches. The proposed method provides instantaneous solutions to a spectrum of complex, multidimensional optimization problems. A micromixer case study is employed to demonstrate this methodology. An agent, operating on a Deep Reinforcement Learning (DRL) architecture, serves as the optimizer to explore the relationships between key problem parameters. This optimizer interacts with an environment constituted by a parametric Physics-Informed Neural Network (PINN), which responds to the agent's actions at a significantly higher speed than traditional numerical methods. The agent's objective, conditioned on the Schmidt number is to discover the optimal geometric and physical parameters that maximize the micromixer's efficiency. After training the agent across a wide range of Schmidt numbers, we analyzed the resulting optimal designs. Across this entire spectrum, the achieved efficiency was consistently greater than the baseline, normalized value. The maximum efficiency occurred at a Schmidt number of 13.3, demonstrating an improvement of approximately 32%. Finally, a comparative analysis with a Genetic Algorithm was conducted under equivalent conditions to underscore the advantages of the proposed method.

Paperid: 1035, https://arxiv.org/pdf/2511.06853.pdf

Abstract:
The resolving ability of wide-field fluorescence microscopy is fundamentally limited by out-of-focus background owing to its low axial resolution, particularly for densely labeled biological samples. To address this, we developed ET2dNet, a deep learning-based EPI-TIRF cross-modality network that achieves TIRF-comparable background subtraction and axial super-resolution from a single wide-field image without requiring hardware modifications. The model employs a physics-informed hybrid architecture, synergizing supervised learning with registered EPI-TIRF image pairs and self-supervised physical modeling via convolution with the point spread function. This framework ensures exceptional generalization across microscope objectives, enabling few-shot adaptation to new imaging setups. Rigorous validation on cellular and tissue samples confirms ET2dNet's superiority in background suppression and axial resolution enhancement, while maintaining compatibility with deconvolution techniques for lateral resolution improvement. Furthermore, by extending this paradigm through knowledge distillation, we developed ET3dNet, a dedicated three-dimensional reconstruction network that produces artifact-reduced volumetric results. ET3dNet effectively removes out-of-focus background signals even when the input image stack lacks the source of background. This framework makes axial super-resolution imaging more accessible by providing an easy-to-deploy algorithm that avoids additional hardware costs and complexity, showing great potential for live cell studies and clinical histopathology.

Paperid: 1036, https://arxiv.org/pdf/2511.06244.pdf

Abstract:
Motion blur, caused by relative movement between camera and scene during exposure, significantly degrades image quality and impairs downstream computer vision tasks such as object detection, tracking, and recognition in dynamic environments. While deep learning-based motion deblurring methods have achieved remarkable progress, existing approaches face fundamental challenges in capturing the long-range spatial dependencies inherent in motion blur patterns. Traditional convolutional methods rely on limited receptive fields and require extremely deep networks to model global spatial relationships. These limitations motivate the need for alternative approaches that incorporate physical priors to guide feature evolution during restoration. In this paper, we propose a progressive training framework that integrates physics-informed PDE dynamics into state-of-the-art restoration architectures. By leveraging advection-diffusion equations to model feature evolution, our approach naturally captures the directional flow characteristics of motion blur while enabling principled global spatial modeling. Our PDE-enhanced deblurring models achieve superior restoration quality with minimal overhead, adding only approximately 1\% to inference GMACs while providing consistent improvements in perceptual quality across multiple state-of-the-art architectures. Comprehensive experiments on standard motion deblurring benchmarks demonstrate that our physics-informed approach improves PSNR and SSIM significantly across four diverse architectures, including FFTformer, NAFNet, Restormer, and Stripformer. These results validate that incorporating mathematical physics principles through PDE-based global layers can enhance deep learning-based image restoration, establishing a promising direction for physics-informed neural network design in computer vision applications.

Paperid: 1037, https://arxiv.org/pdf/2511.06042.pdf

Abstract:
We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement interpolation. During the training stage, we couple the Hamilton-Jacobi (HJ) residual in the OT formulation with the original flow matching loss function. Our approach avoids inner optimization subproblems that are present in previous one-step OFM approaches. During the prediction stage, our approach supports both one-step (Brenier-map) and multi-step ODE sampling from the same learned potential, leveraging the straightness of the OT flow. We validate scalability and performance on standard OT benchmarks.

Paperid: 1038, https://arxiv.org/pdf/2511.04576.pdf

Abstract:
PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter space exploration prohibitively expensive. Recent machine learning advances, particularly physics-informed neural networks (PINNs) and neural operators, have revolutionized parametric PDE solving by learning solution operators that generalize across parameter spaces. We critically analyze two main paradigms: (1) PINNs, which embed physical laws as soft constraints and excel at inverse problems with sparse data, and (2) neural operators (e.g., DeepONet, Fourier Neural Operator), which learn mappings between infinite-dimensional function spaces and achieve unprecedented generalization. Through comparisons across fluid dynamics, solid mechanics, heat transfer, and electromagnetics, we show neural operators can achieve computational speedups of $10^3$ to $10^5$ times faster than traditional solvers for multi-query scenarios, while maintaining comparable accuracy. We provide practical guidance for method selection, discuss theoretical foundations (universal approximation, convergence), and identify critical open challenges: high-dimensional parameters, complex geometries, and out-of-distribution generalization. This work establishes a unified framework for understanding parametric PDE solvers via operator learning, offering a comprehensive, incrementally updated resource for this rapidly evolving field

Paperid: 1039, https://arxiv.org/pdf/2511.03241.pdf

Abstract:
Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or discontinuous. Existing deep learning approaches either require extensive labeled datasets or are limited to specific measurement types, often leading to failure in such regimes and restricting their practical applicability. Here, a novel generative neural operator framework, IGNO, is introduced to overcome these limitations. IGNO unifies the solution of inverse problems from both point measurements and operator-valued data without labeled training pairs. This framework encodes high-dimensional, potentially discontinuous coefficient fields into a low-dimensional latent space, which drives neural operator decoders to reconstruct both coefficients and PDE solutions. Training relies purely on physics constraints through PDE residuals, while inversion proceeds via efficient gradient-based optimization in latent space, accelerated by an a priori normalizing flow model. Across a diverse set of challenging inverse problems, including recovery of discontinuous coefficients from solution-based measurements and the EIT problem with operator-based measurements, IGNO consistently achieves accurate, stable, and scalable inversion even under severe noise. It consistently outperforms the state-of-the-art method under varying noise levels and demonstrates strong generalization to out-of-distribution targets. These results establish IGNO as a unified and powerful framework for tackling challenging inverse problems across computational science domains.

Paperid: 1040, https://arxiv.org/pdf/2511.00043.pdf

Abstract:
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations (ODEs). While traditional numerical methods a re effective for many ODEs, they often struggle to achieve convergence in problems involving high stiffness, shocks, irregular domains, singular perturbations, high dimensions, or boundary discontinuities. Alternatively, PINNs offer a powerful approach for handling challenging numerical scenarios. In this study, classical ODE problems are employed as controlled testbeds to systematically evaluate the accuracy, training efficiency, and generalization capability under controlled conditions of the PINNs framework. Although not a universal solution, PINNs can achieve superior results by embedding physical laws directly into the learning process. We first analyze the existence and uniqueness properties of several benchmark problems and subsequently validate the PINNs methodology on these model systems. Our results demonstrate that for complex problems to converge to correct solutions, the loss function components data loss, initial condition loss, and residual loss must be appropriately balanced through careful weighting. We further establish that systematic tuning of hyperparameters, including network depth, layer width, activation functions, learning rate, optimization algorithms, w eight initialization schemes, and collocation point sampling, plays a crucial role in achieving accurate solutions. Additionally, embedding prior knowledge and imposing hard constraints on the network architecture, without loss the generality of the ODE system, significantly enhances the predictive capability of PINNs.

Paperid: 1041, https://arxiv.org/pdf/2510.27187.pdf

Abstract:
This paper presents a physics-informed machine learning approach for synthesizing optimal feedback control policy for infinite-horizon optimal control problems by solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation(PDE). The optimal control policy is derived analytically for affine dynamical systems with separable and strictly convex control costs, expressed as a function of the gradient of the value function. The resulting HJB-PDE is then solved by approximating the value function using the Extreme Theory of Functional Connections (X-TFC) - a hybrid approach that combines the Theory of Functional Connections (TFC) with the Extreme Learning Machine (ELM) algorithm. This approach ensures analytical satisfaction of boundary conditions and significantly reduces training cost compared to traditional Physics-Informed Neural Networks (PINNs). We benchmark the method on linear and non-linear systems with known analytical solutions as well as demonstrate its effectiveness on control tasks such as spacecraft optimal de-tumbling control.

Paperid: 1042, https://arxiv.org/pdf/2510.26365.pdf

Abstract:
In this paper, local Hölder regularization is incorporated into a physics-informed neural networks (PINNs) framework for solving elliptic partial differential equations (PDEs). Motivated by the interior regularity properties of linear elliptic PDEs, a modified loss function is constructed by introducing local Hölder regularization term. To approximate this term effectively, a variable-distance discrete sampling strategy is developed. Error estimates are established to assess the generalization performance of the proposed method. Numerical experiments on a range of elliptic problems demonstrate notable improvements in both prediction accuracy and robustness compared to standard physics-informed neural networks.

Paperid: 1043, https://arxiv.org/pdf/2510.25925.pdf

Abstract:
In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the governing equation of heat transfer by conduction is reconstructed through equation discovery using fractional-order derivatives, enabling the identification of the fractional derivative order that best describes the physical behavior. In the simulation phase, the thermal conductivity is treated as a physical parameter, and a parametric simulation is performed to analyze its influence on the temperature field. In the optimization phase, the focus is placed on the inverse problem, where the goal is to infer unknown physical properties from observed data. The effectiveness of the PINN approach is evaluated across these three fundamental engineering problem types and compared against conventional numerical methods. The results demonstrate that although PINNs may not yet outperform traditional numerical solvers in terms of speed and accuracy for forward problems, they offer a powerful and flexible framework for parametric simulation, optimization, and equation discovery, making them highly valuable for inverse and data-driven modeling applications.

Paperid: 1044, https://arxiv.org/pdf/2510.25921.pdf

Abstract:
Scanning tunnelling microscopy (STM) enables atomic-resolution imaging and atom manipulation, but its utility is often limited by tip degradation and slow serial data acquisition. Fabrication adds another layer of complexity since the tip is often subjected to large voltages, which may alter the shape of its apex, requiring it to be conditioned. Here, we propose a machine learning (ML) approach for image repair and super-resolution to alleviate both challenges. Using a dataset of only 36 pristine experimental images of Si(001):H, we demonstrate that a physics-informed synthetic data generation pipeline can be used to train several state-of-the-art flow-matching and diffusion models. Quantitative evaluation with metrics such as the CLIP Maximum Mean Discrepancy (CMMD) score and structural similarity demonstrates that our models are able to effectively restore images and offer a two- to fourfold reduction in image acquisition time by accurately reconstructing images from sparsely sampled data. Our framework has the potential to significantly increase STM experimental throughput by offering a route to reducing the frequency of tip-conditioning procedures and to enhancing frame rates in existing high-speed STM systems.

Paperid: 1045, https://arxiv.org/pdf/2510.25563.pdf

Abstract:
The accurate prediction of oceanographic variables is crucial for understanding climate change, managing marine resources, and optimizing maritime activities. Traditional ocean forecasting relies on numerical models; however, these approaches face limitations in terms of computational cost and scalability. In this study, we adapt Aurora, a foundational deep learning model originally designed for atmospheric forecasting, to predict sea surface temperature (SST) in the Canary Upwelling System. By fine-tuning this model with high-resolution oceanographic reanalysis data, we demonstrate its ability to capture complex spatiotemporal patterns while reducing computational demands. Our methodology involves a staged fine-tuning process, incorporating latitude-weighted error metrics and optimizing hyperparameters for efficient learning. The experimental results show that the model achieves a low RMSE of 0.119K, maintaining high anomaly correlation coefficients (ACC $\approx 0.997$). The model successfully reproduces large-scale SST structures but faces challenges in capturing finer details in coastal regions. This work contributes to the field of data-driven ocean forecasting by demonstrating the feasibility of using deep learning models pre-trained in different domains for oceanic applications. Future improvements include integrating additional oceanographic variables, increasing spatial resolution, and exploring physics-informed neural networks to enhance interpretability and understanding. These advancements can improve climate modeling and ocean prediction accuracy, supporting decision-making in environmental and economic sectors.

Paperid: 1046, https://arxiv.org/pdf/2510.22941.pdf

Abstract:
Compounding climate hazards, such as wildfire-induced outages and urban heatwaves, challenge the stability and equity of cities. We present a Hazard-Responsive Digital Twin (H-RDT) that combines physics-informed neural network modeling, multimodal data fusion, and equity-aware risk analytics for urban-scale response. In a synthetic district with diverse building archetypes and populations, a simulated wildfire-outage-heatwave cascade shows that H-RDT maintains stable indoor temperature predictions (approximately 31 to 33 C) under partial sensor loss, reproducing outage-driven surges and recovery. The reinforcement learning based fusion module adaptively reweights IoT, UAV, and satellite inputs to sustain spatiotemporal coverage, while the equity-adjusted mapping isolates high-vulnerability clusters (schools, clinics, low-income housing). Prospective interventions, such as preemptive cooling-center activation and microgrid sharing, reduce population-weighted thermal risk by 11 to 13 percent, shrink the 95th-percentile (tail) risk by 7 to 17 percent, and cut overheating hours by up to 9 percent. Beyond the synthetic demonstration, the framework establishes a transferable foundation for real-city implementation, linking physical hazard modeling with social equity and decision intelligence. The H-RDT advances digital urban resilience toward adaptive, learning-based, and equity-centered decision support for climate adaptation.

Paperid: 1047, https://arxiv.org/pdf/2510.22190.pdf

Abstract:
Wide-angle tail (WAT) and narrow-angle tail (NAT) radio active galactic nuclei (RAGNs) are key tracers of dense environments in galaxy groups and clusters, yet no machine-learning classifier of bent RAGNs has been trained using both unlabeled data and purely visually inspected labels. We release the RGC Python package, which includes two newly preprocessed labeled datasets of 639 WATs and NATs derived from a publicly available catalog of visually inspected sources, along with a semi-supervised RGC model that leverages 20,000 unlabeled RAGNs. The two labeled datasets in RGC were preprocessed using PyBDSF which retains spurious sources, and Photutils which removes them. The RGC model integrates the self-supervised framework BYOL (Bootstrap YOur Latent) with the supervised E2CNN (E2-equivariant Convolutional Neural Network) to form a semi-supervised binary classifier. The RGC model, when trained and evaluated on a dataset devoid of spurious sources, reaches peak performance, attaining an accuracy of 88.88% along with F1-scores of 0.90 for WATs and 0.85 for NATs. The model's attention patterns amid class imbalance suggest that this work can serve as a stepping stone toward developing physics-informed foundation models capable of identifying a broad range of AGN physical properties.

Paperid: 1048, https://arxiv.org/pdf/2510.14310.pdf

Abstract:
The accurate representation of numerous physical, chemical, and biological processes relies heavily on differential equations (DEs), particularly nonlinear differential equations (NDEs). While understanding these complex systems necessitates obtaining solutions to their governing equations, the derivation of precise approximations for NDEs remains a formidable task in computational mathematics. Although established techniques such as the finite element method (FEM) have long been foundational, remarkable promise for approximating continuous functions with high efficacy has recently been demonstrated by advancements in physics-informed deep-learning feedforward neural networks. In this work, a novel application of PINNs is presented for the approximation of the challenging Electrohydrodynamic (EHD) problem. A specific $L^2$-type \textit{total loss function} is employed, notably without reliance on any prior knowledge of the exact solution. A comprehensive comparative study is conducted, juxtaposing the approximation capabilities of the proposed neural network with those of the conventional FEM. The PINN training regimen is composed of two critical steps: forward propagation for adjustments to gradient and curvature, and backpropagation for the refinement of hyperparameters. The critical challenge of identifying optimal neural network architectures and hyperparameter configurations for efficient optimization is meticulously investigated. Excellent performance is shown to be delivered by the neural network even with a limited training dataset. Simultaneously, it is demonstrated that the accuracy of the FEM can be substantially enhanced through the judicious selection of smaller mesh sizes.

Paperid: 1049, https://arxiv.org/pdf/2508.19398.pdf

Abstract:
The region of attraction is a key metric of the robustness of systems. This paper addresses the numerical solution of the generalized Zubov's equation, which produces a special Lyapunov function characterizing the robust region of attraction for perturbed systems. To handle the highly nonlinear characteristic of the generalized Zubov's equation, we propose a physics-informed neural network framework that employs a policy iteration training scheme with rollout to approximate the viscosity solution. In addition to computing the optimal disturbance during the policy improvement process, we incorporate neural network-generated value estimates as anchor points to facilitate the training procedure to prevent singularities in both low- and high-dimensional systems. Numerical simulations validate the effectiveness of the proposed approach.

Paperid: 1050, https://arxiv.org/pdf/2508.17902.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are becoming a popular method for solving PDEs, due to their mesh-free nature and their ability to handle high-dimensional problems where traditional numerical solvers often struggle. Despite their promise, the practical application of PINNs is still constrained by several fac- tors, a primary one being their often-limited accuracy. This paper is dedicated to enhancing the accuracy of PINNs by introducing spectral-prior guided multistage strategy. We propose two methods: Spectrum- Informed Multistage Physics-Informed Neural Networks (SI-MSPINNs) and Multistage Physics-Informed Neural Networks with Spectrum Weighted Random Fourier Features (RFF-MSPINNs). The SI-MSPINNs integrate the core mechanism of Spectrum-Informed Multistage Neural Network (SI-MSNNs) and PINNs, in which we extract the Dominant Spectral Pattern (DSP) of residuals by the discrete Fourier transform. This DSP guides the network initialization to alleviate spectral bias, and gradually optimizes the resolution accuracy using a multistage strategy. The RFF-MSPINNs combines random Fourier features with spectral weighting methods, dynamically adjusting the frequency sampling distribution based on the residual power spectral density, allowing the network to prioritize learning high-energy physical modes. Through experimental verification of the Burgers equation and the Helmholtz equation, we show that both models significantly improve the accuracy of the original PINNs.

Paperid: 1051, https://arxiv.org/pdf/2508.17303.pdf

Abstract:
This study proposes a Physics-Informed Neural Network (PINN) framework to predict the low-cycle fatigue (LCF) life of irradiated austenitic and ferritic/martensitic (F/M) steels used in nuclear reactors. These materials experience cyclic loading and irradiation at elevated temperatures, causing complex degradation that traditional empirical models fail to capture accurately. The developed PINN model incorporates physical fatigue life constraints into its loss function, improving prediction accuracy and generalizability. Trained on 495 data points, including both irradiated and unirradiated conditions, the model outperforms traditional machine learning models like Random Forest, Gradient Boosting, eXtreme Gradient Boosting, and the conventional Neural Network. SHapley Additive exPlanations analysis identifies strain amplitude, irradiation dose, and testing temperature as dominant features, each inversely correlated with fatigue life, consistent with physical understanding. PINN captures saturation behaviour in fatigue life at higher strain amplitudes in F/M steels. Overall, the PINN framework offers a reliable and interpretable approach for predicting fatigue life in irradiated alloys, enabling informed alloy selection.

Paperid: 1052, https://arxiv.org/pdf/2508.15530.pdf

Abstract:
X-ray phase contrast imaging significantly improves the visualization of structures with weak or uniform absorption, broadening its applications across a wide range of scientific disciplines. Propagation-based phase contrast is particularly suitable for time- or dose-critical in vivo/in situ/operando (tomography) experiments because it requires only a single intensity measurement. However, the phase information of the wave field is lost during the measurement and must be recovered. Conventional algebraic and iterative methods often rely on specific approximations or boundary conditions that may not be met by many samples or experimental setups. In addition, they require manual tuning of reconstruction parameters by experts, making them less adaptable for complex or variable conditions. Here we present a self-learning approach for solving the inverse problem of phase retrieval in the near-field regime of Fresnel theory using a single intensity measurement (hologram). A physics-informed generative adversarial network is employed to reconstruct both the phase and absorbance of the unpropagated wave field in the sample plane from a single hologram. Unlike most deep learning approaches for phase retrieval, our approach does not require paired, unpaired, or simulated training data. This significantly broadens the applicability of our approach, as acquiring or generating suitable training data remains a major challenge due to the wide variability in sample types and experimental configurations. The algorithm demonstrates robust and consistent performance across diverse imaging conditions and sample types, delivering quantitative, high-quality reconstructions for both simulated data and experimental datasets acquired at beamline P05 at PETRA III (DESY, Hamburg), operated by Helmholtz-Zentrum Hereon. Furthermore, it enables the simultaneous retrieval of both phase and absorption information.

Paperid: 1053, https://arxiv.org/pdf/2508.15343.pdf

Abstract:
In this work, a novel Eig-PIELM framework is proposed that extends physics-informed extreme learning machine for an efficient and accurate solution of linear eigenvalue problems. The method reformulates the governing differential equations into a compact algebraic system solvable in a single step. Boundary conditions are enforced exactly via an algebraic projection onto the boundary-admissible subspace, eliminating the computational overhead of penalty parameters, and backpropagation while preserving the computational advantages of extreme learning machines. The proposed framework is mesh-free and yields both eigenvalues and mode shapes simultaneously in one linear solve. The robustness and accuracy of the proposed framework is demonstrated through a range of benchmark problems. We believe that the mesh-free nature, solution structure and accuracy of Eig-PIELM makes it particularly valuable for parametric studies in mechanical, acoustic, and electromechanical systems where rapid frequency spectrum analysis is critical.

Paperid: 1054, https://arxiv.org/pdf/2508.14137.pdf

Abstract:
The Macroscopic Fundamental Diagram is a popular tool used to describe traffic dynamics in an aggregated way, with applications ranging from traffic control to incident analysis. However, estimating the MFD for a given network requires large numbers of loop detectors, which is not always available in practice. This article proposes a framework harnessing meta-learning, a subcategory of machine learning that trains models to understand and adapt to new tasks on their own, to alleviate the data scarcity challenge. The developed model is trained and tested by leveraging data from multiple cities and exploiting it to model the MFD of other cities with different shares of detectors and topological structures. The proposed meta-learning framework is applied to an ad-hoc Multi-Task Physics-Informed Neural Network, specifically designed to estimate the MFD. Results show an average MSE improvement in flow prediction ranging between ~ 17500 and 36000 (depending on the subset of loop detectors tested). The meta-learning framework thus successfully generalizes across diverse urban settings and improves performance on cities with limited data, demonstrating the potential of using meta-learning when a limited number of detectors is available. Finally, the proposed framework is validated against traditional transfer learning approaches and tested with FitFun, a non-parametric model from the literature, to prove its transferability.

Paperid: 1055, https://arxiv.org/pdf/2508.12593.pdf

Abstract:
Traffic state estimation (TSE) fundamentally involves solving high-dimensional spatiotemporal partial differential equations (PDEs) governing traffic flow dynamics from limited, noisy measurements. While Physics-Informed Neural Networks (PINNs) enforce PDE constraints point-wise, this paper adopts a physics-informed deep operator network (PI-DeepONet) framework that reformulates TSE as an operator learning problem. Our approach trains a parameterized neural operator that maps sparse input data to the full spatiotemporal traffic state field, governed by the traffic flow conservation law. Crucially, unlike PINNs that enforce PDE constraints point-wise, PI-DeepONet integrates traffic flow conservation model and the fundamental diagram directly into the operator learning process, ensuring physical consistency while capturing congestion propagation, spatial correlations, and temporal evolution. Experiments on the NGSIM dataset demonstrate superior performance over state-of-the-art baselines. Further analysis reveals insights into optimal function generation strategies and branch network complexity. Additionally, the impact of input function generation methods and the number of functions on model performance is explored, highlighting the robustness and efficacy of proposed framework.

Paperid: 1056, https://arxiv.org/pdf/2508.10718.pdf

Abstract:
Accurate prediction of electronic band structures in two-dimensional materials remains a fundamental challenge, with existing methods struggling to balance computational efficiency and physical accuracy. We present the Symmetry-Constrained Multi-Scale Physics-Informed Neural Network (SCMS-PINN) v35, which directly learns graphene band structures while rigorously enforcing crystallographic symmetries through a multi-head architecture. Our approach introduces three specialized ResNet-6 pathways -- K-head for Dirac physics, M-head for saddle points, and General head for smooth interpolation -- operating on 31 physics-informed features extracted from k-points. Progressive Dirac constraint scheduling systematically increases the weight parameter from 5.0 to 25.0, enabling hierarchical learning from global topology to local critical physics. Training on 10,000 k-points over 300 epochs achieves 99.99\% reduction in training loss (34.597 to 0.003) with validation loss of 0.0085. The model predicts Dirac point gaps within 30.3 $Î¼$eV of theoretical zero and achieves average errors of 53.9 meV (valence) and 40.5 meV (conduction) across the Brillouin zone. All twelve C$_{6v}$ operations are enforced through systematic averaging, guaranteeing exact symmetry preservation. This framework establishes a foundation for extending physics-informed learning to broader two-dimensional materials for accelerated discovery.

Paperid: 1057, https://arxiv.org/pdf/2508.09627.pdf

Abstract:
Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and Geometry- Aware Spatio-Spectral Graph Neural Operator ($Ï$G-Sp$^2$GNO) for learning the solution operators of time-independent and time-dependent PDEs. The proposed approach first improves upon the recently developed Sp$^2$GNO by enabling geometry awareness and subsequently exploits the governing physics to learn the underlying solution operator in a simulation-free setup. While the spatio-spectral structure present in the proposed architecture allows multiscale learning, two separate strategies for enabling geometry awareness is introduced in this paper. For time dependent problems, we also introduce a novel hybrid physics informed loss function that combines higher-order time-marching scheme with upscaled theory inspired stochastic projection scheme. This allows accurate integration of the physics-information into the loss function. The performance of the proposed approach is illustrated on number of benchmark examples involving regular and complex domains, variation in geometry during inference, and time-independent and time-dependent problems. The results obtained illustrate the efficacy of the proposed approach as compared to the state-of-the-art physics-informed neural operator algorithms in the literature.

Paperid: 1058, https://arxiv.org/pdf/2508.06122.pdf

Abstract:
This study applied representation learning algorithms to satellite images and evaluated the learned latent spaces with classifications of various weather events. The algorithms investigated include the classical linear transformation, i.e., principal component analysis (PCA), state-of-the-art deep learning method, i.e., convolutional autoencoder (CAE), and a residual network pre-trained with large image datasets (PT). The experiment results indicated that the latent space learned by CAE consistently showed higher threat scores for all classification tasks. The classifications with PCA yielded high hit rates but also high false-alarm rates. In addition, the PT performed exceptionally well at recognizing tropical cyclones but was inferior in other tasks. Further experiments suggested that representations learned from higher-resolution datasets are superior in all classification tasks for deep-learning algorithms, i.e., CAE and PT. We also found that smaller latent space sizes had minor impact on the classification task's hit rate. Still, a latent space dimension smaller than 128 caused a significantly higher false alarm rate. Though the CAE can learn latent spaces effectively and efficiently, the interpretation of the learned representation lacks direct connections to physical attributions. Therefore, developing a physics-informed version of CAE can be a promising outlook for the current work.

Paperid: 1059, https://arxiv.org/pdf/2508.03730.pdf

Abstract:
Location-aware devices continuously generate massive volumes of trajectory data, creating demand for efficient compression. Line simplification is a common solution but typically assumes 2D trajectories and ignores time synchronization and motion continuity. We propose PILOT-C, a novel trajectory compression framework that integrates frequency-domain physics modeling with error-bounded optimization. Unlike existing line simplification methods, PILOT-C supports trajectories in arbitrary dimensions, including 3D, by compressing each spatial axis independently. Evaluated on four real-world datasets, PILOT-C achieves superior performance across multiple dimensions. In terms of compression ratio, PILOT-C outperforms CISED-W, the current state-of-the-art SED-based line simplification algorithm, by an average of 19.2%. For trajectory fidelity, PILOT-C achieves an average of 32.6% reduction in error compared to CISED-W. Additionally, PILOT-C seamlessly extends to three-dimensional trajectories while maintaining the same computational complexity, achieving a 49% improvement in compression ratios over SQUISH-E, the most efficient line simplification algorithm on 3D datasets.

Paperid: 1060, https://arxiv.org/pdf/2508.03120.pdf

Abstract:
Accurately identifying the material composition of objects is a critical capability for AI robots powered by large language models (LLMs) to perform context-aware manipulation. Radar technologies offer a promising sensing modality for material recognition task. When combined with deep learning, radar technologies have demonstrated strong potential in identifying the material of various objects. However, existing radar-based solutions are often constrained to closed-set object categories and typically require task-specific data collection to train deep learning models, largely limiting their practical applicability. This raises an important question: Can we leverage the powerful reasoning capabilities of pre-trained LLMs to directly infer material composition from raw radar signals? Answering this question is non-trivial due to the inherent redundancy of radar signals and the fact that pre-trained LLMs have no prior exposure to raw radar data during training. To address this, we introduce LLMaterial, the first study to investigate the feasibility of using LLM to identify materials directly from radar signals. First, we introduce a physics-informed signal processing pipeline that distills high-redundancy radar raw data into a set of compact intermediate parameters that encapsulate the material's intrinsic characteristics. Second, we adopt a retrieval-augmented generation (RAG) strategy to provide the LLM with domain-specific knowledge, enabling it to interpret and reason over the extracted intermediate parameters. Leveraging this integration, the LLM is empowered to perform step-by-step reasoning on the condensed radar features, achieving open-set material recognition directly from raw radar signals. Preliminary results show that LLMaterial can effectively distinguish among a variety of common materials, highlighting its strong potential for real-world material identification applications.

Paperid: 1061, https://arxiv.org/pdf/2507.20929.pdf

Abstract:
Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We break through this barrier with a hybrid Fourier-neural architecture for the Euler-Bernoulli beam equation, achieving unprecedented L2 error of $1.94 \times 10^{-7}$-a 17-fold improvement over standard PINNs and $15-500\times$ better than traditional numerical methods. Our approach synergistically combines a truncated Fourier series capturing dominant modal behavior with a deep neural network providing adaptive residual corrections. A systematic harmonic optimization study revealed a counter-intuitive discovery: exactly 10 harmonics yield optimal performance, with accuracy catastrophically degrading from $10^{-7}$ to $10^{-1}$ beyond this threshold. The two-phase optimization strategy (Adam followed by L-BFGS) and adaptive weight balancing enable stable ultra-precision convergence. GPU-accelerated implementation achieves sub-30-minute training despite fourth-order derivative complexity. By addressing 12 critical gaps in existing approaches-from architectural rigidity to optimization landscapes-this work demonstrates that ultra-precision is achievable through proper design, opening new paradigms for scientific computing where machine learning can match or exceed traditional numerical methods.

Paperid: 1062, https://arxiv.org/pdf/2507.16431.pdf

Abstract:
Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional neural operator (PICNO) to solve the Helmholtz equation efficiently. The PICNO takes both the background wavefield corresponding to a homogeneous medium and the velocity model as input function space, generating the scattered wavefield as the output function space. Our workflow integrates PDE constraints directly into the training process, enabling the neural operator to not only fit the available data but also capture the underlying physics governing wave phenomena. PICNO allows for high-resolution reasonably accurate predictions even with limited training samples, and it demonstrates significant improvements over a purely data-driven convolutional neural operator (CNO), particularly in predicting high-frequency wavefields. These features and improvements are important for waveform inversion down the road.

Paperid: 1063, https://arxiv.org/pdf/2507.11640.pdf

Abstract:
Stirred tanks are vital in chemical and biotechnological processes, particularly as bioreactors. Although computational fluid dynamics (CFD) is widely used to model the flow in stirred tanks, its high computational cost$-$especially in multi-query scenarios for process design and optimization$-$drives the need for efficient data-driven surrogate models. However, acquiring sufficiently large datasets can be costly. Physics-informed neural networks (PINNs) offer a promising solution to reduce data requirements while maintaining accuracy by embedding underlying physics into neural network (NN) training. This study quantifies the data requirements of vanilla PINNs for developing surrogate models of a flow field in a 2D stirred tank. We compare these requirements with classical supervised neural networks and boundary-informed neural networks (BINNs). Our findings demonstrate that surrogate models can achieve prediction errors around 3% across Reynolds numbers from 50 to 5000 using as few as six datapoints. Moreover, employing an approximation of the velocity profile in place of real data labels leads to prediction errors of around 2.5%. These results indicate that even with limited or approximate datasets, PINNs can be effectively trained to deliver high accuracy comparable to high-fidelity data.

Paperid: 1064, https://arxiv.org/pdf/2507.09757.pdf

Abstract:
We introduce the Energy Dissipation Rate guided Adaptive Sampling (EDRAS) strategy, a novel method that substantially enhances the performance of Physics-Informed Neural Networks (PINNs) in solving thermodynamically consistent partial differential equations (PDEs) over arbitrary domains. EDRAS leverages the local energy dissipation rate density as a guiding metric to identify and adaptively re-sample critical collocation points from both the interior and boundary of the computational domain. This dynamical sampling approach improves the accuracy of residual-based PINNs by aligning the training process with the underlying physical structure of the system. In this study, we demonstrate the effectiveness of EDRAS using the Allen-Cahn phase field model in irregular geometries, achieving up to a sixfold reduction in the relative mean square error compared to traditional residual-based adaptive refinement (RAR) methods. Moreover, we compare EDRAS with other residual-based adaptive sampling approaches and show that EDRAS is not only computationally more efficient but also more likely to identify high-impact collocation points. Through numerical solutions of the Allen-Cahn equation with both static (Neumann) and dynamic boundary conditions in 2D disk- and ellipse-shaped domains solved using PINN coupled with EDRAS, we gain significant insights into how dynamic boundary conditions influence bulk phase evolution and thermodynamic behavior. The proposed approach offers an effective, physically informed enhancement to PINN frameworks for solving thermodynamically consistent models, making PINN a robust and versatile computational tool for investigating complex thermodynamic processes in arbitrary geometries.

Paperid: 1065, https://arxiv.org/pdf/2507.08118.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical constraints into the loss function. However, standard optimizers such as Adam often struggle to balance competing loss terms, particularly in stiff or ill-conditioned systems. In this work, we propose a PDE-aware optimizer that adapts parameter updates based on the variance of per-sample PDE residual gradients. This method addresses gradient misalignment without incurring the heavy computational costs of second-order optimizers such as SOAP. We benchmark the PDE-aware optimizer against Adam and SOAP on 1D Burgers', Allen-Cahn and Korteweg-de Vries(KdV) equations. Across both PDEs, the PDE-aware optimizer achieves smoother convergence and lower absolute errors, particularly in regions with sharp gradients. Our results demonstrate the effectiveness of PDE residual-aware adaptivity in enhancing stability in PINNs training. While promising, further scaling on larger architectures and hardware accelerators remains an important direction for future research.

Paperid: 1066, https://arxiv.org/pdf/2507.05874.pdf

Abstract:
Modern power systems face significant challenges in state estimation and real-time monitoring, particularly regarding response speed and accuracy under faulty conditions or cyber-attacks. This paper proposes a hybrid approach using physics-informed neural networks (PINNs) to enhance the accuracy and robustness, of power system state estimation. By embedding physical laws into the neural network architecture, PINNs improve estimation accuracy for transmission grid applications under both normal and faulty conditions, while also showing potential in addressing security concerns such as data manipulation attacks. Experimental results show that the proposed approach outperforms traditional machine learning models, achieving up to 83% higher accuracy on unseen subsets of the training dataset and 65% better performance on entirely new, unrelated datasets. Experiments also show that during a data manipulation attack against a critical bus in a system, the PINN can be up to 93% more accurate than an equivalent neural network.

Paperid: 1067, https://arxiv.org/pdf/2507.05783.pdf

Abstract:
Cardiac diseases are among the leading causes of morbidity and mortality worldwide, which requires accurate and timely diagnostic strategies. In this study, we introduce an innovative approach that combines deep learning image registration with physics-informed regularization to predict the biomechanical properties of moving cardiac tissues and extract features for disease classification. We utilize the energy strain formulation of Neo-Hookean material to model cardiac tissue deformations, optimizing the deformation field while ensuring its physical and biomechanical coherence. This explainable approach not only improves image registration accuracy, but also provides insights into the underlying biomechanical processes of the cardiac tissues. Evaluation on the Automated Cardiac Diagnosis Challenge (ACDC) dataset achieved Dice scores of 0.945 for the left ventricular cavity, 0.908 for the right ventricular cavity, and 0.905 for the myocardium. Subsequently, we estimate the local strains within the moving heart and extract a detailed set of features used for cardiovascular disease classification. We evaluated five classification algorithms, Logistic Regression, Multi-Layer Perceptron, Support Vector Classifier, Random Forest, and Nearest Neighbour, and identified the most relevant features using a feature selection algorithm. The best performing classifier obtained a classification accuracy of 98% in the training set and 100% in the test set of the ACDC dataset. By integrating explainable artificial intelligence, this method empowers clinicians with a transparent understanding of the model's predictions based on cardiac mechanics, while also significantly improving the accuracy and reliability of cardiac disease diagnosis, paving the way for more personalized and effective patient care.

Paperid: 1068, https://arxiv.org/pdf/2507.03853.pdf

Abstract:
Despite the success of deep learning methods in quantum chemistry, their representational capacity is most often confined to neutral, closed-shell molecules. However, real-world chemical systems often exhibit complex characteristics, including varying charges, spins, and environments. We introduce OrbitAll, a geometry- and physics-informed deep learning framework that can represent all molecular systems with electronic structure information. OrbitAll utilizes spin-polarized orbital features from the underlying quantum mechanical method, and combines it with graph neural networks satisfying SE(3)-equivariance. The resulting framework can represent and process any molecular system with arbitrary charges, spins, and environmental effects. OrbitAll demonstrates superior performance and generalization on predicting charged, open-shell, and solvated molecules, while also robustly extrapolating to molecules significantly larger than the training data by leveraging a physics-informed architecture. OrbitAll achieves chemical accuracy using 10 times fewer training data than competing AI models, with a speedup of approximately $10^3$ - $10^4$ compared to density functional theory.

Paperid: 1069, https://arxiv.org/pdf/2507.01687.pdf

Abstract:
The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertainty in complex systems. Our approach enhances the representation of uncertainty in forward problems by combining generative modeling techniques with PINNs. This integration enables in a systematic fashion uncertainty control while maintaining the predictive accuracy of the model. We demonstrate the utility of this method through applications to random differential equations and random partial differential equations (PDEs).

Paperid: 1070, https://arxiv.org/pdf/2506.15405.pdf

Abstract:
Physics-informed neural networks (PINNs) are extensively used to represent various physical systems across multiple scientific domains. The same can be said for cardiac electrophysiology, wherein fully-connected neural networks (FCNNs) have been employed to predict the evolution of an action potential in a 2D space following the two-parameter phenomenological Aliev-Panfilov (AP) model. In this paper, the training behaviour of PINNs is investigated to determine optimal hyperparameters to predict the electrophysiological activity of the myocardium in 3D according to the AP model, with the inclusion of boundary and material parameters. An FCNN architecture is employed with the governing partial differential equations in their strong form, which are scaled consistently with normalization of network inputs. The finite element (FE) method is used to generate training data for the network. Numerical examples with varying spatial dimensions and parameterizations are generated using the trained models. The network predicted fields for both the action potential and the recovery variable are compared with the respective FE simulations. Network losses are weighed with individual scalar values. Their effect on training and prediction is studied to arrive at a method of controlling losses during training.

Paperid: 1071, https://arxiv.org/pdf/2506.14036.pdf

Abstract:
Accurately estimating spatially heterogeneous elasticity parameters, particularly Young's modulus and Poisson's ratio, from noisy displacement measurements remains significantly challenging in inverse elasticity problems. Existing inverse estimation techniques are often limited by instability, pronounced sensitivity to measurement noise, and difficulty in recovering absolute-scale Young's modulus. This work presents a novel Inverse Elasticity Physics-Informed Neural Network (IE-PINN) specifically designed to robustly reconstruct heterogeneous distributions of elasticity parameters from noisy displacement data based on linear elasticity physics. IE-PINN integrates three distinct neural network architectures dedicated to separately modeling displacement fields, strain fields, and elasticity distributions, thereby significantly enhancing stability and accuracy against measurement noise. Additionally, a two-phase estimation strategy is introduced: the first phase recovers relative spatial distributions of Young's modulus and Poisson's ratio, and the second phase calibrates the absolute scale of Young's modulus using imposed loading boundary conditions. Additional methodological innovations, including positional encoding, sine activation functions, and a sequential pretraining protocol, further enhance the model's performance and robustness. Extensive numerical experiments demonstrate that IE-PINN effectively overcomes critical limitations encountered by existing methods, delivering accurate absolute-scale elasticity estimations even under severe noise conditions. This advancement holds substantial potential for clinical imaging diagnostics and mechanical characterization, where measurements typically encounter substantial noise.

Paperid: 1072, https://arxiv.org/pdf/2506.13222.pdf

Abstract:
Electroencephalography (EEG) is extensively employed in medical diagnostics and brain-computer interface (BCI) applications due to its non-invasive nature and high temporal resolution. However, EEG analysis faces significant challenges, including noise, nonstationarity, and inter-subject variability, which hinder its clinical utility. Traditional neural networks often lack integration with biophysical knowledge, limiting their interpretability, robustness, and potential for medical translation. To address these limitations, this study introduces NeuroPhysNet, a novel Physics-Informed Neural Network (PINN) framework tailored for EEG signal analysis and motor imagery classification in medical contexts. NeuroPhysNet incorporates the FitzHugh-Nagumo model, embedding neurodynamical principles to constrain predictions and enhance model robustness. Evaluated on the BCIC-IV-2a dataset, the framework achieved superior accuracy and generalization compared to conventional methods, especially in data-limited and cross-subject scenarios, which are common in clinical settings. By effectively integrating biophysical insights with data-driven techniques, NeuroPhysNet not only advances BCI applications but also holds significant promise for enhancing the precision and reliability of clinical diagnostics, such as motor disorder assessments and neurorehabilitation planning.

Paperid: 1073, https://arxiv.org/pdf/2506.11786.pdf

Abstract:
Accurate real-time estimation of human movement dynamics, including internal joint moments and muscle forces, is essential for applications in clinical diagnostics and sports performance monitoring. Inertial measurement units (IMUs) provide a minimally intrusive solution for capturing motion data, particularly when used in sparse sensor configurations. However, current real-time methods rely on supervised learning, where a ground truth dataset needs to be measured with laboratory measurement systems, such as optical motion capture. These systems are known to introduce measurement and processing errors and often fail to generalize to real-world or previously unseen movements, necessitating new data collection efforts that are time-consuming and impractical. To overcome these limitations, we propose SSPINNpose, a self-supervised, physics-informed neural network that estimates joint kinematics and kinetics directly from IMU data, without requiring ground truth labels for training. We run the network output through a physics model of the human body to optimize physical plausibility and generate virtual measurement data. Using this virtual sensor data, the network is trained directly on the measured sensor data instead of a ground truth. When compared to optical motion capture, SSPINNpose is able to accurately estimate joint angles and joint moments at an RMSD of 8.7 deg and 4.9 BWBH%, respectively, for walking and running at speeds up to 4.9 m/s at a latency of 3.5 ms. Furthermore, the framework demonstrates robustness across sparse sensor configurations and can infer the anatomical locations of the sensors. These results underscore the potential of SSPINNpose as a scalable and adaptable solution for real-time biomechanical analysis in both laboratory and field environments.

Paperid: 1074, https://arxiv.org/pdf/2506.11518.pdf

Abstract:
We propose transformed Diffsuion-Wave fractional Physics-Informed Neural Networks (tDWfPINNs) for efficiently solving time-fractional diffusion-wave equations with fractional order $Î±\in(1,2)$. Conventional numerical methods for these equations often compromise the mesh-free advantage of Physics-Informed Neural Networks (PINNs) or impose high computational costs when computing fractional derivatives. The proposed method avoids first-order derivative calculations at quadrature points by introducing an integrand transformation technique, significantly reducing computational costs associated with fractional derivative evaluation while preserving accuracy. We conduct a comprehensive comparative analysis applying this integrand transformation in conjunction with both Monte Carlo integration and Gauss-Jacobi quadrature schemes across various time-fractional PDEs. Our results demonstrate that tDWfPINNs achieve superior computational efficiency without sacrificing accuracy. Furthermore, we incorporate the proposed approach into adaptive sampling approaches such as the residual-based adaptive distribution (RAD) for the time-fractional Burgers equation with order $Î±\in(1,2)$, which exhibits complex solution dynamics. The experiments show that the Gauss-Jacobi method typically outperforms the Monte Carlo approach; however, careful consideration is required when selecting the number of quadrature points. Overall, the proposed tDWfPINNs offer a significant advancement in the numerical solution of time-fractional diffusion-wave equations, providing an accurate and scalable mesh-free alternative for challenging fractional models.

Paperid: 1075, https://arxiv.org/pdf/2506.04354.pdf

Abstract:
BridgeNet is a novel hybrid framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs). Traditional PINNs, which typically rely on fully connected architectures, often struggle to capture complex spatial hierarchies and enforce intricate boundary conditions. In contrast, BridgeNet leverages adaptive CNN layers for effective local feature extraction and incorporates a dynamically weighted loss function that rigorously enforces physical constraints. Extensive numerical experiments across various test cases demonstrate that BridgeNet not only achieves significantly lower error metrics and faster convergence compared to conventional PINN approaches but also maintains robust stability in high-dimensional settings. This work represents a substantial advancement in computational physics, offering a scalable and accurate solution methodology with promising applications in fields ranging from financial mathematics to complex system dynamics.

Paperid: 1076, https://arxiv.org/pdf/2506.00056.pdf

Abstract:
Artificial intelligence (AI) is reshaping inverse design in manufacturing, enabling high-performance discovery in materials, products, and processes. However, purely data-driven approaches often struggle in realistic manufacturing settings characterized by sparse data, high-dimensional design spaces, and complex constraints. This perspective proposes an integrated framework built on three complementary pillars: domain knowledge to establish physically meaningful objectives and constraints while removing variables with limited relevance, physics-informed machine learning to enhance generalization under limited or biased data, and large language model-based interfaces to support intuitive, human-centered interaction. Using injection molding as an illustrative example, we demonstrate how these components can operate in practice and conclude by highlighting key challenges for applying such approaches in realistic manufacturing environments.

Paperid: 1077, https://arxiv.org/pdf/2505.20769.pdf

Abstract:
Thermally induced laser noise poses a critical limitation to the sensitivity of quantum sensor arrays employing ultra-stable amplified lasers, primarily stemming from nonlinear gain-temperature coupling effects in tapered amplifiers (TAs). To address this challenge, we present a robust intelligent control strategy that synergistically integrates an encoder-decoder physics-informed gated recurrent unit (PI-GRU) network with a model predictive control (MPC) framework. Our methodology incorporates physical soft constraints into the neural network architecture, yielding a predictive model with enhanced physical consistency that demonstrates robust extrapolation capabilities beyond the training data distribution. Leveraging the PI-GRU model's accurate multi-step predictive performance, we implement a hierarchical parallel MPC architecture capable of real-time thermal instability compensation. This hybrid approach achieves cross-domain consistent thermal stabilization in TAs under diverse laser power operations. Remarkably, while trained exclusively on low-power operational data, our system demonstrates exceptional generalization, improving prediction accuracy by 58.2% and temperature stability by 69.1% in previously unseen high-power operating regimes, as experimentally validated. The novel synchronization of physics-informed neural networks with advanced MPC frameworks presented in this work establishes a groundbreaking paradigm for addressing robustness challenges in cross-domain predictive control applications, overcoming conventional modeling limitations.

Paperid: 1078, https://arxiv.org/pdf/2505.15972.pdf

Abstract:
Extremum Seeking (ES) is an effective real-time optimization method for PDE systems in cascade with nonlinear quadratic maps. To address PDEs in the feedback loop, a boundary control law and a re-design of the additive probing signal are mandatory. The latter, commonly called "trajectory generation" or "motion planning," involves designing perturbation signals that anticipate their propagation through PDEs. Specifically, this requires solving motion planning problems for systems governed by parabolic and hyperbolic PDEs. Physics-Informed Neural Networks (PINN) is a powerful tool for solving PDEs by embedding physical laws as constraints in the neural network's loss function, enabling efficient solutions for high-dimensional, nonlinear, and complex problems. This paper proposes a novel construction integrating PINN and ES, automating the motion planning process for specific PDE systems and eliminating the need for case-by-case analytical derivations. The proposed strategy efficiently extracts perturbation signals, optimizing the PDE system.

Paperid: 1079, https://arxiv.org/pdf/2505.15329.pdf

Abstract:
Invertible neural architectures have recently attracted attention for their compactness, interpretability, and information-preserving properties. In this work, we propose the Fourier-Invertible Neural Encoder (FINE), which combines invertible monotonic activation functions with reversible filter structures, and could be extended using Invertible ResNets. This architecture is examined in learning low-dimensional representations of one-dimensional nonlinear wave interactions and exact circular translation symmetry. Dimensionality is preserved across layers, except for a Fourier truncation step in the latent space, which enables dimensionality reduction while maintaining shift equivariance and interpretability. Our results demonstrate that FINE significantly outperforms classical linear methods such as Discrete Fourier Transformation (DFT) and Proper Orthogonal Decomposition (POD), and achieves reconstruction accuracy better than conventional deep autoencoders with convolutional layers (CNN) - while using substantially smaller models and offering superior physical interpretability. These findings suggest that invertible single-neuron networks, when combined with spectral truncation, offer a promising framework for learning compact and interpretable representations of physics datasets, and symmetry-aware representation learning in physics-informed machine learning.

Paperid: 1080, https://arxiv.org/pdf/2505.10894.pdf

Abstract:
This paper proposes CTP, a novel deep learning framework that integrates convolutional neural network(CNN), Transformer architectures, and physics-informed neural network(PINN) for ocean front prediction. Ocean fronts, as dynamic interfaces between distinct water masses, play critical roles in marine biogeochemical and physical processes. Existing methods such as LSTM, ConvLSTM, and AttentionConv often struggle to maintain spatial continuity and physical consistency over multi-step forecasts. CTP addresses these challenges by combining localized spatial encoding, long-range temporal attention, and physical constraint enforcement. Experimental results across south China sea(SCS) and Kuroshio(KUR) regions from 1993 to 2020 demonstrate that CTP achieves state-of-the-art(SOTA) performance in both single-step and multi-step predictions, significantly outperforming baseline models in accuracy, $F_1$ score, and temporal stability.

Paperid: 1081, https://arxiv.org/pdf/2505.09977.pdf

Abstract:
Disordered materials such as glasses, unlike crystals, lack long range atomic order and have no periodic unit cells, yielding a high dimensional configuration space with widely varying properties. The complexity not only increases computational costs for atomistic simulations but also makes it difficult for generative AI models to deliver accurate property predictions and realistic structure generation. In this work, we introduce GlassVAE, a hierarchical graph variational autoencoder that uses graph representations to learn compact, rotation, translation, and permutation invariant embeddings of atomic configurations. The resulting structured latent space not only enables efficient generation of novel, physically plausible structures but also supports exploration of the glass energy landscape. To enforce structural realism and physical fidelity, we augment GlassVAE with two physics informed regularizers, a radial distribution function (RDF) loss that captures characteristic short and medium range ordering and an energy regression loss that reflects the broad configurational energetics. Both theoretical analysis and experimental results highlight the critical impact of these regularizers. By encoding high dimensional atomistic data into a compact latent vector and decoding it into structures with accurate energy predictions, GlassVAE provides a fast, physics aware path for modeling and designing disordered materials.

Paperid: 1082, https://arxiv.org/pdf/2505.07765.pdf

Abstract:
We propose a novel framework for solving nonlinear PDEs using sparse radial basis function (RBF) networks. Sparsity-promoting regularization is employed to prevent over-parameterization and reduce redundant features. This work is motivated by longstanding challenges in traditional RBF collocation methods, along with the limitations of physics-informed neural networks (PINNs) and Gaussian process (GP) approaches, aiming to blend their respective strengths in a unified framework. The theoretical foundation of our approach lies in the function space of Reproducing Kernel Banach Spaces (RKBS) induced by one-hidden-layer neural networks of possibly infinite width. We prove a representer theorem showing that the sparse optimization problem in the RKBS admits a finite solution and establishes error bounds that offer a foundation for generalizing classical numerical analysis. The algorithmic framework is based on a three-phase algorithm to maintain computational efficiency through adaptive feature selection, second-order optimization, and pruning of inactive neurons. Numerical experiments demonstrate the effectiveness of our method and highlight cases where it offers notable advantages over GP approaches. This work opens new directions for adaptive PDE solvers grounded in rigorous analysis with efficient, learning-inspired implementation.

Paperid: 1083, https://arxiv.org/pdf/2505.06275.pdf

Abstract:
Wave-like images-from attosecond streaking spectrograms to optical spectra, audio mel-spectrograms and periodic video frames-encode critical harmonic structures that elude conventional feature extractors. We propose a unified, matrix-equivalent framework that reinterprets convolution and attention as linear transforms on flattened inputs, revealing filter weights as basis vectors spanning latent feature subspaces. To infuse spectral priors we apply elementwise $\sin(\cdot)$ mappings to each weight matrix. Embedding these transforms into CNN, ViT and Capsule architectures yields Sin-Basis Networks with heightened sensitivity to periodic motifs and built-in invariance to spatial shifts. Experiments on a diverse collection of wave-like image datasets-including 80,000 synthetic attosecond streaking spectrograms, thousands of Raman, photoluminescence and FTIR spectra, mel-spectrograms from AudioSet and cycle-pattern frames from Kinetics-demonstrate substantial gains in reconstruction accuracy, translational robustness and zero-shot cross-domain transfer. Theoretical analysis via matrix isomorphism and Mercer-kernel truncation quantifies how sinusoidal reparametrization enriches expressivity while preserving stability in data-scarce regimes. Sin-Basis Networks thus offer a lightweight, physics-informed approach to deep learning across all wave-form imaging modalities.

Paperid: 1084, https://arxiv.org/pdf/2505.05691.pdf

Abstract:
The motion planning problem involves finding a collision-free path from a robot's starting to its target configuration. Recently, self-supervised learning methods have emerged to tackle motion planning problems without requiring expensive expert demonstrations. They solve the Eikonal equation for training neural networks and lead to efficient solutions. However, these methods struggle in complex environments because they fail to maintain key properties of the Eikonal equation, such as optimal value functions and geodesic distances. To overcome these limitations, we propose a novel self-supervised temporal difference metric learning approach that solves the Eikonal equation more accurately and enhances performance in solving complex and unseen planning tasks. Our method enforces Bellman's principle of optimality over finite regions, using temporal difference learning to avoid spurious local minima while incorporating metric learning to preserve the Eikonal equation's essential geodesic properties. We demonstrate that our approach significantly outperforms existing self-supervised learning methods in handling complex environments and generalizing to unseen environments, with robot configurations ranging from 2 to 12 degrees of freedom (DOF).

Paperid: 1085, https://arxiv.org/pdf/2505.01438.pdf

Abstract:
Material stress analysis is a critical aspect of material design and performance optimization. Under dynamic loading, the global stress evolution in materials exhibits complex spatiotemporal characteristics, especially in two-phase random materials (TRMs). Such kind of material failure is often associated with stress concentration, and the phase boundaries are key locations where stress concentration occurs. In practical engineering applications, the spatiotemporal resolution of acquired microstructural data and its dynamic stress evolution is often limited. This poses challenges for deep learning methods in generating high-resolution spatiotemporal stress fields, particularly for accurately capturing stress concentration regions. In this study, we propose a framework for global stress generation and spatiotemporal super-resolution in TRMs under dynamic loading. First, we introduce a diffusion model-based approach, named as Spatiotemporal Stress Diffusion (STS-diffusion), for generating global spatiotemporal stress data. This framework incorporates Space-Time U-Net (STU-net), and we systematically investigate the impact of different attention positions on model accuracy. Next, we develop a physics-informed network for spatiotemporal super-resolution, termed as Spatiotemporal Super-Resolution Physics-Informed Operator (ST-SRPINN). The proposed ST-SRPINN is an unsupervised learning method. The influence of data-driven and physics-informed loss function weights on model accuracy is explored in detail. Benefiting from physics-based constraints, ST-SRPINN requires only low-resolution stress field data during training and can upscale the spatiotemporal resolution of stress fields to arbitrary magnifications.

Paperid: 1086, https://arxiv.org/pdf/2505.01159.pdf

Abstract:
In this article, our goal is to solve two-parameter singular perturbation problems (SPPs) in one- and two-dimensions using an adapted Physics-Informed Neural Networks (PINNs) approach. Such problems are of major importance in engineering and sciences as it appears in control theory, fluid and gas dynamics, financial modelling and so on. Solutions of such problems exhibit boundary and/or interior layers, which make them difficult to handle. It has been validated in the literature that standard PINNs have low accuracy and can't handle such problems efficiently. Recently Cao et. al \cite{cao2023physics} proposed a new parameter asymptotic PINNs (PA-PINNs) to solve one-parameter singularly perturbed convection-dominated problems. It was observed that PA-PINNs works better than standard PINNs and gPINNs in terms of accuracy, convergence and stability. In this article, for the first time robustness of PA-PINNs will be validated for solving two-parameter SPPs.

Paperid: 1087, https://arxiv.org/pdf/2504.21501.pdf

Abstract:
In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient descent sometimes behaves inefficiently in deep learning because of the high non-convexity of loss functions and the vanishing gradient issue. Our idea is to introduce auxiliary variables to separate the layers of the deep neural networks and reformulate the loss functions for ease of optimization. We design the self-adaptive weights to preserve the consistency between the reformulated loss and the original mean squared loss, which guarantees that optimizing the new loss helps optimize the original problem. Numerical experiments are presented to verify the consistency and show the effectiveness and robustness of our models over gradient descent.

Paperid: 1088, https://arxiv.org/pdf/2504.21377.pdf

Abstract:
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant coefficients. The control task is formulated as an inference problem by conditioning the Gaussian process prior on the setpoints and incorporating pointwise soft-constraints as further virtual setpoints. We apply this method to systems of nonlinear differential equations, obtaining a local approximation through the linearization around an equilibrium point. In the case of an asymptotically stable equilibrium point convergence is given through the Bayesian inference schema of the Gaussian Process. Results for this are demonstrated in a numerical example.

Paperid: 1089, https://arxiv.org/pdf/2504.18854.pdf

Abstract:
Stress analysis is an important part of material design. For materials with complex microstructures, such as two-phase random materials (TRMs), material failure is often accompanied by stress concentration. Phase interfaces in two-phase materials are critical for stress concentration. Therefore, the prediction error of stress at phase boundaries is crucial. In practical engineering, the pixels of the obtained material microstructure images are limited, which limits the resolution of stress images generated by deep learning methods, making it difficult to observe stress concentration regions. Existing Image Super-Resolution (ISR) technologies are all based on data-driven supervised learning. However, stress images have natural physical constraints, which provide new ideas for new ISR technologies. In this study, we constructed a stress prediction framework for TRMs. First, the framework uses a proposed Multiple Compositions U-net (MC U-net) to predict stress in low-resolution material microstructures. By considering the phase interface information of the microstructure, the MC U-net effectively reduces the problem of excessive prediction errors at phase boundaries. Secondly, a Mixed Physics-Informed Neural Network (MPINN) based method for stress ISR (SRPINN) was proposed. By introducing the constraints of physical information, the new method does not require paired stress images for training and can increase the resolution of stress images to any multiple. This enables a multiscale analysis of the stress concentration regions at phase boundaries. Finally, we performed stress analysis on TRMs with different phase volume fractions and loading states through transfer learning. The results show the proposed stress prediction framework has satisfactory accuracy and generalization ability.

Paperid: 1090, https://arxiv.org/pdf/2504.18091.pdf

Abstract:
Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN solutions is often limited by the treatment of boundary conditions. Conventional penalty-based methods, which incorporate boundary conditions as penalty terms in the loss function, cannot guarantee exact satisfaction of the given boundary conditions and are highly sensitive to the choice of penalty parameters. This paper demonstrates that distance functions, specifically R-functions, can be leveraged to enforce boundary conditions, overcoming these limitations. R-functions provide normalized distance fields, enabling accurate representation of boundary geometries, including non-convex domains, and facilitating various types of boundary conditions. We extend this distance function-based boundary condition imposition method to inverse problems using PINNs and introduce an adaptive weight tuning technique to ensure reliable and efficient inverse analysis. We demonstrate the efficacy of the method through several numerical experiments. Numerical results show that the proposed method solves inverse problems more accurately and efficiently than penalty-based methods, even in the presence of complex non-convex geometries. This approach offers a reliable and efficient framework for inverse analysis using PINNs, with potential applications across a wide range of engineering problems.

Paperid: 1091, https://arxiv.org/pdf/2504.16553.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from slow convergence and instability, particularly for high-frequency wavefields. For scattered acoustic wavefield simulation based on Helmholtz equation, we derive a hybrid optimization framework that accelerates training convergence by embedding a least-squares (LS) solver directly into the GD loss function. This formulation enables optimal updates for the linear output layer. Our method is applicable with or without perfectly matched layers (PML), and we provide practical tensor-based implementations for both scenarios. Numerical experiments on benchmark velocity models demonstrate that our approach achieves faster convergence, higher accuracy, and improved stability compared to conventional PINN training. In particular, our results show that the LS-enhanced method converges rapidly even in cases where standard GD-based training fails. The LS solver operates on a small normal matrix, ensuring minimal computational overhead and making the method scalable for large-scale wavefield simulations.

Paperid: 1092, https://arxiv.org/pdf/2504.15806.pdf

Abstract:
Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to Multi-layer Perceptrons (MLPs) due to their superior function-fitting abilities in data-driven modeling. In this paper, we propose a novel framework, DAE-KAN, for solving high-index differential-algebraic equations (DAEs) by integrating KANs with Physics-Informed Neural Networks (PINNs). This framework not only preserves the ability of traditional PINNs to model complex systems governed by physical laws but also enhances their performance by leveraging the function-fitting strengths of KANs. Numerical experiments demonstrate that for DAE systems ranging from index-1 to index-3, DAE-KAN reduces the absolute errors of both differential and algebraic variables by 1 to 2 orders of magnitude compared to traditional PINNs. To assess the effectiveness of this approach, we analyze the drift-off error and find that both PINNs and DAE-KAN outperform classical numerical methods in controlling this phenomenon. Our results highlight the potential of neural network methods, particularly DAE-KAN, in solving high-index DAEs with substantial computational accuracy and generalization, offering a promising solution for challenging partial differential-algebraic equations.

Paperid: 1093, https://arxiv.org/pdf/2504.12441.pdf

Abstract:
Accurately modeling friction in robotics remains a core challenge, as robotics simulators like Mujoco and PyBullet use simplified friction models or heuristics to balance computational efficiency with accuracy, where these simplifications and approximations can lead to substantial differences between simulated and physical performance. In this paper, we present a physics-informed friction estimation framework that enables the integration of well-established friction models with learnable components-requiring only minimal, generic measurement data. Our approach enforces physical consistency yet retains the flexibility to adapt to real-world complexities. We demonstrate, on an underactuated and nonlinear system, that the learned friction models, trained solely on small and noisy datasets, accurately simulate dynamic friction properties and reduce the sim-to-real gap. Crucially, we show that our approach enables the learned models to be transferable to systems they are not trained on. This ability to generalize across multiple systems streamlines friction modeling for complex, underactuated tasks, offering a scalable and interpretable path toward bridging the sim-to-real gap in robotics and control.

Paperid: 1094, https://arxiv.org/pdf/2504.11383.pdf

Abstract:
Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is hindered by several challenges: they typically require large volumes of training data generated from high-fidelity solvers, tend to accumulate errors over time in dynamical settings, and often exhibit poor generalization in multiphysics scenarios. This work introduces a novel hybrid framework that integrates physics-informed deep operator network with FEM through domain decomposition and leverages numerical analysis for time marching. Our innovation lies in efficient coupling FE and DeepONet subdomains via a Schwarz method, expecting to solve complex and nonlinear regions by a pretrained DeepONet, while the remainder is handled by conventional FE. To address the challenges of dynamic systems, we embed a time stepping scheme directly into the DeepONet, substantially reducing long-term error propagation. Furthermore, an adaptive subdomain evolution strategy enables the ML-resolved region to expand dynamically, capturing fine-scale features without remeshing. Our framework shows accelerated convergence rates (up to 20% improvement in convergence rates compared to conventional FE coupling approaches) while preserving solution fidelity with error margins consistently below 3%. Our study shows that our proposed hybrid solver: (1) reduces computational costs by eliminating fine mesh requirements, (2) mitigates error accumulation in time-dependent simulations, and (3) enables automatic adaptation to evolving physical phenomena. This work establishes a new paradigm for coupling state of the art physics based and machine learning solvers in a unified framework, offering a robust, reliable, and scalable pathway for high fidelity multiscale simulations.

Paperid: 1095, https://arxiv.org/pdf/2504.09804.pdf

Abstract:
Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling methods and loss function weights for different PDEs, which reduces the efficiency of the solvers. In this paper, we pro- pose a general multi-stage framework, i.e. BO-SA-PINNs to alleviate this issue. In the first stage, Bayesian optimization (BO) is used to select hyperparameters for the training process, and based on the results of the pre-training, the network architecture, learning rate, sampling points distribution and loss function weights suitable for the PDEs are automatically determined. The proposed hyperparameters search space based on experimental results can enhance the efficiency of BO in identifying optimal hyperparameters. After selecting the appropriate hyperparameters, we incorporate a global self-adaptive (SA) mechanism the second stage. Using the pre-trained model and loss information in the second-stage training, the exponential moving average (EMA) method is employed to optimize the loss function weights, and residual-based adaptive refinement with distribution (RAR-D) is used to optimize the sampling points distribution. In the third stage, L-BFGS is used for stable training. In addition, we introduce a new activation function that enables BO-SA-PINNs to achieve higher accuracy. In numerical experiments, we conduct comparative and ablation experiments to verify the performance of the model on Helmholtz, Maxwell, Burgers and high-dimensional Poisson equations. The comparative experiment results show that our model can achieve higher accuracy and fewer iterations in test cases, and the ablation experiments demonstrate the positive impact of every improvement.

Paperid: 1096, https://arxiv.org/pdf/2504.08136.pdf

Abstract:
In this article we develop a Physics Informed Neural Network (PINN) approach to simulate ice sheet dynamics governed by the Shallow Ice Approximation. This problem takes the form of a time-dependent parabolic obstacle problem. Prior work has used this approach to address the stationary obstacle problem and here we extend it to the time dependent problem. Through comprehensive 1D and 2D simulations, we validate the model's effectiveness in capturing complex free-boundary conditions. By merging traditional mathematical modeling with cutting-edge deep learning methods, this approach provides a scalable and robust solution for predicting temporal variations in ice thickness. To illustrate this approach in a real world setting, we simulate the dynamics of the Devon Ice Cap, incorporating aerogeophysical data from 2000 and 2018.

Paperid: 1097, https://arxiv.org/pdf/2504.07802.pdf

Abstract:
The flight time of multirotor unmanned aerial vehicles (UAVs) is typically constrained by their high power consumption. Tethered power systems present a viable solution to extend flight times while maintaining the advantages of multirotor UAVs, such as hover capability and agility. This paper addresses the critical aspect of cable selection for tether-powered multirotor UAVs, considering both hover and forward flight. Existing research often overlooks the trade-offs between cable mass, power losses, and system constraints. We propose a novel methodology to optimize cable selection, accounting for thrust requirements and power efficiency across various flight conditions. The approach combines physics-informed modeling with system identification to combine hover and forward flight dynamics, incorporating factors such as motor efficiency, tether resistance, and aerodynamic drag. This work provides an intuitive and practical framework for optimizing tethered UAV designs, ensuring efficient power transmission and flight performance. Thus allowing for better, safer, and more efficient tethered drones.

Paperid: 1098, https://arxiv.org/pdf/2504.04665.pdf

Abstract:
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has produced highly influential methods, such as neural ordinary differential equations (NODEs). Recent works extend this line of research to consider neural differential-algebraic systems of equations (DAEs), where some unknown relationships within the DAE are learned from data. Training neural DAEs, similarly to neural ODEs, is computationally expensive, as it requires the solution of a DAE for every parameter update. Further, the rigorous consideration of algebraic constraints is difficult within common deep learning training algorithms such as stochastic gradient descent. In this work, we apply the simultaneous approach to neural DAE problems, resulting in a fully discretized nonlinear optimization problem, which is solved to local optimality and simultaneously obtains the neural network parameters and the solution to the corresponding DAE. We extend recent work demonstrating the simultaneous approach for neural ODEs, by presenting a general framework to solve neural DAEs, with explicit consideration of hybrid models, where some components of the DAE are known, e.g. physics-informed constraints. Furthermore, we present a general strategy for improving the performance and convergence of the nonlinear programming solver, based on solving an auxiliary problem for initialization and approximating Hessian terms. We achieve promising results in terms of accuracy, model generalizability and computational cost, across different problem settings such as sparse data, unobserved states and multiple trajectories. Lastly, we provide several promising future directions to improve the scalability and robustness of our approach.

Paperid: 1099, https://arxiv.org/pdf/2504.03244.pdf

Abstract:
In this paper, we propose the Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) to address challenges in solving nonlinear option pricing PDE models, where solutions often exhibit significant curvature or shock waves over time. The AM-PIRN architecture is designed to concurrently minimize PDE residuals and achieve high-fidelity option price approximations by dynamically redistributing training points based on evolving PDE residuals, while maintaining a fixed total number of points. To enhance stability and training efficiency, we integrate a ResNet backbone, replacing conventional fully connected neural networks used in Physics-Informed Neural Networks (PINNs). Numerical experiments across nonlinear option pricing models demonstrate that AM-PIRN outperforms PINN, RAM-PINN, and WAM-PINN in both resolving PDE constraints and accurately estimating option prices. The method's advantages are particularly pronounced in complex or multi-dimensional models, where its adaptive sampling and robust architecture effectively mitigate challenges posed by sharp gradients and high nonlinearity.

Paperid: 1100, https://arxiv.org/pdf/2504.03209.pdf

Abstract:
Neural network-based methods are effective for solving equilibria in Mean-Field Games (MFGs), particularly in high-dimensional settings. However, solving the coupled partial differential equations (PDEs) in MFGs limits their applicability since solving coupled PDEs is computationally expensive. Additionally, modifying boundary conditions, such as the initial state distribution or terminal value function, necessitates extensive retraining, reducing scalability. To address these challenges, we propose a generalized framework, PIONM (Physics-Informed Neural Operator NF-MKV Net), which leverages physics-informed neural operators to solve MFGs equations. PIONM utilizes neural operators to compute MFGs equilibria for arbitrary boundary conditions. The method encodes boundary conditions as input features and trains the model to align them with density evolution, modeled using discrete-time normalizing flows. Once trained, the algorithm efficiently computes the density distribution at any time step for modified boundary condition, ensuring efficient adaptation to different boundary conditions in MFGs equilibria. Unlike traditional MFGs methods constrained by fixed coefficients, PIONM efficiently computes equilibria under varying boundary conditions, including obstacles, diffusion coefficients, initial densities, and terminal functions. PIONM can adapt to modified conditions while preserving density distribution constraints, demonstrating superior scalability and generalization capabilities compared to existing methods.

Paperid: 1101, https://arxiv.org/pdf/2504.01532.pdf

Abstract:
Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. However, when applied to large-scale, spatiotemporally chaotic systems, purely data-driven machine learning methods often suffer from inefficiencies, as they require a large learning model size and a massive amount of training data to achieve acceptable performance. To address this challenge, we incorporate the spatial coupling structure of the target system as an inductive bias in the network design. Specifically, we introduce physics-guided clustered echo state networks, leveraging the efficiency of the echo state networks as a base model. Experimental results on benchmark chaotic systems demonstrate that our physics-informed method outperforms existing echo state network models in learning the target chaotic systems. Additionally, we numerically demonstrate that leveraging coupling knowledge into ESN models can enhance their robustness to variations of training and target system conditions. We further show that our proposed model remains effective even when the coupling knowledge is imperfect or extracted directly from time series data. We believe this approach has the potential to enhance other machine-learning methods.

Paperid: 1102, https://arxiv.org/pdf/2504.01093.pdf

Abstract:
We present a novel approach to hard-constrain Neumann boundary conditions in physics-informed neural networks (PINNs) using Fourier feature embeddings. Neumann boundary conditions are used to described critical processes in various application, yet they are more challenging to hard-constrain in PINNs than Dirichlet conditions. Our method employs specific Fourier feature embeddings to directly incorporate Neumann boundary conditions into the neural network's architecture instead of learning them. The embedding can be naturally extended by high frequency modes to better capture high frequency phenomena. We demonstrate the efficacy of our approach through experiments on a diffusion problem, for which our method outperforms existing hard-constraining methods and classical PINNs, particularly in multiscale and high frequency scenarios.

Paperid: 1103, https://arxiv.org/pdf/2503.20144.pdf

Abstract:
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles to enhance predictions when dealing with sparse, noisy, or incomplete data? Physics-Informed Neural Networks (PINNs) put this idea into practice by incorporating physical equations, such as Partial Differential Equations (PDEs), as soft constraints. This guidance helps the networks find solutions that align with established laws. Recently, researchers have expanded this framework to include Bayesian NNs (BNNs), which allow for uncertainty quantification while still adhering to physical principles. But what happens when the governing equations of a system are not known? In this work, we introduce methods to automatically extract PDEs from historical data. We then integrate these learned equations into three different modeling approaches: PINNs, Bayesian-PINNs (B-PINNs), and Bayesian Linear Regression (BLR). To assess these frameworks, we evaluate them on a real-world Multivariate Time Series (MTS) dataset. We compare their effectiveness in forecasting future states under different scenarios: with and without PDE constraints and accuracy considerations. This research aims to bridge the gap between data-driven discovery and physics-guided learning, providing valuable insights for practical applications.

Paperid: 1104, https://arxiv.org/pdf/2503.17430.pdf

Abstract:
Machine learning simulations of open quantum dynamics often rely on recursive predictors that accumulate error. We develop a non-recursive convolutional neural networks (CNNs) that maps system parameters and a redundant time encoding directly to excitation-energy-transfer populations in the Fenna-Matthews-Olson complex. The encoding-modified logistic plus $\tanh$ functions-normalizes time and resolves fast, transitional, and quasi-steady regimes, while physics-informed labels enforce population conservation and inter-site consistency. Trained only on $0\sim 7 ps$ reference trajectories generated with a Lindblad model in QuTiP, the network accurately predicts $0\sim100 ps$ dynamics across a range of reorganization energies, bath rates, and temperatures. Beyond $20 ps$, the absolute relative error remains below 0.05, demonstrating stable long-time extrapolation. By avoiding step-by-step recursion, the method suppresses error accumulation and generalizes across timescales. These results show that redundant time encoding enables data-efficient inference of long-time quantum dissipative dynamics in realistic pigment-protein complexes, and may aid the data-driven design of light-harvesting materials.

Paperid: 1105, https://arxiv.org/pdf/2503.13123.pdf

Abstract:
Simulating the complex interactions between soft tissues and rigid anatomy is critical for applications in surgical training, planning, and robotic-assisted interventions. Traditional Finite Element Method (FEM)-based simulations, while accurate, are computationally expensive and impractical for real-time scenarios. Learning-based approaches have shown promise in accelerating predictions but have fallen short in modeling soft-rigid interactions effectively. We introduce MIXPINN, a physics-informed Graph Neural Network (GNN) framework for mixed-material simulations, explicitly capturing soft-rigid interactions using graph-based augmentations. Our approach integrates Virtual Nodes (VNs) and Virtual Edges (VEs) to enhance rigid body constraint satisfaction while preserving computational efficiency. By leveraging a graph-based representation of biomechanical structures, MIXPINN learns high-fidelity deformations from FEM-generated data and achieves real-time inference with sub-millimeter accuracy. We validate our method in a realistic clinical scenario, demonstrating superior performance compared to baseline GNN models and traditional FEM methods. Our results show that MIXPINN reduces computational cost by an order of magnitude while maintaining high physical accuracy, making it a viable solution for real-time surgical simulation and robotic-assisted procedures.

Paperid: 1106, https://arxiv.org/pdf/2503.02267.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) offer a promising approach to simulating physical systems. Still, their application is limited by optimization challenges, mainly due to the lack of activation functions that generalize well across several physical systems. Existing activation functions often lack such flexibility and generalization power. To address this issue, we introduce Rational Exponential Activation (REAct), a generalized form of tanh consisting of four learnable shape parameters. Experiments show that REAct outperforms many standard and benchmark activations, achieving an MSE three orders of magnitude lower than tanh on heat problems and generalizing well to finer grids and points beyond the training domain. It also excels at function approximation tasks and improves noise rejection in inverse problems, leading to more accurate parameter estimates across varying noise levels.

Paperid: 1107, https://arxiv.org/pdf/2503.00814.pdf

Abstract:
In numerical simulation, structured mesh generation often requires a lot of time and manpower investment. The general scheme for structured quad mesh generation is to find a mapping between the computational domain and the physical domain. This mapping can be obtained by solving partial differential equations. However, existing structured mesh generation methods are difficult to ensure both efficiency and mesh quality. In this paper, we propose a structured mesh generation method based on physics-informed neural network, PINN-MG. It takes boundary curves as input and then utilizes an attention network to capture the potential mapping between computational and physical domains, generating structured meshes for the input physical domain. PINN-MG introduces the Navier-LamÃ© equation in linear elastic as a partial differential equation term in the loss function, ensuring that the neural network conforms to the law of elastic body deformation when optimizing the loss value. The training process of PINN-MG is completely unsupervised and does not require any prior knowledge or datasets, which greatly reduces the previous workload of producing structured mesh datasets. Experimental results show that PINN-MG can generate higher quality structured quad meshes than other methods, and has the advantages of traditional algebraic methods and differential methods.

Paperid: 1108, https://arxiv.org/pdf/2502.19056.pdf

Abstract:
Fatigue modeling is essential for motion synthesis tasks to model human motions under fatigued conditions and biomechanical engineering applications, such as investigating the variations in movement patterns and posture due to fatigue, defining injury risk mitigation and prevention strategies, formulating fatigue minimization schemes and creating improved ergonomic designs. Nevertheless, employing data-driven methods for synthesizing the impact of fatigue on motion, receives little to no attention in the literature. In this work, we present Fatigue-PINN, a deep learning framework based on Physics-Informed Neural Networks, for modeling fatigued human movements, while providing joint-specific fatigue configurations for adaptation and mitigation of motion artifacts on a joint level, resulting in more realistic animations. To account for muscle fatigue, we simulate the fatigue-induced fluctuations in the maximum exerted joint torques by leveraging a PINN adaptation of the Three-Compartment Controller model to exploit physics-domain knowledge for improving accuracy. This model also introduces parametric motion alignment with respect to joint-specific fatigue, hence avoiding sharp frame transitions. Our results indicate that Fatigue-PINN accurately simulates the effects of externally perceived fatigue on open-type human movements being consistent with findings from real-world experimental fatigue studies. Since fatigue is incorporated in torque space, Fatigue-PINN provides an end-to-end encoder-decoder-like architecture, to ensure transforming joint angles to joint torques and vice-versa, thus, being compatible with motion synthesis frameworks operating on joint angles.

Paperid: 1109, https://arxiv.org/pdf/2502.17134.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have gained increasing attention for solving partial differential equations, including the Helmholtz equation, due to their flexibility and mesh-free formulation. However, their low-frequency bias limits their accuracy and convergence speed for high-frequency wavefield simulations. To alleviate these problems, we propose a simplified PINN framework that incorporates Gabor functions, designed to capture the oscillatory and localized nature of wavefields more effectively. Unlike previous attempts that rely on auxiliary networks to learn Gabor parameters, we redefine the network's task to map input coordinates to a custom Gabor coordinate system, simplifying the training process without increasing the number of trainable parameters compared to a simple PINN. We validate the proposed method across multiple velocity models, including the complex Marmousi and Overthrust models, and demonstrate its superior accuracy, faster convergence, and better robustness features compared to both traditional PINNs and earlier Gabor-based PINNs. Additionally, we propose an efficient integration of a Perfectly Matched Layer (PML) to enhance wavefield behavior near the boundaries. These results suggest that our approach offers an efficient and accurate alternative for scattered wavefield modeling and lays the groundwork for future improvements in PINN-based seismic applications.

Paperid: 1110, https://arxiv.org/pdf/2502.11153.pdf

Abstract:
Selecting optimal kernels for regression in physical systems remains a challenge, often relying on trial-and-error with standard functions. In this work, we establish a mathematical correspondence between support vector machine kernels and quantum propagators, demonstrating that kernel efficacy is determined by its spectral alignment with the system's Green's function. Based on this isomorphism, we propose a unified, physics-informed framework for kernel selection and design. For systems with known propagator forms, we derive analytical selection rules that map standard kernels to physical operators. For complex systems where the Green's function is analytically intractable, we introduce a constructive numerical method using the Kernel Polynomial Method with Jackson smoothing to generate custom, physics-aligned kernels. Numerical experiments spanning electrical conductivity, electronic band structure, anharmonic oscillators, and photonic crystals demonstrate that this framework consistently performs well as long as there is an alignment with a Green's function.

Paperid: 1111, https://arxiv.org/pdf/2502.07325.pdf

Abstract:
This paper proposes a Curriculum-Transfer-Learning based physics-informed neural network (CTL-PINN) for long-term simulation of physical and mechanical behaviors. The main innovation of CTL-PINN lies in decomposing long-term problems into a sequence of short-term subproblems. Initially, the standard PINN is employed to solve the first sub-problem. As the simulation progresses, subsequent time-domain problems are addressed using a curriculum learning approach that integrates information from previous steps. Furthermore, transfer learning techniques are incorporated, allowing the model to effectively utilize prior training data and solve sequential time domain transfer problems. CTL-PINN combines the strengths of curriculum learning and transfer learning, overcoming the limitations of standard PINNs, such as local optimization issues, and addressing the inaccuracies over extended time domains encountered in CL-PINN and the low computational efficiency of TL-PINN. The efficacy and robustness of CTL-PINN are demonstrated through applications to nonlinear wave propagation, Kirchhoff plate dynamic response, and the hydrodynamic model of the Three Gorges Reservoir Area, showcasing its superior capability in addressing long-term computational challenges.

Paperid: 1112, https://arxiv.org/pdf/2502.07293.pdf

Abstract:
Using machine learning (ML) to construct interatomic interactions and thus potential energy surface (PES) has become a common strategy for materials design and simulations. However, those current models of machine learning interatomic potential (MLIP) provide no relevant physical constrains, and thus may owe intrinsic out-of-domain difficulty which underlies the challenges of model generalizability and physical scalability. Here, by incorporating physics-informed Universal-Scaling law and nonlinearity-embedded interaction function, we develop a Super-linear MLIP with both Ultra-Small parameterization and greatly expanded expressive capability, named SUS2-MLIP. Due to the global scaling rooting in universal equation of state (UEOS), SUS2-MLIP not only has significantly-reduced parameters by decoupling the element space from coordinate space, but also naturally outcomes the out-of-domain difficulty and endows the potentials with inherent generalizability and scalability even with relatively small training dataset. The nonlinearity-enbeding transformation for interaction function expands the expressive capability and make the potentials super-linear. The SUS2-MLIP outperforms the state-of-the-art MLIP models with its exceptional computational efficiency especially for multiple-element materials and physical scalability in property prediction. This work not only presents a highly-efficient universal MLIP model but also sheds light on incorporating physical constraints into artificial-intelligence-aided materials simulation.

Paperid: 1113, https://arxiv.org/pdf/2502.03670.pdf

Abstract:
Stochastic partial differential equations (SPDEs) describe the evolution of random processes over space and time, but their solutions are often analytically intractable and computationally expensive to estimate. In this paper, we propose the Learned Expectation Collapser (LEC), a physics-informed neural framework designed to approximate the expected value of linear SPDE solutions without requiring domain discretization. By leveraging randomized sampling of both space-time coordinates and noise realizations during training, LEC trains standard feedforward neural networks to minimize residual loss across multiple stochastic samples. We hypothesize and empirically confirm that this training regime drives the network to converge toward the expected value of the solution of the SPDE. Using the stochastic heat equation as a testbed, we evaluate performance across a diverse set of 144 experimental configurations that span multiple spatial dimensions, noise models, and forcing functions. The results show that the model consistently learns accurate approximations of the expected value of the solution in lower dimensions and a predictable decrease in accuracy with increased spatial dimensions, with improved stability and robustness under increased Monte Carlo sampling. Our findings offer new insight into how neural networks implicitly learn statistical structure from stochastic differential operators and suggest a pathway toward scalable, simulator-free SPDE solvers.

Paperid: 1114, https://arxiv.org/pdf/2501.17281.pdf

Abstract:
Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to significant improvements in modeling physical processes described by differential equations. Despite their promising outcomes, vanilla PINNs face limitations when dealing with stiff systems, known as failure modes. In response, we propose a novel approach, stiff transfer learning for physics-informed neural networks (STL-PINNs), to effectively tackle stiff ordinary differential equations (ODEs) and partial differential equations (PDEs). Our methodology involves training a Multi-Head-PINN in a low-stiff regime, and obtaining the final solution in a high stiff regime by transfer learning. This addresses the failure modes related to stiffness in PINNs while maintaining computational efficiency by computing "one-shot" solutions. The proposed approach demonstrates superior accuracy and speed compared to PINNs-based methods, as well as comparable computational efficiency with implicit numerical methods in solving stiff-parameterized linear and polynomial nonlinear ODEs and PDEs under stiff conditions. Furthermore, we demonstrate the scalability of such an approach and the superior speed it offers for simulations involving initial conditions and forcing function reparametrization.

Paperid: 1115, https://arxiv.org/pdf/2501.15849.pdf

Abstract:
This work investigates data-driven prediction and control of Hammerstein-Wiener systems using physics-informed Gaussian process models. Data-driven prediction algorithms have been developed for structured nonlinear systems based on Willems' fundamental lemma. However, existing frameworks cannot treat output nonlinearities and require a dictionary of basis functions for Hammerstein systems. In this work, an implicit predictor structure is considered, leveraging the multi-step-ahead ARX structure for the linear part of the model. This implicit function is learned by Gaussian process regression with kernel functions designed from Gaussian process priors for the nonlinearities. The linear model parameters are estimated as hyperparameters by assuming a stable spline hyperprior. The implicit Gaussian process model provides explicit output prediction by optimizing selected optimality criteria. The model is also applied to receding horizon control with the expected control cost and chance constraint satisfaction guarantee. Numerical results demonstrate that the proposed prediction and control algorithms are superior to black-box Gaussian process models.

Paperid: 1116, https://arxiv.org/pdf/2501.11323.pdf

Abstract:
Reconfigurable intelligent surface (RIS) is a two-dimensional periodic structure integrated with a large number of reflective elements, which can manipulate electromagnetic waves in a digital way, offering great potentials for wireless communication and radar detection applications. However, conventional RIS designs highly rely on extensive full-wave EM simulations that are extremely time-consuming. To address this challenge, we propose a machine-learning-assisted approach for efficient RIS design. An accurate and fast model to predict the reflection coefficient of RIS element is developed by combining a multi-layer perceptron neural network (MLP) and a dual-port network, which can significantly reduce tedious EM simulations in the network training. A RIS has been practically designed based on the proposed method. To verify the proposed method, the RIS has also been fabricated and measured. The experimental results are in good agreement with the simulation results, which validates the efficacy of the proposed method in RIS design.

Paperid: 1117, https://arxiv.org/pdf/2501.09034.pdf

Abstract:
This review examines the current state of research on microscale cellular changes during the drying of plant-based food materials (PBFM), with particular emphasis on computational modelling approaches. The review addresses the critical need for advanced computational methods in microscale investigations. We systematically analyse experimental studies in PBFM drying, highlighting their contributions and limitations in capturing cellular-level phenomena, including challenges in data acquisition and measurement accuracy under varying drying conditions. The evolution of computational models for microstructural investigations is thoroughly examined, from traditional numerical methods to contemporary state-of-the-art approaches, with specific focus on their ability to handle the complex, nonlinear properties of plant cellular materials. Special attention is given to the emergence of data-driven models and their limitations in predicting microscale cellular behaviour during PBFM drying, particularly addressing challenges in dataset acquisition and model generalization. The review provides an in-depth analysis of Physics-Informed Machine Learning (PIML) frameworks, examining their theoretical foundations, current applications in related fields, and unique advantages in combining physical principles with neural network architectures. Through this comprehensive assessment, we identify critical gaps in existing methodologies, evaluate the trade-offs between different modelling approaches, and provide insights into future research directions for improving our understanding of cellular-level transformations during PBFM drying processes. The review concludes with recommendations for integrating experimental and computational approaches to advance the field of food preservation technology.

Paperid: 1118, https://arxiv.org/pdf/2501.03911.pdf

Abstract:
This paper broaches the peridynamic inverse problem of determining the horizon size of the kernel function in a one-dimensional model of a linear microelastic material. We explore different kernel functions, including V-shaped, distributed, and tent kernels. The paper presents numerical experiments using PINNs to learn the horizon parameter for problems in one and two spatial dimensions. The results demonstrate the effectiveness of PINNs in solving the peridynamic inverse problem, even in the presence of challenging kernel functions. We observe and prove a one-sided convergence behavior of the Stochastic Gradient Descent method towards a global minimum of the loss function, suggesting that the true value of the horizon parameter is an unstable equilibrium point for the PINN's gradient flow dynamics.

Paperid: 1119, https://arxiv.org/pdf/2501.00780.pdf

Abstract:
We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for this equation rely on the interacting particle method combined with techniques based on the ItÃ´-Taylor expansion. The convergence rate of this approach is determined by two parameters: the number of particles $N$ and the time step size $h$ for each Euler iteration. However, for extended time horizons or equations with larger Lipschitz coefficients, this method is often limited, as it requires a significant increase in Euler iterations to achieve the desired precision $Îµ$. To overcome the challenges posed by the difficulty of parallelizing the simulation of continuous interacting particle systems, which involve solving high-dimensional coupled SDEs, we propose a meshless MV-SDE solver grounded in Physics-Informed Neural Networks (PINNs) that does not rely on the propagation of chaos result. Our method constructs a pseudo MV-SDE using ItÃ´ calculus, then quantifies the discrepancy between this equation and the original MV-SDE, with the error minimized through a loss function. This loss is controlled via an optimization algorithm, independent of the time step size, and we provide an error estimate for the loss function. The advantages of our approach are demonstrated through corresponding simulations.

Paperid: 1120, https://arxiv.org/pdf/2412.12709.pdf

Abstract:
Strongly lensed quasars provide valuable insights into the rate of cosmic expansion, the distribution of dark matter in foreground deflectors, and the characteristics of quasar hosts. However, detecting them in astronomical images is difficult due to the prevalence of non-lensing objects. To address this challenge, we developed a generative deep learning model called VariLens, built upon a physics-informed variational autoencoder. This model seamlessly integrates three essential modules: image reconstruction, object classification, and lens modeling, offering a fast and comprehensive approach to strong lens analysis. VariLens is capable of rapidly determining both (1) the probability that an object is a lens system and (2) key parameters of a singular isothermal ellipsoid (SIE) mass model -- including the Einstein radius ($Î¸_\mathrm{E}$), lens center, and ellipticity -- in just milliseconds using a single CPU. A direct comparison of VariLens estimates with traditional lens modeling for 20 known lensed quasars within the Subaru Hyper Suprime-Cam (HSC) footprint shows good agreement, with both results consistent within $2Ï$ for systems with $Î¸_\mathrm{E}<3$ arcsecs. To identify new lensed quasar candidates, we begin with an initial sample of approximately 80 million sources, combining HSC data with multiwavelength information from various surveys. After applying a photometric preselection aimed at locating $z>1.5$ sources, the number of candidates was reduced to 710,966. Subsequently, VariLens highlights 13,831 sources, each showing a high likelihood of being a lens. A visual assessment of these objects results in 42 promising candidates that await spectroscopic confirmation. These results underscore the potential of automated deep learning pipelines to efficiently detect and model strong lenses in large datasets.

Paperid: 1121, https://arxiv.org/pdf/2412.09453.pdf

Abstract:
PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems. These challenges become evident when comparing the limitations of PINN with the well-established numerical methods commonly used in solid mechanics, such as the finite element method (FEM). Specifically: a) PINN models generate solutions over an infinite domain, which conflicts with the finite boundaries typical of most solid structures; and b) the solution space utilised by PINN is Euclidean, which is inadequate for addressing the complex geometries often present in solid structures. This work presents a PINN architecture for general solid mechanics problems, referred to as the Finite-PINN model. The model is designed to effectively tackle two key challenges, while retaining as much of the original PINN framework as possible. To this end, the Finite-PINN incorporates finite geometric encoding into the neural network inputs, thereby transforming the solution space from a conventional Euclidean space into a hybrid Euclidean-topological space. The model is comprehensively trained using both strong-form and weak-form loss formulations, enabling its application to a wide range of forward and inverse problems in solid mechanics. For forward problems, the Finite-PINN model efficiently approximates solutions to solid mechanics problems when the geometric information of a given structure has been preprocessed. For inverse problems, it effectively reconstructs full-field solutions from very sparse observations by embedding both physical laws and geometric information within its architecture.

Paperid: 1122, https://arxiv.org/pdf/2412.03161.pdf

Abstract:
Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely on large amounts of labeled training data, which is impractical for most real-world applications. Moreover, these supervised models may fail to capture the underlying physical principles accurately. To address these limitations, we propose a novel architecture called Physics-Informed Deep Inverse Operator Networks (PI-DIONs), which can learn the solution operator of PDE-based inverse problems without labeled training data. We extend the stability estimates established in the inverse problem literature to the operator learning framework, thereby providing a robust theoretical foundation for our method. These estimates guarantee that the proposed model, trained on a finite sample and grid, generalizes effectively across the entire domain and function space. Extensive experiments are conducted to demonstrate that PI-DIONs can effectively and accurately learn the solution operators of the inverse problems without the need for labeled data.

Paperid: 1123, https://arxiv.org/pdf/2412.00113.pdf

Abstract:
Traditional electrostatic simulation are meshed-based methods which convert partial differential equations into an algebraic system of equations and their solutions are approximated through numerical methods. These methods are time consuming and any changes in their initial or boundary conditions will require solving the numerical problem again. Newer computational methods such as the physics informed neural net (PINN) similarly require re-training when boundary conditions changes. In this work, we propose an end-to-end deep learning approach to model parameter changes to the boundary conditions. The proposed method is demonstrated on the test problem of a long air-filled capacitor structure. The proposed approach is compared to plain vanilla deep learning (NN) and PINN. It is shown that our method can significantly outperform both NN and PINN under dynamic boundary condition as well as retaining its full capability as a forward model.

Paperid: 1124, https://arxiv.org/pdf/2411.16698.pdf

Abstract:
We propose a novel design paradigm for arbitrarily capable deep photonic networks of cascaded Mach-Zehnder Interferometers (MZIs) for on-chip universal polarization handling. Using a device architecture made of cascaded Mach-Zehnder interferometers, we modify and train the phase difference between interferometer arms for both polarizations through wide operation bandwidths. Three proof-of-concept polarization handling devices are illustrated using a software-defined, physics-informed neural framework, to achieve user-specified target device responses as functions of polarization and wavelength. These devices include a polarization splitter, a polarization-independent power splitter, and an arbitrary polarization-dependent splitter to illustrate the capabilities of the design framework. The performance for all three devices is optimized using transfer matrix calculations; and their final responses are verified through 3D-FDTD simulations. All devices demonstrate state-of-the-art performance metrics with over 20 dB extinction, and flat-top transmission bands through bandwidths of 120 nm. In addition to the functional diversity enabled, the optimization for each device is completed in under a minute, highlighting the computational efficiency of the design paradigm presented. These results demonstrate the versatility of the deep photonic network design ecosystem in polarization management, unveiling promising prospects for advanced on-chip applications in optical communications, sensing, and computing.

Paperid: 1125, https://arxiv.org/pdf/2411.09915.pdf

Abstract:
With the popularity of electric vehicles, the demand for lithium-ion batteries is increasing. Temperature significantly influences the performance and safety of batteries. Battery thermal management systems can effectively control the temperature of batteries; therefore, the performance and safety can be ensured. However, the development process of battery thermal management systems is time-consuming and costly due to the extensive training dataset needed by data-driven models requiring enormous computational costs for finite element analysis. Therefore, a new approach to constructing surrogate models is needed in the era of AI. Physics-informed machine learning enforces the physical laws in surrogate models, making it the perfect candidate for estimating battery pack temperature distribution. In this study, we first developed a 21700 battery pack indirect liquid cooling system with cold plates on the top and bottom with thermal paste surrounding the battery cells. Then, the simplified finite element model was built based on experiment results. Due to the high coolant flow rate, the cold plates can be considered as constant temperature boundaries, while battery cells are the heat sources. The physics-informed convolutional neural network served as a surrogate model to estimate the temperature distribution of the battery pack. The loss function was constructed considering the heat conduction equation based on the finite difference method. The physics-informed loss function helped the convergence of the training process with less data. As a result, the physics-informed convolutional neural network showed more than 15 percents improvement in accuracy compared to the data-driven method with the same training data.

Paperid: 1126, https://arxiv.org/pdf/2411.04714.pdf

Abstract:
In this study, we propose a high-performance disparity (depth) estimation method using dual-pixel (DP) images with few parameters. Conventional end-to-end deep-learning methods have many parameters but do not fully exploit disparity constraints, which limits their performance. Therefore, we propose a lightweight disparity estimation method based on a completion-based network that explicitly constrains disparity and learns the physical and systemic disparity properties of DP. By modeling the DP-specific disparity error parametrically and using it for sampling during training, the network acquires the unique properties of DP and enhances robustness. This learning also allows us to use a common RGB-D dataset for training without a DP dataset, which is labor-intensive to acquire. Furthermore, we propose a non-learning-based refinement framework that efficiently handles inherent disparity expansion errors by appropriately refining the confidence map of the network output. As a result, the proposed method achieved state-of-the-art results while reducing the overall system size to 1/5 of that of the conventional method, even without using the DP dataset for training, thereby demonstrating its effectiveness. The code and dataset are available on our project site.

Paperid: 1127, https://arxiv.org/pdf/2410.21025.pdf

Abstract:
Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single spatial region, neglecting the case with multiple interconnected sub-regions, such as gas and thermal systems. To address this, this paper proposes a Physics-Informed Partitioned Coupled Neural Operator (PCNO) to enhance the simulation performance of such networks. Compared to the existing Fourier Neural Operator (FNO), this method designs a joint convolution operator within the Fourier layer, enabling global integration capturing all sub-regions. Additionally, grid alignment layers are introduced outside the Fourier layer to help the joint convolution operator accurately learn the coupling relationship between sub-regions in the frequency domain. Experiments on gas networks demonstrate that the proposed operator not only accurately simulates complex systems but also shows good generalization and low model complexity.

Paperid: 1128, https://arxiv.org/pdf/2410.20212.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. This study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an 'overshoot and relocate' phenomenon in dynamic cases with complex morphologies, showcasing the method's adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The simplicity and effectiveness of our RBAR-causality combined PINN offer promising potential for applications across various physical systems characterized by complex, evolving interfaces.

Paperid: 1129, https://arxiv.org/pdf/2410.20203.pdf

Abstract:
We study numerical algorithms to solve a specific Partial Differential Equation (PDE), namely the Stefan problem, using Physics Informed Neural Networks (PINNs). This problem describes the heat propagation in a liquid-solid phase change system. It implies a heat equation and a discontinuity at the interface where the phase change occurs. In the context of PINNs, this model leads to difficulties in the learning process, especially near the interface of phase change. We present different strategies that can be used in this context. We illustrate our results and compare with classical solvers for PDEs (finite differences).

Paperid: 1131, https://arxiv.org/pdf/2410.13141.pdf

Abstract:
By leveraging neural networks, the emerging field of scientific machine learning (SciML) offers novel approaches to address complex problems governed by partial differential equations (PDEs). In practical applications, challenges arise due to the distributed essence of data, concerns about data privacy, or the impracticality of transferring large volumes of data. Federated learning (FL), a decentralized framework that enables the collaborative training of a global model while preserving data privacy, offers a solution to the challenges posed by isolated data pools and sensitive data issues. Here, this paper explores the integration of FL and SciML to approximate complex functions and solve differential equations. We propose two novel models: federated physics-informed neural networks (FedPINN) and federated deep operator networks (FedDeepONet). We further introduce various data generation methods to control the degree of non-independent and identically distributed (non-iid) data and utilize the 1-Wasserstein distance to quantify data heterogeneity in function approximation and PDE learning. We systematically investigate the relationship between data heterogeneity and federated model performance. Additionally, we propose a measure of weight divergence and develop a theoretical framework to establish growth bounds for weight divergence in federated learning compared to traditional centralized learning. To demonstrate the effectiveness of our methods, we conducted 10 experiments, including 2 on function approximation, 5 PDE problems on FedPINN, and 3 PDE problems on FedDeepONet. These experiments demonstrate that proposed federated methods surpass the models trained only using local data and achieve competitive accuracy of centralized models trained using all data.

Paperid: 1132, https://arxiv.org/pdf/2410.02819.pdf

Abstract:
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their lack of physical invariances, coupled with other significant weaknesses, such as an inability to handle complex geometries or their lack of generalization capabilities, make them unable to compete with classical numerical solvers in industrial settings. In this work, a limitation regarding the use of automatic differentiation in the context of physics-informed learning is highlighted. A hybrid approach combining physics-informed graph neural networks with numerical kernels from finite elements is introduced. After studying the theoretical properties of our model, we apply it to complex geometries, in two and three dimensions. Our choices are supported by an ablation study, and we evaluate the generalisation capacity of the proposed approach.

Paperid: 1133, https://arxiv.org/pdf/2409.18223.pdf

Abstract:
Light field microscopy (LFM) has been widely utilized in various fields for its capability to efficiently capture high-resolution 3D scenes. Despite the rapid advancements in neural representations, there are few methods specifically tailored for microscopic scenes. Existing approaches often do not adequately address issues such as the loss of high-frequency information due to defocus and sample aberration, resulting in suboptimal performance. In addition, existing methods, including RLD, INR, and supervised U-Net, face challenges such as sensitivity to initial estimates, reliance on extensive labeled data, and low computational efficiency, all of which significantly diminish the practicality in complex biological scenarios. This paper introduces PNR (Physics-informed Neural Representation), a method for high-resolution LFM reconstruction that significantly enhances performance. Our method incorporates an unsupervised and explicit feature representation approach, resulting in a 6.1 dB improvement in PSNR than RLD. Additionally, our method employs a frequency-based training loss, enabling better recovery of high-frequency details, which leads to a reduction in LPIPS by at least half compared to SOTA methods (1.762 V.S. 3.646 of DINER). Moreover, PNR integrates a physics-informed aberration correction strategy that optimizes Zernike polynomial parameters during optimization, thereby reducing the information loss caused by aberrations and improving spatial resolution. These advancements make PNR a promising solution for long-term high-resolution biological imaging applications. Our code and dataset will be made publicly available.

Paperid: 1134, https://arxiv.org/pdf/2409.16826.pdf

Abstract:
We present a computational framework for obtaining multidimensional phase-space solutions of systems of non-linear coupled differential equations, using high-order implicit Runge-Kutta Physics- Informed Neural Networks (IRK-PINNs) schemes. Building upon foundational work originally solving differential equations for fields depending on coordinates [J. Comput. Phys. 378, 686 (2019)], we adapt the scheme to a context where the coordinates are treated as functions. This modification enables us to efficiently solve equations of motion for a particle in an external field. Our scheme is particularly useful for explicitly time-independent and periodic fields. We apply this approach to successfully solve the equations of motion for a mass particle placed in a central force field and a charged particle in a periodic electric field.

Paperid: 1135, https://arxiv.org/pdf/2409.13876.pdf

Abstract:
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.

Paperid: 1136, https://arxiv.org/pdf/2409.11847.pdf

Abstract:
Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including ones that may involve limited data availability. However, tackling solutions of differential equations with rapid oscillations, steep gradients, or singular behavior becomes challenging for PINNs. Considering these challenges, we designed an efficient wavelet-based PINNs (W-PINNs) model to address this class of differential equations. Here, we represent the solution in wavelet space using a family of smooth-compactly supported wavelets. This framework represents the solution of a differential equation with significantly fewer degrees of freedom while still retaining the dynamics of complex physical phenomena. The architecture allows the training process to search for a solution within the wavelet space, making the process faster and more accurate. Further, the proposed model does not rely on automatic differentiations for derivatives involved in differential equations and does not require any prior information regarding the behavior of the solution, such as the location of abrupt features. Thus, through a strategic fusion of wavelets with PINNs, W-PINNs excel at capturing localized nonlinear information, making them well-suited for problems showing abrupt behavior in certain regions, such as singularly perturbed and multiscale problems. The efficiency and accuracy of the proposed neural network model are demonstrated in various 1D and 2D test problems, i.e., the FitzHugh-Nagumo (FHN) model, the Helmholtz equation, the Maxwell's equation, lid-driven cavity flow, and the Allen-Cahn equation, along with other highly singularly perturbed nonlinear differential equations. The proposed model significantly improves with traditional PINNs, recently developed wavelet-based PINNs, and other state-of-the-art methods.

Paperid: 1137, https://arxiv.org/pdf/2409.11743.pdf

Abstract:
Energy efficiency of buildings is considered to be one of the major means of achieving the net-zero carbon goal around the world. The big part of the energy savings are supposed to be coming from optimizing the operation of the building heating, ventilation, and air conditioning (HVAC) systems. There is a natural trade-off between the energy efficiency and the indoor comfort level, and finding an optimal operating schedule/regime requires knowing the occupancy of different spaces inside of the building. Moreover, the COVID-19 pandemic has also revealed the need to sustain the high quality of the indoor air in order to reduce the risk of spread of infection. Occupancy detection from indoor sensors is thus an important practical problem. In the present paper, we propose detection of occupancy based on the carbon dioxide measurements inside the building. In particular, a new approach based on the, so-called, switching auto-regressive process with Markov regime is presented and justified by the physical model of the carbon dioxide concentration dynamics. We demonstrate the efficiency of the method compared to simple Hidden Markov approaches on simulated and real-life data. We also show that the model is flexible and can be generalized to account for different ventilation regimes, simultaneously detecting the occupancy and the ventilation rate.

Paperid: 1138, https://arxiv.org/pdf/2409.11138.pdf

Abstract:
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and in particular Hamiltonian Neural Networks have emerged as a mechanism to incorporate structural inductive bias into the NN model. By ensuring physical invariances are conserved, the models exhibit significantly better sample complexity and out-of-distribution accuracy than standard NNs. Learning the Hamiltonian as a function of its canonical variables, typically position and velocity, from sample observations of the system thus becomes a critical task in system identification and long-term prediction of system behavior. However, to truly preserve the long-run physical conservation properties of Hamiltonian systems, one must use symplectic integrators for a forward pass of the system's simulation. While symplectic schemes have been used in the literature, they are thus far limited to situations when they reduce to explicit algorithms, which include the case of separable Hamiltonians or augmented non-separable Hamiltonians. We extend it to generalized non-separable Hamiltonians, and noting the self-adjoint property of symplectic integrators, we bypass computationally intensive backpropagation through an ODE solver. We show that the method is robust to noise and provides a good approximation of the system Hamiltonian when the state variables are sampled from a noisy observation. In the numerical results, we show the performance of the method concerning Hamiltonian reconstruction and conservation, indicating its particular advantage for non-separable systems.

Paperid: 1139, https://arxiv.org/pdf/2409.08063.pdf

Abstract:
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and infinity. A traditional numerical method for solving the resulting high-dimensional coupled system of PDEs is replaced by deep learning techniques. In order to achieve this, physics-informed neural networks (PINNs), which typically operate on the strong residual of the PDE and can therefore be applied in a wide range of settings, are considered. As a second approach, the Deep Ritz method, which is a neural network that minimizes the Ritz energy functional to find the weak solution, is employed. While the second approach only works in special cases, it overcomes the necessity of testing in variational problems while maintaining mathematical rigor and ensuring the existence of a unique solution. Furthermore, the residual is of a lower differentiation order, reducing the training cost considerably. The efficiency of the method is demonstrated on several model problems.

Paperid: 1140, https://arxiv.org/pdf/2409.03239.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are regarded as state-of-the-art tools for addressing highly nonlinear problems based on partial differential equations. Despite their broad range of applications, PINNs encounter several performance challenges, including issues related to efficiency, minimization of computational cost, and enhancement of accuracy. Burgers' equation, a fundamental equation in fluid dynamics that is extensively used in PINNs, provides flexible results with the Adam optimizer that does not account for past gradients. This paper introduces a novel strategy for solving Burgers' equation by incorporating DiffGrad with PINNs, a method that leverages the difference between current and immediately preceding gradients to enhance performance. A comprehensive computational analysis is conducted using optimizers such as Adam, Adamax, RMSprop, and DiffGrad to evaluate and compare their effectiveness. Our approach includes visualizing the solutions over space at various time intervals to demonstrate the accuracy of the network. The results show that DiffGrad not only improves the accuracy of the solution but also reduces training time compared to the other optimizers.

Paperid: 1141, https://arxiv.org/pdf/2409.00651.pdf

Abstract:
In this study, we explore the application of Physics-Informed Neural Networks (PINNs) to the analysis of bifurcation phenomena in ecological migration models. By integrating the fundamental principles of diffusion-advection-reaction equations with deep learning techniques, we address the complexities of species migration dynamics, particularly focusing on the detection and analysis of Hopf bifurcations. Traditional numerical methods for solving partial differential equations (PDEs) often involve intricate calculations and extensive computational resources, which can be restrictive in high-dimensional problems. In contrast, PINNs offer a more flexible and efficient alternative, bypassing the need for grid discretization and allowing for mesh-free solutions. Our approach leverages the DeepXDE framework, which enhances the computational efficiency and applicability of PINNs in solving high-dimensional PDEs. We validate our results against conventional methods and demonstrate that PINNs not only provide accurate bifurcation predictions but also offer deeper insights into the underlying dynamics of diffusion processes. Despite these advantages, the study also identifies challenges such as the high computational costs and the sensitivity of PINN performance to network architecture and hyperparameter settings. Future work will focus on optimizing these algorithms and expanding their application to other complex systems involving bifurcations. The findings from this research have significant implications for the modeling and analysis of ecological systems, providing a powerful tool for predicting and understanding complex dynamical behaviors.

Paperid: 1142, https://arxiv.org/pdf/2409.00644.pdf

Abstract:
Physics-informed deep learning (PIDL)-based models have recently garnered remarkable success in traffic state estimation (TSE). However, the prior knowledge used to guide regularization training in current mainstream architectures is based on deterministic physical models. The drawback is that a solely deterministic model fails to capture the universally observed traffic flow dynamic scattering effect, thereby yielding unreliable outcomes for traffic control. This study, for the first time, proposes stochastic physics-informed deep learning (SPIDL) for traffic state estimation. The idea behind such SPIDL is simple and is based on the fact that a stochastic fundamental diagram provides the entire range of possible speeds for any given density with associated probabilities. Specifically, we select percentile-based fundamental diagram and distribution-based fundamental diagram as stochastic physics knowledge, and design corresponding physics-uninformed neural networks for effective fusion, thereby realizing two specific SPIDL models, namely \text{$Î±$}-SPIDL and \text{$\cal B$}-SPIDL. The main contribution of SPIDL lies in addressing the "overly centralized guidance" caused by the one-to-one speed-density relationship in deterministic models during neural network training, enabling the network to digest more reliable knowledge-based constraints.Experiments on the real-world dataset indicate that proposed SPIDL models achieve accurate traffic state estimation in sparse data scenarios. More importantly, as expected, SPIDL models reproduce well the scattering effect of field observations, demonstrating the effectiveness of fusing stochastic physics model knowledge with deep learning frameworks.

Paperid: 1143, https://arxiv.org/pdf/2601.22111.pdf

Abstract:
Accurate reconstruction of atmospheric wind fields is essential for applications such as weather forecasting, hazard prediction, and wind energy assessment, yet conventional instruments leave spatio-temporal gaps within the lower atmospheric boundary layer. Unmanned aircraft systems (UAS) provide flexible in situ measurements, but individual platforms sample wind only along their flight trajectories, limiting full wind-field recovery. This study presents a framework for reconstructing four-dimensional atmospheric wind fields using measurements obtained from a coordinated UAS swarm. A synthetic turbulence environment and high-fidelity multirotor simulation are used to generate training and evaluation data. Local wind components are estimated from UAS dynamics using a bidirectional long short-term memory network (Bi-LSTM) and assimilated into a physics-informed neural network (PINN) to reconstruct a continuous wind field in space and time. For local wind estimation, the bidirectional LSTM achieves root-mean-square errors (RMSE) of 0.064 and 0.062 m/s for the north and east components in low-wind conditions, increasing to 0.122 to 0.129 m/s under moderate winds and 0.271 to 0.273 m/s in high-wind conditions, while the vertical component exhibits higher error, with RMSE values of 0.029 to 0.091 m/s. The physics-informed reconstruction recovers the dominant spatial and temporal structure of the wind field up to 1000 m altitude while preserving mean flow direction and vertical shear. Under moderate wind conditions, the reconstructed mean wind field achieves an overall RMSE between 0.118 and 0.154 m/s across evaluated UAS configurations, with the lowest error obtained using a five-UAS swarm. These results demonstrate that coordinated UAS measurements enable accurate and scalable four-dimensional wind-field reconstruction without dedicated wind sensors or fixed infrastructure.

Paperid: 1144, https://arxiv.org/pdf/2601.20978.pdf

Abstract:
In this paper, we investigate several techniques for modeling the one-dimensional advection equation for a specific class of problems with discontinuous initial and boundary conditions using physics-informed neural networks (PINNs). To mitigate the spectral bias phenomenon, we employ a Fourier feature mapping layer as the input representation, adopt a two-stage training strategy in which the Fourier feature parameters and the neural network weights are optimized sequentially, and incorporate adaptive loss weighting. To further enhance the approximation accuracy, a median filter is applied to the spatial data, and the predicted solution is constrained through a bounded linear mapping. Moreover, for certain nonlinear problems, we introduce a modified loss function inspired by the upwind numerical scheme to alleviate the excessive smoothing of discontinuous solutions typically observed in neural network approximations.

Paperid: 1145, https://arxiv.org/pdf/2601.20905.pdf

Abstract:
High-quality Fourier Transform Infrared (FTIR) imaging usually needs extensive signal averaging to reduce noise and drift which severely limits clinical speed. Deep learning can accelerate imaging by reconstructing spectra from rapid, single-scan inputs. However, separating noise and baseline drift simultaneously without ground truth is an ill-posed inverse problem. Standard black-box architectures often rely on statistical approximations that introduce spectral hallucinations or fail to generalize to unstable atmospheric conditions. To solve these issues we propose a physics-informed cascade Unet that separates denoising and baseline correction tasks using a new, deterministic Physics Bridge. This architecture forces the network to separate random noise from chemical signals using an embedded SNIP layer to enforce spectroscopic constraints instead of learning statistical approximations. We benchmarked this approach against a standard single Unet and a traditional Savitzky-Golay/SNIP workflow. We used a dataset of human hypopharyngeal carcinoma cells (FaDu). The cascade model outperformed all other methods, achieving a 51.3% reduction in RMSE compared to raw single-scan inputs, surpassing both the single Unet (40.2%) and the traditional workflow (33.7%). Peak-aware metrics show that the cascade architecture eliminates spectral hallucinations found in standard deep learning. It also preserves peak intensity with much higher fidelity than traditional smoothing. These results show that the cascade Unet is a robust solution for diagnostic-grade FTIR imaging. It enables imaging speeds 32 times faster than current methods.

Paperid: 1146, https://arxiv.org/pdf/2601.20496.pdf

Abstract:
Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art methods either use spatial statistics or rely on examples of dense fields in the training phase, which often are not available, and thus rely on synthetic data. Here, we present a reconstruction method that generates dense fields from sparse measurements, without assuming availability of the spatial statistics, nor of examples of the dense fields. This is made possible through the introduction of an automatically differentiable numerical simulator into the training phase of the method. The method is shown to have superior results over statistical and neural network based methods on a set of three standard problems from fluid mechanics.

Paperid: 1147, https://arxiv.org/pdf/2601.19818.pdf

Abstract:
The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems. However, unlike classical numerical methods that offer established convergence guarantees, neural network-based approximations typically lack rigorous error bounds. Furthermore, the non-deterministic nature of their optimization makes it difficult to mathematically certify their accuracy. To address these challenges, we propose a "Learn and Verify" framework that provides computable, mathematically rigorous error bounds for the solutions of differential equations. By combining a novel Doubly Smoothed Maximum (DSM) loss for training with interval arithmetic for verification, we compute rigorous a posteriori error bounds as machine-verifiable proofs. Numerical experiments on nonlinear Ordinary Differential Equations (ODEs), including problems with time-varying coefficients and finite-time blow-up, demonstrate that the proposed framework successfully constructs rigorous enclosures of the true solutions, establishing a foundation for trustworthy scientific machine learning.

Paperid: 1148, https://arxiv.org/pdf/2601.17207.pdf

Abstract:
We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through residual-based loss terms, NewPINNs integrates the solver directly into the training loop and defines learning objectives through solver-consistency. The neural network produces candidate solution states that are advanced by the numerical solver, and training minimizes the discrepancy between the network prediction and the solver-evolved state. This pull-push interaction enables the network to learn physically admissible solutions through repeated exposure to the solver's action, without requiring problem-specific loss engineering or explicit evaluation of differential equation residuals. By delegating the enforcement of physics, boundary conditions, and numerical stability to established numerical solvers, NewPINNs mitigates several well-known failure modes of standard physics-informed neural networks, including optimization pathologies, sensitivity to loss weighting, and poor performance in stiff or nonlinear regimes. We demonstrate the effectiveness of the proposed approach across multiple forward and inverse problems involving finite volume, finite element, and spectral solvers.

Paperid: 1149, https://arxiv.org/pdf/2601.17154.pdf

Abstract:
Inverter-based resources (IBRs) exhibit fast transient dynamics during network disturbances, which often cannot be properly captured by phasor and SCADA measurements. This shortcoming has recently been addressed with the advent of waveform measurement units (WMUs), which provide high-resolution, time-synchronized raw voltage and current waveform samples from multiple locations in the power system. However, transient model learning based on synchro-waveform measurements remains constrained by the scarcity of network disturbances and the complexity of the underlying nonlinear dynamics of IBRs. We propose to address these problems by developing a data-efficient physics-informed machine learning (PIML) framework for synchro-waveform analytics that estimates the IBR terminal current response from only a few network disturbance signatures. Here, the physics of the electrical circuits are used to compensate for limited data availability by constraining the learning process through known circuit relationships. Two cases are considered, with known and unknown circuit parameters. In the latter case, the framework jointly learns the transient dynamics of the IBRs and the parameters of the electrical circuit. Case studies using WMU disturbance data across multiple sampling rates shows consistently lower current estimation error with substantially fewer training events than a purely data-driven baseline.

Paperid: 1150, https://arxiv.org/pdf/2601.12704.pdf

Abstract:
The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets. We develop a physics-informed (PI) machine learning algorithm based on a radial basis function neural network (RBFNN) that concurrently optimizes the network architecture and predicts the target option price. The physics-informed radial basis function neural network (PIRBFNN) combines the strengths of the traditional radial basis function collocation method and the physics-informed neural network machine learning approach to effectively solve PDE problems in the financial context. By employing a PDE residual-based technique to adaptively refine the distribution of hidden neurons during the training process, the PIRBFNN facilitates accurate and efficient handling of multidimensional option pricing models featuring non-smooth payoff conditions. The validity of the proposed method is demonstrated through a set of experiments encompassing a single-asset European put option, a double-asset exchange option, and a four-asset basket call option.

Paperid: 1151, https://arxiv.org/pdf/2601.12341.pdf

Abstract:
Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical laws in training by enforcing equation residuals. However, these struggle to model nonlinear dynamics, suffering from limited generalization across problems and long training times. To address these limitations, we propose a perturbation-guided transfer learning framework for PINNs (PTL-PINN), which integrates perturbation theory with transfer learning to efficiently solve nonlinear equations. Unlike gradient-based transfer learning, PTL-PINNs solve an approximate linear perturbative system using closed-form expressions, enabling rapid generalization with the time complexity of matrix-vector multiplication. We show that PTL-PINNs achieve accuracy comparable to various Runge-Kutta methods, with computational speeds up to one order of magnitude faster. To benchmark performance, we solve a broad set of problems, including nonlinear oscillators across various damping regimes, the equilibrium-centered Lotka-Volterra system, the KPP-Fisher and the Wave equation. Since perturbation theory sets the accuracy bound of PTL-PINNs, we systematically evaluate its practical applicability. This work connects long-standing perturbation methods with PINNs, demonstrating how perturbation theory can guide foundational models to solve nonlinear systems with speeds comparable to those of classical solvers.

Paperid: 1153, https://arxiv.org/pdf/2601.11638.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems by embedding physical laws into the learning process. However, rigorously quantifying how well a PINN captures the complete dynamical behavior of the system, beyond simple trajectory prediction, remains a challenge. This paper proposes a novel experimental framework to address this by employing Fisher information for differentiable dynamical systems, denoted $g_F^C$. This Fisher information, distinct from its statistical counterpart, measures inherent uncertainties in deterministic systems, such as sensitivity to initial conditions, and is related to the phase space curvature and the net stretching action of the state space evolution. We hypothesize that if a PINN accurately learns the underlying dynamics of a physical system, then the Fisher information landscape derived from the PINN's learned equations of motion will closely match that of the original analytical model. This match would signify that the PINN has achieved comprehensive fidelity capturing not only the state evolution but also crucial geometric and stability properties. We outline an experimental methodology using the dynamical model of a car to compute and compare $g_F^C$ for both the analytical model and a trained PINN. The comparison, based on the Jacobians of the respective system dynamics, provides a quantitative measure of the PINN's fidelity in representing the system's intricate dynamical characteristics.

Paperid: 1154, https://arxiv.org/pdf/2601.11406.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard PINN framework to solve the challenging one-dimensional nonlinear Fisher-KPP equation, a critical model in reaction-diffusion dynamics describing phenomena such as population spread and flame propagation. We detail a comprehensive methodology, encompassing the neural network architecture, the physics-informed loss function, and an in-depth investigation into retraining strategies aimed at optimizing model performance. Our approach is rigorously validated through a direct comparison of the PINN solution against both the known analytical solution and a numerical solution derived from the Finite Difference Method (FDM). Through this work, we elucidate the intricate balance between model complexity, training efficiency, and accuracy. Results highlight the PINN's remarkable capability in accurately approximating the solution to this complex PDE, while also shedding light on the critical aspects and challenges of model retraining, particularly concerning the optimizer's state. This study provides a thorough quantitative error analysis, demonstrating the efficacy of PINNs as a viable and competitive alternative to traditional numerical methods for solving nonlinear differential equations, and discusses their broader applications across various scientific domains.

Paperid: 1155, https://arxiv.org/pdf/2601.10222.pdf

Abstract:
Optimization is central to both modern machine learning (ML) and scientific machine learning (SciML), yet the structure of the underlying optimization problems differs substantially across these domains. Classical ML typically relies on stochastic, sample-separable objectives that favor first-order and adaptive gradient methods. In contrast, SciML often involves physics-informed or operator-constrained formulations in which differential operators induce global coupling, stiffness, and strong anisotropy in the loss landscape. As a result, optimization behavior in SciML is governed by the spectral properties of the underlying physical models rather than by data statistics, frequently limiting the effectiveness of standard stochastic methods and motivating deterministic or curvature-aware approaches. This document provides a unified introduction to optimization methods in ML and SciML, emphasizing how problem structure shapes algorithmic choices. We review first- and second-order optimization techniques in both deterministic and stochastic settings, discuss their adaptation to physics-constrained and data-driven SciML models, and illustrate practical strategies through tutorial examples, while highlighting open research directions at the interface of scientific computing and scientific machine learning.

Paperid: 1156, https://arxiv.org/pdf/2601.09818.pdf

Abstract:
Kolmogorov-Arnold Networks (KANs) require significantly smaller architectures compared to multilayer perceptron (MLP)-based approaches, while retaining expressive power through spline-based activations. We propose a shallow KAN framework that directly approximates the temperature distribution T(x,t) and the moving interface $Γ(t)$, enforcing the governing PDEs, phase equilibrium, and Stefan condition through physics-informed residuals. To enhance accuracy, we employ interface-focused collocation resampling. Numerical experiments in one and two dimensions show that the framework achieves accurate reconstructions of both temperature fields and interface dynamics, highlighting the potential of KANs as a compact and efficient alternative for moving boundary PDEs. First, we validate the model with semi-infinite analytical solutions. Subsequently, the model is extended to 2D using a level-set based formulation for interface propagation, which is solved within the KAN framework. This work demonstrates that KANs are capable of solving complex moving boundary problems without the need for measurement data.

Paperid: 1157, https://arxiv.org/pdf/2601.07640.pdf

Abstract:
This paper develops an approach for multi-step forecasting of dynamical systems by integrating probabilistic input forecasting with physics-informed output prediction. Accurate multi-step forecasting of time series systems is important for the automatic control and optimization of physical processes, enabling more precise decision-making. While mechanistic-based and data-driven machine learning (ML) approaches have been employed for time series forecasting, they face significant limitations. Incomplete knowledge of process mathematical models limits mechanistic-based direct employment, while purely data-driven ML models struggle with dynamic environments, leading to poor generalization. To address these limitations, this paper proposes a dual-level strategy for physics-informed forecasting of dynamical systems. On the first level, input variables are forecast using a hybrid method that integrates a long short-term memory (LSTM) network into probabilistic state transition models (STMs). On the second level, these stochastically predicted inputs are sequentially fed into a physics-informed neural network (PINN) to generate multi-step output predictions. The experimental results of the paper demonstrate that the hybrid input forecasting models achieve a higher log-likelihood and lower mean squared errors (MSE) compared to conventional STMs. Furthermore, the PINNs driven by the input forecasting models outperform their purely data-driven counterparts in terms of MSE and log-likelihood, exhibiting stronger generalization and forecasting performance across multiple test cases.

Paperid: 1158, https://arxiv.org/pdf/2601.06462.pdf

Abstract:
Applying Physics-Informed Gaussian Process Regression to the eigenvalue problem $(\mathcal{L}-λ)u = 0$ poses a fundamental challenge, where the null source term results in a trivial predictive mean and a degenerate marginal likelihood. Drawing inspiration from system identification, we construct a transfer function-type indicator for the unknown eigenvalue/eigenfunction using the physics-informed Gaussian Process posterior. We demonstrate that the posterior covariance is only non-trivial when $λ$ corresponds to an eigenvalue of the partial differential operator $\mathcal{L}$, reflecting the existence of a non-trivial eigenspace, and any sample from the posterior lies in the eigenspace of the linear operator. We demonstrate the effectiveness of the proposed approach through several numerical examples with both linear and non-linear eigenvalue problems.

Paperid: 1159, https://arxiv.org/pdf/2601.02149.pdf

Abstract:
We propose a neural network-based model capable of learning the broad landscape of working regimes in quantum dot simulators, and using this knowledge to autotune these devices - based on transport measurements - toward obtaining Majorana modes in the structure. The model is trained in an unsupervised manner on synthetic data in the form of conductance maps, using a physics-informed loss that incorporates key properties of Majorana zero modes. We show that, with appropriate training, a deep vision-transformer network can efficiently memorize relation between Hamiltonian parameters and structures on conductance maps and use it to propose parameters update for a quantum dot chain that drive the system toward topological phase. Starting from a broad range of initial detunings in parameter space, a single update step is sufficient to generate nontrivial zero modes. Moreover, by enabling an iterative tuning procedure - where the system acquires updated conductance maps at each step - we demonstrate that the method can address a much larger region of the parameter space.

Paperid: 1160, https://arxiv.org/pdf/2601.01756.pdf

Abstract:
In this paper, we present a Wachspress-based transfinite formulation on convex polygonal domains for exact enforcement of Dirichlet boundary conditions in physics-informed neural networks. This approach leverages prior advances in geometric design such as blending functions and transfinite interpolation over convex domains. For prescribed Dirichlet boundary function $\mathcal{B}$, the transfinite interpolant of $\mathcal{B}$, $g : \bar P \to C^0(\bar P)$, $\textit{lifts}$ functions from the boundary of a two-dimensional polygonal domain to its interior. The trial function is expressed as the difference between the neural network's output and the extension of its boundary restriction into the interior of the domain, with $g$ added to it. This ensures kinematic admissibility of the trial function in the deep Ritz method. Wachspress coordinates for an $n$-gon are used in the transfinite formula, which generalizes bilinear Coons transfinite interpolation on rectangles to convex polygons. The neural network trial function has a bounded Laplacian, thereby overcoming a limitation in a previous contribution where approximate distance functions were used to exactly enforce Dirichlet boundary conditions. For a point $\boldsymbol{x} \in \bar{P}$, Wachspress coordinates, $\boldsymbolλ : \bar P \to [0,1]^n$, serve as a geometric feature map for the neural network: $\boldsymbolλ$ encodes the boundary edges of the polygonal domain. This offers a framework for solving problems on parametrized convex geometries using neural networks. The accuracy of physics-informed neural networks and deep Ritz is assessed on forward, inverse, and parametrized geometric Poisson boundary-value problems.

Paperid: 1161, https://arxiv.org/pdf/2601.00866.pdf

Abstract:
Recent advancements in physics-informed neural networks (PINNs) and their variants have garnered substantial focus from researchers due to their effectiveness in solving both forward and inverse problems governed by differential equations. In this research, a modified Auxiliary physics-informed neural network (A-PINN) framework with balanced adaptive optimizers is proposed for the analysis of structural vibration problems. In order to accurately represent structural systems, it is critical for capturing vibration phenomena and ensuring reliable predictive analysis. So, our investigations are crucial for gaining deeper insight into the robustness of scientific machine learning models for solving vibration problems. Further, to rigorously evaluate the performance of A-PINN, we conducted different numerical simulations to approximate the Euler-Bernoulli beam equations under the various scenarios. The numerical results substantiate the enhanced performance of our model in terms of both numerical stability and predictive accuracy. Our model shows improvement of at least 40% over the baselines.

Paperid: 1162, https://arxiv.org/pdf/2601.00491.pdf

Abstract:
Physics-informed neural networks have been widely applied to solid mechanics problems. However, balancing the governing partial differential equations and boundary conditions remains challenging, particularly in fracture mechanics, where accurate predictions strongly depend on refined sampling near crack tips. To overcome these limitations, a Kolosov-Muskhelishvili informed neural network with Williams enrichment is developed in this study. Benefiting from the holomorphic representation, the governing equations are satisfied by construction, and only boundary points are required for training. Across a series of benchmark problems, the Kolosov-Muskhelishvili informed neural network shows excellent agreement with analytical and finite element method references, achieving average relative errors below 1\% and $R^2$ above 0.99 for both mode I and mode II loadings. Furthermore, three crack propagation criteria (maximum tangential stress, maximum energy release rate, and principle of local symmetry) are integrated into the framework using a transfer learning strategy to predict crack propagation directions. The predicted paths are nearly identical across all criteria, and the transfer learning strategy reduces the required training time by more than 70\%. Overall, the developed framework provides a unified, mesh-free, and physically consistent approach for accurate and efficient crack propagation analysis.

Paperid: 1163, https://arxiv.org/pdf/2601.00342.pdf

Abstract:
In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional approaches often rely on linearized equations or finite, truncated domains, which introduce non-negligible errors and limit applicability in real-world scenarios. In this study, we propose a novel framework utilizing Physics-Informed Neural Networks (PINNs) to solve the full nonlinear compressible potential equation in an unbounded (infinite) domain. We address the unbounded-domain and convergence challenges inherent in standard PINNs by incorporating a coordinate transformation and embedding physical asymptotic constraints directly into the network architecture. Furthermore, we employ a Multi-Stage PINN (MS-PINN) approach to iteratively minimize residuals, achieving solution accuracy approaching machine precision. We validate this framework by simulating flow over circular and elliptical geometries, comparing our results against traditional finite-domain and linearized solutions. Our findings quantify the noticeable discrepancies introduced by domain truncation and linearization, particularly at higher Mach numbers, and demonstrate that this new framework is a robust, high-fidelity tool for computational fluid dynamics.

Paperid: 1164, https://arxiv.org/pdf/2601.00081.pdf

Abstract:
Wearable technologies have the potential to transform ambulatory and at-home hemodynamic monitoring by providing continuous assessments of cardiovascular health metrics and guiding clinical management. However, existing cuffless wearable devices for blood pressure (BP) monitoring often rely on methods lacking theoretical foundations, such as pulse wave analysis or pulse arrival time, making them vulnerable to physiological and experimental confounders that undermine their accuracy and clinical utility. Here, we developed a smartwatch device with real-time electrical bioimpedance (BioZ) sensing for cuffless hemodynamic monitoring. We elucidate the biophysical relationship between BioZ and BP via a multiscale analytical and computational modeling framework, and identify physiological, anatomical, and experimental parameters that influence the pulsatile BioZ signal at the wrist. A signal-tagged physics-informed neural network incorporating fluid dynamics principles enables calibration-free estimation of BP and radial and axial blood velocity. We successfully tested our approach with healthy individuals at rest and after physical activity including physical and autonomic challenges, and with patients with hypertension and cardiovascular disease in outpatient and intensive care settings. Our findings demonstrate the feasibility of BioZ technology for cuffless BP and blood velocity monitoring, addressing critical limitations of existing cuffless technologies.

Paperid: 1165, https://arxiv.org/pdf/2512.24634.pdf

Abstract:
We present a comparative study of classical numerical solvers, such as Petviashvili's method or finite difference with Newton iterations, and neural network-based methods for computing ground states or profiles of solitary-wave solutions to the one-dimensional dispersive PDEs that include the nonlinear Schrödinger, the nonlinear Klein-Gordon and the generalized KdV equations. We confirm that classical approaches retain high-order accuracy and strong computational efficiency for single-instance problems in the one-dimensional setting. Physics-informed neural networks (PINNs) are also able to reproduce qualitative solutions but are generally less accurate and less efficient in low dimensions than classical solvers due to expensive training and slow convergence. We also investigate the operator-learning methods, which, although computationally intensive during training, can be reused across many parameter instances, providing rapid inference after pretraining, making them attractive for applications involving repeated simulations or real-time predictions. For single-instance computations, however, the accuracy of operator-learning methods remains lower than that of classical methods or PINNs, in general.

Paperid: 1166, https://arxiv.org/pdf/2512.23624.pdf

Abstract:
We present NeuroSPICE, a physics-informed neural network (PINN) framework for device and circuit simulation. Unlike conventional SPICE, which relies on time-discretized numerical solvers, NeuroSPICE leverages PINNs to solve circuit differential-algebraic equations (DAEs) by minimizing the residual of the equations through backpropagation. It models device and circuit waveforms using analytical equations in time domain with exact temporal derivatives. While PINNs do not outperform SPICE in speed or accuracy during training, they offer unique advantages such as surrogate models for design optimization and inverse problems. NeuroSPICE's flexibility enables the simulation of emerging devices, including highly nonlinear systems such as ferroelectric memories.

Paperid: 1167, https://arxiv.org/pdf/2512.22283.pdf

Abstract:
Physics-informed neural networks (PINNs) have led to significant advancements in scientific computing by integrating fundamental physical principles with advanced data-driven techniques. However, when dealing with problems characterized by multi-scale or high-frequency features, PINNs encounter persistent and severe challenges related to stiffness in gradient flow and spectral bias, which significantly limit their predictive capabilities. To address these issues, this paper proposes a Dynamic Balancing Adaptive Weighting Physics-Informed Kolmogorov-Arnold Network (DBAW-PIKAN), designed to mitigate such gradient-related failure modes and overcome the bottlenecks in function representation. The core of DBAW-PIKAN combines the Kolmogorov-Arnold network architecture, based on learnable B-splines, with an adaptive weighting strategy that incorporates a dynamic decay upper bound. Compared to baseline models, the proposed method accelerates the convergence process and improves solution accuracy by at least an order of magnitude without introducing additional computational complexity. A series of numerical benchmarks, including the Klein-Gordon, Burgers, and Helmholtz equations, demonstrate the significant advantages of DBAW-PIKAN in enhancing both accuracy and generalization performance.

Paperid: 1168, https://arxiv.org/pdf/2512.21633.pdf

Abstract:
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed Neural Networks (PINNs) and Deep Galerkin Methods, often face challenges in generalization and long-time prediction efficiency due to their dependence on full space-time approximations. To address these issues, we propose a novel and scalable framework that significantly enhances the Neural Galerkin Method (NGM) by incorporating the Meta-Auto-Decoder (MAD) paradigm. Our approach leverages space-time decoupling to enable more stable and efficient time integration, while meta-learning-driven adaptation allows rapid generalization to unseen parameter configurations with minimal retraining. Furthermore, randomized sparse updates effectively reduce computational costs without compromising accuracy. Together, these advancements enable our method to achieve physically consistent, long-horizon predictions for complex parameterized evolution equations with significantly lower computational overhead. Numerical experiments on benchmark problems demonstrate that our methods performs comparatively well in terms of accuracy, robustness, and adaptability.

Paperid: 1169, https://arxiv.org/pdf/2512.20747.pdf

Abstract:
Solar active regions (ARs) do not appear randomly but cluster along longitudinally warped toroidal bands ('toroids') that encode information about magnetic structures in the tachocline, where global-scale organization likely originates. Global MagnetoHydroDynamic Shallow-Water Tachocline (MHD-SWT) models have shown potential to simulate such toroids, matching observations qualitatively. For week-scale early prediction of flare-producing AR emergence, forward-integration of these toroids is necessary. This requires model initialization with a dynamically self-consistent MHD state-vector that includes magnetic, flow fields, and shell-thickness variations. However, synoptic magnetograms provide only geometric shape of toroids, not the state-vector needed to initialize MHD-SWT models. To address this challenging task, we develop PINNBARDS, a novel Physics-Informed Neural Network (PINN)-Based AR Distribution Simulator, that uses observational toroids and MHD-SWT equations to derive initial state-vector. Using Feb-14-2024 SDO/HMI synoptic map, we show that PINN converges to physically consistent, predominantly antisymmetric toroids, matching observed ones. Although surface data provides north and south toroids' central latitudes, and their latitudinal widths, they cannot determine tachocline field strengths, connected to AR emergence. We explore here solutions across a broad parameter range, finding hydrodynamically-dominated structures for weak fields (~2 kG) and overly rigid behavior for strong fields (~100 kG). We obtain best agreement with observations for 20-30 kG toroidal fields, and ~10 degree bandwidth, consistent with low-order longitudinal mode excitation. To our knowledge, PINNBARDS serves as the first method for reconstructing state-vectors for hidden tachocline magnetic structures from surface patterns; potentially leading to weeks ahead prediction of flare-producing AR-emergence.

Paperid: 1170, https://arxiv.org/pdf/2512.19280.pdf

Abstract:
Axial piston pumps are crucial components in fluid power systems, where reliable fault diagnosis is essential for ensuring operational safety and efficiency. Traditional data-driven methods require extensive labeled fault data, which is often impractical to obtain, while model-based approaches suffer from parameter uncertainties. This paper proposes a digital twin (DT)-driven zero-shot fault diagnosis framework utilizing fluid-borne noise (FBN) signals. The framework calibrates a high-fidelity DT model using only healthy-state data, generates synthetic fault signals for training deep learning classifiers, and employs a physics-informed neural network (PINN) as a virtual sensor for flow ripple estimation. Gradient-weighted class activation mapping (Grad-CAM) is integrated to visualize the decision-making process of neural networks, revealing that large kernels matching the subsequence length in time-domain inputs and small kernels in time-frequency domain inputs enable higher diagnostic accuracy by focusing on physically meaningful features. Experimental validations demonstrate that training on signals from the calibrated DT model yields diagnostic accuracies exceeding 95\% on real-world benchmarks, while uncalibrated models result in significantly lower performance, highlighting the framework's effectiveness in data-scarce scenarios.

Paperid: 1171, https://arxiv.org/pdf/2512.19196.pdf

Abstract:
Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and the bottleneck of evaluating second-order diffusion terms. Existing deep learning approaches, such as Physics-Informed Neural Networks, face computational challenges as dimensionality increases, driven by the $O(d^2)$ complexity of automatic differentiation for second-order derivatives. While recent probability flow approaches bypass this by learning score functions or matching velocity fields, they often involve serial operations or depend on sampling efficiency in complex distributions. To address these issues, we propose the Adaptive Probability Flow Residual Minimization (A-PFRM) method. We reformulate the second-order FP equation into an equivalent first-order deterministic Probability Flow ODE (PF-ODE) constraint, which avoids explicit Hessian computation. Unlike score matching or velocity matching, A-PFRM solves this problem by minimizing the residual of the continuity equation induced by the PF-ODE. We leverage Continuous Normalizing Flows combined with the Hutchinson Trace Estimator to reduce the training complexity to linear scale $O(d)$, achieving an effective $O(1)$ wall-clock time on GPUs. To address data sparsity in high dimensions, we apply a generative adaptive sampling strategy and theoretically prove that dynamically aligning collocation points with the evolving probability mass is a necessary condition to bound the approximation error. Experiments on diverse benchmarks -- ranging from anisotropic Ornstein-Uhlenbeck (OU) processes and high-dimensional Brownian motions with time-varying diffusion terms, to Geometric OU processes featuring non-Gaussian solutions -- demonstrate that A-PFRM effectively mitigates the CoD, maintaining high accuracy and constant temporal cost for problems up to 100 dimensions.

Paperid: 1172, https://arxiv.org/pdf/2512.18104.pdf

Abstract:
Aleatoric uncertainties - irremovable variability in microstructure morphology, constituent behavior, and processing conditions - pose a major challenge to developing uncertainty-robust digital twins. We introduce the Variational Deep Material Network (VDMN), a physics-informed surrogate model that enables efficient and probabilistic forward and inverse predictions of material behavior. The VDMN captures microstructure-induced variability by embedding variational distributions within its hierarchical, mechanistic architecture. Using an analytic propagation scheme based on Taylor-series expansion and automatic differentiation, the VDMN efficiently propagates uncertainty through the network during training and prediction. We demonstrate its capabilities in two digital-twin-driven applications: (1) as an uncertainty-aware materials digital twin, it predicts and experimentally validates the nonlinear mechanical variability in additively manufactured polymer composites; and (2) as an inverse calibration engine, it disentangles and quantitatively identifies overlapping sources of uncertainty in constituent properties. Together, these results establish the VDMN as a foundation for uncertainty-robust materials digital twins.

Paperid: 1173, https://arxiv.org/pdf/2512.17607.pdf

Abstract:
Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by finite element methods are widely adopted, recent research suggests that easy prioritization can also be effective. Nevertheless, we find that both approaches exhibit notable trade-offs and inconsistent performance across PDE types. To address this issue, we develop a hybrid strategy that combines the strengths of hard and easy prioritization through an alternating training algorithm. On PDEs with steep gradients, nonlinearity, and high dimensionality, the proposed method achieves consistently high accuracy, with relative L2 errors mostly in the range of O(10^-5) to O(10^-6), significantly surpassing baseline methods. Moreover, it offers greater reliability across diverse problems, whereas compared approaches often suffer from variable accuracy depending on the PDE. This work provides new insights into designing hybrid training strategies to enhance the performance and robustness of PINNs.

Paperid: 1174, https://arxiv.org/pdf/2512.17001.pdf

Abstract:
This paper presents a Multi-Robot Multi-Source Term Estimation (MRMSTE) framework that enables teams of mobile robots to collaboratively sample gas concentrations and infer the parameters of an unknown number of airborne releases. The framework is built on a hybrid Bayesian inference scheme that represents the joint multi-source probability density and incorporates physics-informed state transitions, including source birth, removal, and merging induced by atmospheric dispersion. A superposition-based measurement model is naturally accommodated, allowing sparse concentration measurements to be exploited efficiently. To guide robot deployment, we introduce a wind-aware coverage control (WCC) strategy that integrates the evolving multi-source belief with local wind information to prioritize regions of high detection likelihood. Unlike conventional coverage control or information-theoretic planners, WCC explicitly accounts for anisotropic plume transport when modelling sensor performance, leading to more effective sensor placement for multi-source estimation. Monte Carlo studies demonstrate faster convergence and improved separation of individual source beliefs compared to traditional coverage-based strategies and small-scale static sensor networks. Real-world experiments with CO2 releases using TurtleBot platforms further validate the proposed approach, demonstrating its practicality for scalable multi-robot gas-sensing applications.

Paperid: 1175, https://arxiv.org/pdf/2512.15771.pdf

Abstract:
Partial Differential Equations (PDEs) are central to modeling complex systems across physical, biological, and engineering domains, yet traditional numerical methods often struggle with high-dimensional or complex problems. Physics-Informed Neural Networks (PINNs) have emerged as an efficient alternative by embedding physics-based constraints into deep learning frameworks, but they face challenges in achieving high accuracy and handling complex boundary conditions. In this work, we extend the Time-Evolving Natural Gradient (TENG) framework to address Dirichlet boundary conditions, integrating natural gradient optimization with numerical time-stepping schemes, including Euler and Heun methods, to ensure both stability and accuracy. By incorporating boundary condition penalty terms into the loss function, the proposed approach enables precise enforcement of Dirichlet constraints. Experiments on the heat equation demonstrate the superior accuracy of the Heun method due to its second-order corrections and the computational efficiency of the Euler method for simpler scenarios. This work establishes a foundation for extending the framework to Neumann and mixed boundary conditions, as well as broader classes of PDEs, advancing the applicability of neural network-based solvers for real-world problems.

Paperid: 1176, https://arxiv.org/pdf/2512.14855.pdf

Abstract:
Machine learning (ML) has been increasingly applied in concrete research to optimize performance and mixture design. However, one major challenge in applying ML to cementitious materials is the limited size and diversity of available databases. A promising solution is the development of multi-modal databases that integrate both numerical and graphical data. Conventional ML frameworks in cement research are typically restricted to a single data modality. Graph neural network (GNN) represents a new generation of neural architectures capable of learning from data structured as graphs, capturing relationships through irregular or topology-dependent connections rather than fixed spatial coordinates. While GNN is inherently designed for graphical data, they can be adapted to extract correlations from numerical datasets and potentially embed physical laws directly into their architecture, enabling explainable and physics-informed predictions. This work is among the first few studies to implement GNNs to design concrete, with a particular emphasis on establishing a clear and reproducible pathway for converting tabular data into graph representations using the k-nearest neighbor (K-NN) approach. Model hyperparameters and feature selection are systematically optimized to enhance prediction performance. The GNN shows performance comparable to the benchmark random forest, which has been demonstrated by many studies to yield reliable predictions for cementitious materials. Overall, this study provides a foundational roadmap for transitioning from traditional ML to advanced AI architectures. The proposed framework establishes a strong foundation for future multi-modal and physics-informed GNN models capable of capturing complex material behaviors and accelerating the design and optimization of cementitious materials.

Paperid: 1177, https://arxiv.org/pdf/2512.14258.pdf

Abstract:
We revisit the problem of physics-informed regression, and propose a method that directly computes the state at the prediction point, simultaneously with the derivative and curvature information of the existing samples. We frame each prediction as a constrained optimisation problem, leveraging multivariate Taylor series expansions and explicitly enforcing physical laws. Each individual query can be processed with low computational cost without any pre- or re-training, in contrast to global function approximator-based solutions such as neural networks. Our comparative benchmarks on a reaction-diffusion system show competitive predictive accuracy relative to a neural network-based solution, while completely eliminating the need for long training loops, and remaining robust to changes in the sampling layout.

Paperid: 1179, https://arxiv.org/pdf/2512.12285.pdf

Abstract:
Accurate estimation of the State of Charge (SOC) is critical for ensuring the safety, reliability, and performance optimization of lithium-ion battery systems. Conventional data-driven neural network models often struggle to fully characterize the inherent complex nonlinearities and memory-dependent dynamics of electrochemical processes, significantly limiting their predictive accuracy and physical interpretability under dynamic operating conditions. To address this challenge, this study proposes a novel neural architecture termed the Fractional Differential Equation Physics-Informed Neural Network (FDIFF-PINN), which integrates fractional calculus with deep learning. The main contributions of this paper include: (1) Based on a fractional-order equivalent circuit model, a discretized fractional-order partial differential equation is constructed. (2) Comparative experiments were conducted using a dynamic charge/discharge dataset of Panasonic 18650PF batteries under multi-temperature conditions (from -10$^{\circ}$C to 20$^{\circ}$C).

Paperid: 1180, https://arxiv.org/pdf/2512.12074.pdf

Abstract:
Inverse problems are extensively studied in applied mathematics, with applications ranging from acoustic tomography for medical diagnosis to geophysical exploration. Physics informed neural networks (PINNs) have emerged as a powerful tool for solving such problems, while Physics informed Kolmogorov Arnold networks (PIKANs) represent a recent benchmark that, in certain problems, promises greater interpretability and accuracy compared to PINNs, due to their nature, being constructed as a composition of polynomials. In this work, we develop a methodology for addressing inverse problems in infinite and semi infinite domains. We introduce a novel sampling strategy for the network's training points, using the negative exponential and normal distributions, alongside a dual network architecture that is trained to learn the solution and parameters of an equation with the same loss function. This design enables the solution of inverse problems without explicitly imposing boundary conditions, as long as the solutions tend to stabilize when leaving the domain of interest. The proposed architecture is implemented using both PINNs and PIKANs, and their performance is compared in terms of accuracy with respect to a known solution as well as computational time and response to a noisy environment. Our results demonstrate that, in this setting, PINNs provide a more accurate and computationally efficient solution, solving the inverse problem 1,000 times faster and in the same order of magnitude, yet with a lower relative error than PIKANs.

Paperid: 1181, https://arxiv.org/pdf/2512.12001.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) and more recently Physics-Informed Kolmogorov-Arnold Networks (PIKANs) have emerged as promising approaches for solving partial differential equations (PDEs) without reliance on extensive labeled data. In this work, we propose a novel multi-resolution Hybrid Wavelet-Fourier-Enhanced Physics-Informed Kolmogorov-Arnold Network (HWF-PIKAN) for solving advection problems based on collisionless Boltzmann equation (CBE) with both continuous and discontinuous initial conditions. To validate the effectiveness of the proposed model, we conduct systematic benchmarks on classical advection equations in one and two dimensions. These tests demonstrate the model's ability to accurately capture smooth and abrupt features. We then extend the application of HWF-PIKAN to the high-dimensional phase-space setting by solving the CBE in a continuous-velocity manner. This leverages the Hamiltonian concept of phase-space dynamics to model the statistical behavior of particles in a collisionless system, where advection governs the evolution of a probability distribution function or number density. Comparative analysis against Vanilla PINN, Vanilla PIKAN, as well as Fourier-enhanced and Wavelet-enhanced PIKAN variants, shows that the proposed hybrid model significantly improves solution accuracy and convergence speed. This study highlights the power of multi-resolution spectral feature embeddings in advancing physics-informed deep learning frameworks for complex kinetic equations in both space-time and phase-space.

Paperid: 1182, https://arxiv.org/pdf/2512.11860.pdf

Abstract:
Classical numerical methods solve partial differential equations (PDEs) efficiently on regular meshes, but many of them become unstable on irregular domains. In practice, multiphysics interactions such as diffusion, damage, and healing often take place on irregular meshes. We develop an operator-consistent graph neural network (OCGNN-PINN) that approximates PDE evolution under physics-informed constraints. It couples node-edge message passing with a consistency loss enforcing the gradient-divergence relation through the graph incidence matrix, ensuring that discrete node and edge dynamics remain structurally coupled during temporal rollout. We evaluate the model on diffusion processes over physically driven evolving meshes and real-world scanned surfaces. The results show improved temporal stability and prediction accuracy compared with graph convolutional and multilayer perceptron baselines, approaching the performance of Crank-Nicolson solvers on unstructured domains.

Paperid: 1183, https://arxiv.org/pdf/2512.11250.pdf

Abstract:
This work develops a control-centric framework for a custom 4-DOF rigid-body manipulator by coupling a reduced-order Pontryagin's Maximum Principle (PMP) controller with a physics-informed Gradient Descent stage. The reduced PMP model provides a closed-form optimal control law for the joint accelerations, while the Gradient Descent module determines the corresponding time horizons by minimizing a cost functional built directly from the full Rigid-Body Dynamics. Structural-mechanics reaction analysis is used only to initialize feasible joint velocities-most critically the azimuthal component-ensuring that the optimizer begins in a physically admissible region. The resulting kinematic trajectories and dynamically consistent time horizons are then supplied to the symbolic Euler-Lagrange model to yield closed-form inverse-dynamics inputs. This pipeline preserves a strict control-theoretic structure while embedding the physical constraints and loading behavior of the manipulator in a computationally efficient way.

Paperid: 1184, https://arxiv.org/pdf/2512.10886.pdf

Abstract:
Parabolic trough Concentrating Solar Power (CSP) plants operate large hydraulic networks of collector loops that must deliver a uniform outlet temperature despite spatially heterogeneous optical performance, heat losses, and pressure drops. While loop temperatures are measured, loop-level mass flows and receiver heat-loss parameters are unobserved, making it impossible to diagnose hydraulic imbalances or receiver degradation using standard monitoring tools. We present a physics-informed learning framework that infers (i) loop-level mass-flow ratios and (ii) time-varying receiver heat-transfer coefficients directly from routine operational data. The method exploits nocturnal homogenization periods -- when hot oil is circulated through a non-irradiated field -- to isolate hydraulic and thermal-loss effects. A differentiable conjugate heat-transfer model is discretized and embedded into an end-to-end learning pipeline optimized using historical plant data from the 50 MW Andasol 3 solar field. The model accurately reconstructs loop temperatures (RMSE $<2^\circ$C) and produces physically meaningful estimates of loop imbalances and receiver heat losses. Comparison against drone-based infrared thermography (QScan) shows strong correspondence, correctly identifying all areas with high-loss receivers. This demonstrates that noisy real-world CSP operational data contain enough information to recover latent physical parameters when combined with appropriate modeling and differentiable optimization.

Paperid: 1185, https://arxiv.org/pdf/2512.09754.pdf

Abstract:
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant challenges remain -- particularly regarding training stability and the lack of rigorous theoretical guarantees, especially when compared to classical mesh-based methods. In this work, we focus on the inverse problem of identifying a spatially varying parameter in a constitutive model of three-dimensional elasticity, using measurements of the system's state. This setting is especially relevant for non-invasive diagnosis in cardiac biomechanics, where one must also carefully account for the type of boundary data available. To address this inverse problem, we adopt an all-at-once optimisation framework, simultaneously estimating the state and parameter through a least-squares loss that encodes both available data and the governing physics. For this formulation, we prove stability estimates ensuring that our approach yields a stable approximation of the underlying ground-truth parameter of the physical system independent of a specific discretisation. We then proceed with a neural network-based discretisation and compare it to traditional mesh-based approaches. Our theoretical findings are complemented by illustrative numerical examples.

Paperid: 1186, https://arxiv.org/pdf/2512.09576.pdf

Abstract:
Environmental variables are increasingly affecting agricultural decision-making, yet accessible and scalable tools for soil assessment remain limited. This study presents a robust and scalable modeling system for estimating soil properties in croplands, including soil organic carbon (SOC), total nitrogen (N), available phosphorus (P), exchangeable potassium (K), and pH, using remote sensing data and environmental covariates. The system employs a hybrid modeling approach, combining the indirect methods of modeling soil through proxies and drivers with direct spectral modeling. We extend current approaches by using interpretable physics-informed covariates derived from radiative transfer models (RTMs) and complex, nonlinear embeddings from a foundation model. We validate the system on a harmonized dataset that covers Europes cropland soils across diverse pedoclimatic zones. Evaluation is conducted under a robust validation framework that enforces strict spatial blocking, stratified splits, and statistically distinct train-test sets, which deliberately make the evaluation harder and produce more realistic error estimates for unseen regions. The models achieved their highest accuracy for SOC and N. This performance held across unseen locations, under both spatial cross-validation and an independent test set. SOC obtained a MAE of 5.12 g/kg and a CCC of 0.77, and N obtained a MAE of 0.44 g/kg and a CCC of 0.77. We also assess uncertainty through conformal calibration, achieving 90 percent coverage at the target confidence level. This study contributes to the digital advancement of agriculture through the application of scalable, data-driven soil analysis frameworks that can be extended to related domains requiring quantitative soil evaluation, such as carbon markets.

Paperid: 1187, https://arxiv.org/pdf/2512.07162.pdf

Abstract:
Real-time calibration of stochastic volatility models (SVMs) is computationally bottlenecked by the need to repeatedly solve coupled partial differential equations (PDEs). In this work, we propose DeepSVM, a physics-informed Deep Operator Network (PI-DeepONet) designed to learn the solution operator of the Heston model across its entire parameter space. Unlike standard data-driven deep learning (DL) approaches, DeepSVM requires no labelled training data. Rather, we employ a hard-constrained ansatz that enforces terminal payoffs and static no-arbitrage conditions by design. Furthermore, we use Residual-based Adaptive Refinement (RAR) to stabilize training in difficult regions subject to high gradients. Overall, DeepSVM achieves a final training loss of $10^{-5}$ and predicts highly accurate option prices across a range of typical market dynamics. While pricing accuracy is high, we find that the model's derivatives (Greeks) exhibit noise in the at-the-money (ATM) regime, highlighting the specific need for higher-order regularization in physics-informed operator learning.

Paperid: 1188, https://arxiv.org/pdf/2512.06783.pdf

Abstract:
Applications providing automated coaching for physical training are increasing in popularity, for example physical therapy. These applications rely on accurate and robust pose estimation using monocular video streams. State-of-the-art models like BlazePose excel in real-time pose tracking, but their lack of anatomical constraints indicates improvement potential by including physical knowledge. We present a real-time post-processing algorithm fusing the strengths of BlazePose 3D and 2D estimations using a weighted optimization, penalizing deviations from expected bone length and biomechanical models. Bone length estimations are refined to the individual anatomy using a Kalman filter with adapting measurement trust. Evaluation using the Physio2.2M dataset shows a 10.2 percent reduction in 3D MPJPE and a 16.6 percent decrease in errors of angles between body segments compared to BlazePose 3D estimation. Our method provides a robust, anatomically consistent pose estimation based on a computationally efficient video-to-3D pose estimation, suitable for automated physiotherapy, healthcare, and sports coaching on consumer-level laptops and mobile devices. The refinement runs on the backend with anonymized data only.

Paperid: 1189, https://arxiv.org/pdf/2512.06427.pdf

Abstract:
Proper initialisation strategy is of primary importance to mitigate gradient explosion or vanishing when training neural networks. Yet, the impact of initialisation parameters still lacks a precise theoretical understanding for several well-established architectures. Here, we propose a new initialisation for networks with sinusoidal activation functions such as \texttt{SIREN}, focusing on gradients control, their scaling with network depth, their impact on training and on generalization. To achieve this, we identify a closed-form expression for the initialisation of the parameters, differing from the original \texttt{SIREN} scheme. This expression is derived from fixed points obtained through the convergence of pre-activation distribution and the variance of Jacobian sequences. Controlling both gradients and targeting vanishing pre-activation helps preventing the emergence of inappropriate frequencies during estimation, thereby improving generalization. We further show that this initialisation strongly influences training dynamics through the Neural Tangent Kernel framework (NTK). Finally, we benchmark \texttt{SIREN} with the proposed initialisation against the original scheme and other baselines on function fitting and image reconstruction. The new initialisation consistently outperforms state-of-the-art methods across a wide range of reconstruction tasks, including those involving physics-informed neural networks.

Paperid: 1190, https://arxiv.org/pdf/2512.03923.pdf

Abstract:
Solving partial differential equations (PDEs) for reservoir seepage is critical for optimizing oil and gas field development and predicting production performance. Traditional numerical methods suffer from mesh-dependent errors and high computational costs, while classical Physics-Informed Neural Networks (PINNs) face bottlenecks in parameter efficiency, high-dimensional expression, and strong nonlinear fitting. To address these limitations, we propose a Discrete Variable (DV)-Circuit Quantum-Classical Physics-Informed Neural Network (QCPINN) and apply it to three typical reservoir seepage models for the first time: the pressure diffusion equation for heterogeneous single-phase flow, the nonlinear Buckley-Leverett (BL) equation for two-phase waterflooding, and the convection-diffusion equation for compositional flow considering adsorption. The QCPINN integrates classical preprocessing/postprocessing networks with a DV quantum core, leveraging quantum superposition and entanglement to enhance high-dimensional feature mapping while embedding physical constraints to ensure solution consistency. We test three quantum circuit topologies (Cascade, Cross-mesh, Alternate) and demonstrate through numerical experiments that QCPINNs achieve high prediction accuracy with fewer parameters than classical PINNs. Specifically, the Alternate topology outperforms others in heterogeneous single-phase flow and two-phase BL equation simulations, while the Cascade topology excels in compositional flow with convection-dispersion-adsorption coupling. Our work verifies the feasibility of QCPINN for reservoir engineering applications, bridging the gap between quantum computing research and industrial practice in oil and gas engineering.

Paperid: 1191, https://arxiv.org/pdf/2512.03050.pdf

Abstract:
Machine learning (ML) has emerged as a powerful tool for accelerating the computational design and production of materials. In materials science, ML has primarily supported large-scale discovery of novel compounds using first-principles data and digital twin applications for optimizing manufacturing processes. However, applying general-purpose ML frameworks to complex industrial materials such as steel remains a challenge. A key obstacle is accurately capturing the intricate relationship between chemical composition, processing parameters, and the resulting microstructure and properties. To address this, we introduce a computational framework that combines physical insights with ML to develop a physics-informed continuous cooling transformation (CCT) model for steels. Our model, trained on a dataset of 4,100 diagrams, is validated against literature and experimental data. It demonstrates high computational efficiency, generating complete CCT diagrams with 100 cooling curves in under 5 seconds. It also shows strong generalizability across alloy steels, achieving phase classification F1 scores above 88% for all phases. For phase transition temperature regression, it attains mean absolute errors (MAE) below 20 °C across all phases except bainite, which shows a slightly higher MAE of 27 °C. This framework can be extended with additional generic and customized ML models to establish a universal digital twin platform for heat treatment. Integration with complementary simulation tools and targeted experiments will further support accelerated materials design workflows.

Paperid: 1192, https://arxiv.org/pdf/2512.02803.pdf

Abstract:
This paper presents the modeling of autonomous vehicles with high maneuverability used in an experimental framework for educational purposes. Since standard bicycle models typically neglect wide steering angles, we develop modified planar bicycle models and combine them with both parametric and non-parametric identification techniques that progressively incorporate physical knowledge. The resulting models are systematically compared to evaluate the tradeoff between model accuracy and computational requirements, showing that physics-informed neural network models surpass the purely physical baseline in accuracy at lower computational cost.

Paperid: 1193, https://arxiv.org/pdf/2512.02618.pdf

Abstract:
Heat transfer in semiconductor devices is dominated by chip and substrate assemblies, where heat generated within a finite chip layer dissipates into a semi-infinite substrate with much higher thermophysical properties. This mismatch produces steep interfacial temperature gradients, making the transient thermal response highly sensitive to the interface. Conventional numerical solvers require excessive discretization to resolve these dynamics, while physics-informed neural networks (PINNs) often exhibit unstable convergence and loss of physical consistency near the material interface. To address these challenges, we introduce HeatTransFormer, a physics-guided Transformer architecture for interface-dominated diffusion problems. The framework integrates physically informed spatiotemporal sampling, a Laplace-based activation emulating analytical diffusion solutions, and a mask-free attention mechanism supporting bidirectional spatiotemporal coupling. These components enable the model to resolve steep gradients, maintain physical consistency, and remain stable where PINNs typically fail. HeatTransFormer produces coherent temperature fields across the interface when applied to a finite layer and semi-infinite substrate configuration. Coupled with a physics-constrained inverse strategy, it further enables reliable identification of three unknown thermal properties simultaneously using only external measurements. Overall, this work demonstrates that physics-guided Transformer architectures provide a unified framework for forward and inverse modeling in interface-dominated thermal systems.

Paperid: 1194, https://arxiv.org/pdf/2512.02079.pdf

Abstract:
Fast, efficient, robust communication during wildfire and other emergency responses is critical. One way to achieve this is by coordinating swarms of autonomous aerial vehicles carrying communications equipment to form an ad-hoc network connecting emergency response personnel to both each other and central command. However, operating in such extreme environments may lead to individual networking agents being damaged or rendered inoperable, which could bring down the network and interrupt communications. To overcome this challenge and enable multi-agent UAV networking in difficult environments, this paper introduces and formalizes the problem of Robust Task Networking Under Attrition (RTNUA), which extends connectivity maintenance in multi-robot systems to explicitly address proactive redundancy and attrition recovery. We introduce Physics-Informed Robust Employment of Multi-Agent Networks ($Φ$IREMAN), a topological algorithm leveraging physics-inspired potential fields to solve this problem. Through simulation across 25 problem configurations, $Φ$IREMAN consistently outperforms the DCCRS baseline, and on large-scale problems with up to 100 tasks and 500 drones, maintains $>99.9\%$ task uptime despite substantial attrition, demonstrating both effectiveness and scalability.

Paperid: 1195, https://arxiv.org/pdf/2512.00760.pdf

Abstract:
Demographic forecasting remains a fundamental challenge for policy planning in rapidly evolving nations such as India, where fertility transitions, policy interventions, and age structured dynamics interact in complex ways. In this study, we present a hybrid modelling framework that integrates policy-aware fertility functions into a Physics-Informed Neural Network (PINN) enhanced with Long Short-Term Memory (LSTM) networks to capture physical constraints and temporal dependencies in population dynamics. The model is applied to India's age structured population from 2024 to 2054 under three fertility-policy scenarios: continuation of current fertility decline, stricter population control, and relaxed fertility promotion. The governing transport-reaction partial differential equation is formulated with India-specific demographic indicators, including age-specific fertility and mortality rates. PINNs embed the core population equation and policy-driven fertility changes, while LSTM layers improve long-term forecasting across decades. Results show that fertility policies substantially shape future age distribution, dependency ratios, and workforce size. Stricter controls intensify ageing and reduce labour force participation, whereas relaxed policies support workforce growth but increase population pressure. Our findings suggest that the hybrid LSTM-PINN is an effective approach for demographic forecasting, offering accuracy with interpretability. Beyond methodological novelty, this work provides actionable insights for India's demographic policy debates, highlighting the need for balanced fertility interventions to ensure sustainable socio-economic development.

Paperid: 1196, https://arxiv.org/pdf/2511.23409.pdf

Abstract:
Physics-informed neural networks (PINNs) often struggle with multi-scale PDEs featuring sharp gradients and nontrivial boundary conditions, as the physics residual and boundary enforcement compete during optimization. We present a dual-network framework that decomposes the solution as $u = u_{\text{D}} + u_{\text{B}}$, where $u_{\text{D}}$ (domain network) captures interior dynamics and $u_{\text{B}}$ (boundary network) handles near-boundary corrections. Both networks share a unified physics residual while being softly specialized via distance-weighted priors ($w_{\text{bd}} = \exp(-d/τ)$) that are cosine-annealed during training. Boundary conditions are enforced through an augmented Lagrangian method, eliminating manual penalty tuning. Training proceeds in two phases: Phase~1 uses uniform collocation to establish network roles and stabilize boundary satisfaction; Phase~2 employs focused sampling (e.g. ring sampling near $\partialΩ$) with annealed role weights to efficiently resolve localized features. We evaluate our model on four benchmarks, including the 1D Fokker-Planck equation, the Laplace equation, the Poisson equation, and the 1D wave equation. Across Laplace and Poisson benchmarks, our method reduces error by $36-90\%$, improves boundary satisfaction by $21-88\%$, and decreases MAE by $2.2-9.3\times$ relative to a single-network PINN. Ablations isolate contributions of (i)~soft boundary-interior specialization, (ii)~annealed role regularization, and (iii)~the two-phase curriculum. The method is simple to implement, adds minimal computational overhead, and broadly applies to PDEs with sharp solutions and complex boundary data.

Paperid: 1197, https://arxiv.org/pdf/2511.23307.pdf

Abstract:
This paper presents a framework for physics-informed learning in complex cyber-physical systems governed by differential equations with both unknown dynamics and algebraic invariants. First, we formalize the Hybrid Recurrent Physics-Informed Neural Network (HRPINN), a general-purpose architecture that embeds known physics as a hard structural constraint within a recurrent integrator to learn only residual dynamics. Second, we introduce the Projected HRPINN (PHRPINN), a novel extension that integrates a predict-project mechanism to strictly enforce algebraic invariants by design. The framework is supported by a theoretical analysis of its representational capacity. We validate HRPINN on a real-world battery prognostics DAE and evaluate PHRPINN on a suite of standard constrained benchmarks. The results demonstrate the framework's potential for achieving high accuracy and data efficiency, while also highlighting critical trade-offs between physical consistency, computational cost, and numerical stability, providing practical guidance for its deployment.

Paperid: 1198, https://arxiv.org/pdf/2511.22522.pdf

Abstract:
We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving non-linear differential equations of motion. First, we introduce holographic inverse problems and demonstrate how PIML can reconstruct bulk spacetime and effective potentials from boundary quantum data. To illustrate this, two case studies are explored: the QCD equation of state in holographic QCD and $T$-linear resistivity in holographic strange metals. Additionally, we explicitly show how such holographic problems can be analogized to inverse problems in classical mechanics, modeling frictional forces with neural networks. We also explore Kolmogorov-Arnold Networks (KANs) as an alternative to traditional neural networks, offering more efficient solutions in certain cases. This manuscript aim to provide a systematic framework for using neural networks in inverse problems, serving as a comprehensive reference for researchers in machine learning for high-energy physics, with methodologies that also have broader applications in mathematics, engineering, and the natural sciences.

Paperid: 1199, https://arxiv.org/pdf/2511.21784.pdf

Abstract:
Real-time, physically-consistent predictions on low-power edge devices is critical for the next generation embodied AI systems, yet it remains a major challenge. Physics-Informed Neural Networks (PINNs) combine data-driven learning with physics-based constraints to ensure the model's predictions are with underlying physical principles.However, PINNs are energy-intensive and struggle to strictly enforce physical conservation laws. Brain-inspired spiking neural networks (SNNs) have emerged as a promising solution for edge computing and real-time processing. However, naively converting PINNs to SNNs degrades physical fidelity and fails to address long-term generalization issues. To this end, this paper introduce a novel Physics-Informed Spiking Neural Network (PISNN) framework. Importantly, to ensure strict physical conservation, we design the Conservative Leaky Integrate-and-Fire (C-LIF) neuron, whose dynamics structurally guarantee local mass preservation. To achieve robust temporal generalization, we introduce a novel Conservative Flux Quantization (CFQ) strategy, which redefines neural spikes as discrete packets of physical flux. Our CFQ learns a time-invariant physical evolution operator, enabling the PISNN to become a general-purpose solver -- conservative-by-construction. Extensive experiments show that our PISNN excels on diverse benchmarks. For both the canonical 1D heat equation and the more challenging 2D Laplace's Equation, it accurately simulates the system dynamics while maintaining perfect mass conservation by design -- a feat that is challenging for conventional PINNs. This work establishes a robust framework for fusing the rigor of scientific computing with the efficiency of neuromorphic engineering, paving the way for complex, long-term, and energy-efficient physics predictions for intelligent systems.

Paperid: 1200, https://arxiv.org/pdf/2511.21276.pdf

Abstract:
Accurate and efficient seismic response prediction is essential for the design of resilient structures. While the Finite Element Method (FEM) remains the standard for nonlinear seismic analysis, its high computational demands limit its scalability and real time applicability. Recent developments in deep learning, particularly Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Long Short Term Memory (LSTM) models, have shown promise in reducing the computational cost of nonlinear seismic analysis of structures. However, these data driven models often struggle to generalize and capture the underlying physics, leading to reduced reliability. We propose a novel Physics Informed U Net LSTM framework that integrates physical laws with deep learning to enhance both accuracy and efficiency. By embedding domain specific constraints into the learning process, the proposed model achieves improved predictive performance over conventional Machine Learning architectures. This hybrid approach bridges the gap between purely data driven methods and physics based modeling, offering a robust and computationally efficient alternative for seismic response prediction of structures.

Paperid: 1201, https://arxiv.org/pdf/2511.19952.pdf

Abstract:
Forward Collision Warning systems are crucial for vehicle safety and autonomous driving, yet current methods often fail to balance precise multi-agent interaction modeling with real-time decision adaptability, evidenced by the high computational cost for edge deployment and the unreliability stemming from simplified interaction models.To overcome these dual challenges-computational complexity and modeling insufficiency-along with the high false alarm rates of traditional static-threshold warnings, this paper introduces an integrated FCW framework that pairs a Hierarchical Spatio-Temporal Attention Network with a Dynamic Risk Threshold Adjustment algorithm. HSTAN employs a decoupled architecture (Graph Attention Network for spatial, cascaded GRU with self-attention for temporal) to achieve superior performance and efficiency, requiring only 12.3 ms inference time (73% faster than Transformer methods) and reducing the Average Displacement Error (ADE) to 0.73m (42.2% better than Social_LSTM) on the NGSIM dataset. Furthermore, Conformalized Quantile Regression enhances reliability by generating prediction intervals (91.3% coverage at 90% confidence), which the DTRA module then converts into timely warnings via a physics-informed risk potential function and an adaptive threshold mechanism inspired by statistical process control.Tested across multi-scenario datasets, the complete system demonstrates high efficacy, achieving an F1 score of 0.912, a low false alarm rate of 8.2%, and an ample warning lead time of 2.8 seconds, validating the framework's superior performance and practical deployment feasibility in complex environments.

Paperid: 1202, https://arxiv.org/pdf/2511.19916.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) encounter significant training difficulties when applied to doubly-clamped beam problems, and the underlying causes are not fully understood. This study investigates the PINN loss landscape to identify the failure mechanisms of two primary formulations: the high-order strong formulation and the energy-based formulation. The results demonstrate that the Strong Formulation suffers from landscape ill-conditioning driven by the boundary conditions (BCs), leading to convergence issues in the doubly-clamped case. Conversely, while the energy-based formulation requires only lower-order derivatives, its loss functional can become indefinite, causing optimization difficulties near saddle points. Based on strain field benchmarks against Finite Element Method (FEM), it is found that the strong formulation, combined with a BC handling method and the L-BFGS optimizer, yields the best performance across three classical boundary condition cases. These findings clarify distinct, formulation-dependent failure modes, offering a diagnostic foundation for developing robust physics-based surrogate models for complex beam systems.

Paperid: 1203, https://arxiv.org/pdf/2511.19114.pdf

Abstract:
As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the Grad-Shafranov equation (GSE) is essential for real-time plasma control and analysis. Traditional numerical solvers achieve high precision but are computationally prohibitive, while data-driven surrogates infer quickly but fail to enforce physical laws and generalize poorly beyond training distributions. To address this challenge, we present a Physics-Informed Neural Operator (PINO) that directly learns the GSE solution operator, mapping shape parameters of last closed flux surface to equilibrium solutions for realistic nonlinear current profiles. Comprehensive benchmarking of five neural architectures identifies the novel Transformer-KAN (Kolmogorov-Arnold Network) Neural Operator (TKNO) as achieving highest accuracy (0.25% mean L2 relative error) under supervised training (only data-driven). However, all data-driven models exhibit large physics residuals, indicating poor physical consistency. Our unsupervised training can reduce the residuals by nearly four orders of magnitude through embedding physics-based loss terms without labeled data. Critically, semi-supervised learning--integrating sparse labeled data (100 interior points) with physics constraints--achieves optimal balance: 0.48% interpolation error and the most robust extrapolation performance (4.76% error, 8.9x degradation factor vs 39.8x for supervised models). Accelerated by TensorRT optimization, our models enable millisecond-level inference, establishing PINO as a promising pathway for next-generation fusion control systems.

Paperid: 1204, https://arxiv.org/pdf/2511.18243.pdf

Abstract:
Current control algorithms for aerial robots struggle with robustness in dynamic environments and adverse conditions. Model-based reinforcement learning (RL) has shown strong potential in handling these challenges while remaining sample-efficient. Additionally, Dreamer has demonstrated that online model-based RL can be achieved using a recurrent world model trained on replay buffer data. However, applying Dreamer to aerial systems has been quite challenging due to its sample inefficiency and poor generalization of dynamics models. Our work explores a physics-informed approach to world model learning and improves policy performance. The world model treats the quadcopter as a free-body system and predicts the net forces and moments acting on it, which are then passed through a 6-DOF Runge-Kutta integrator (RK4) to predict future state rollouts. In this paper, we compare this physics-informed method to a standard RNN-based world model. Although both models perform well on the training data, we observed that they fail to generalize to new trajectories, leading to rapid divergence in state rollouts, preventing policy convergence.

Paperid: 1205, https://arxiv.org/pdf/2511.16148.pdf

Abstract:
In recent years, there has been an increasing need for Nuclear Power Plants (NPPs) to improve flexibility in order to match the rapid growth of renewable energies. The Operator Assistance Predictive System (OAPS) developed by Framatome addresses this problem through Model Predictive Control (MPC). In this work, we aim to improve MPC methods through data-driven simulation schemes. Thus, from a set of nonlinear stiff ordinary differential equations (ODEs), this paper introduces two surrogate models acting as alternative simulation schemes to enhance nuclear reactor core simulation. We show that both data-driven and physics-informed models can rapidly integrate complex dynamics, with a very low computational time (up to 1000x time reduction).

Paperid: 1206, https://arxiv.org/pdf/2511.15543.pdf

Abstract:
Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that provide the maximum amount of information about the unknown parameters, in particular for the case of distributed-parameter systems, where spatial variations are important. Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful machine-learning (ML) tool for parameter estimation, particularly in cases with sparse or noisy measurements, overcoming some of the limitations of traditional optimization-based and Bayesian approaches. Despite the widespread use of PINNs for solving inverse problems, relatively little attention has been given to how their performance depends on sensor placement. This study addresses this gap by introducing a comprehensive PINN-based framework that simultaneously tackles optimal sensor placement and parameter estimation. Our approach involves training a PINN model in which the parameters of interest are included as additional inputs. This enables the efficient computation of sensitivity functions through automatic differentiation, which are then used to determine optimal sensor locations exploiting the D-optimality criterion. The framework is validated on two illustrative distributed-parameter reaction-diffusion-advection problems of increasing complexity. The results demonstrate that our PINNs-based methodology consistently achieves higher accuracy compared to parameter values estimated from intuitively or randomly selected sensor positions.

Paperid: 1207, https://arxiv.org/pdf/2511.15445.pdf

Abstract:
Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing partial differential equations (PDEs) such as the Helmholtz equation. However, these methods face significant computational challenges when applied to high-frequency wave problems in complex two-dimensional domains. This work investigates Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a promising alternative. These methods leverage domain decomposition, partitioning the computational domain into overlapping sub-domains, each governed by a local neural network. We assess their accuracy and computational efficiency in solving the Helmholtz equation for the homogeneous case, demonstrating their potential to mitigate the limitations of traditional approaches.

Paperid: 1208, https://arxiv.org/pdf/2511.14730.pdf

Abstract:
Restoring power distribution systems (PDS) after large-scale outages requires sequential switching operations that reconfigure feeder topology and coordinate distributed energy resources (DERs) under nonlinear constraints such as power balance, voltage limits, and thermal ratings. These challenges make conventional optimization and value-based RL approaches computationally inefficient and difficult to scale. This paper applies a Heterogeneous-Agent Reinforcement Learning (HARL) framework, instantiated through Heterogeneous-Agent Proximal Policy Optimization (HAPPO), to enable coordinated restoration across interconnected microgrids. Each agent controls a distinct microgrid with different loads, DER capacities, and switch counts, introducing practical structural heterogeneity. Decentralized actor policies are trained with a centralized critic to compute advantage values for stable on-policy updates. A physics-informed OpenDSS environment provides full power flow feedback and enforces operational limits via differentiable penalty signals rather than invalid action masking. The total DER generation is capped at 2400 kW, and each microgrid must satisfy local supply-demand feasibility. Experiments on the IEEE 123-bus and IEEE 8500-node systems show that HAPPO achieves faster convergence, higher restored power, and smoother multi-seed training than DQN, PPO, MAES, MAGDPG, MADQN, Mean-Field RL, and QMIX. Results demonstrate that incorporating microgrid-level heterogeneity within the HARL framework yields a scalable, stable, and constraint-aware solution for complex PDS restoration.

Paperid: 1209, https://arxiv.org/pdf/2511.13734.pdf

Abstract:
The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding. Physics-Informed Neural Networks (PINNs) embed the governing equations into the learning process, enabling mesh-free solution of PDEs, yet they often struggle to capture steep gradients, discontinuities, and complex nonlinear wave interactions. To address these limitations, we employ the Extended Physics-Informed Neural Network (XPINN) framework to solve the nonlinear Buckley-Leverett equation with a nonconvex flux, modeling immiscible two-phase flow in porous media. The computational domain is dynamically decomposed in space and time into evolving pre-shock and post-shock subdomains, allowing localized subnetworks to efficiently learn distinct flow behaviors, with coupling enforced via the Rankine-Hugoniot jump condition to ensure physically consistent flux continuity. We compare XPINN with standard PINNs and its variants, including PINN with artificial viscosity, PINN with Welge construction, and PINN with the Oleinik entropy condition, and across all cases, XPINN consistently outperforms the other methods, accurately resolving sharp fronts and capturing the correct physical behavior. Importantly, XPINN achieves this using the simpler Adam optimizer, whereas some PINN variants require more complex or higher-order strategies such as L-BFGS to reach comparable accuracy, demonstrating that XPINN is a robust and scalable approach for challenging hyperbolic PDEs without artificial diffusion or entropy corrections. The code is available at github.com/saifkhanengr/XPINN-for-Buckley-Leverett.

Paperid: 1210, https://arxiv.org/pdf/2511.11137.pdf

Abstract:
We propose a framework for solving nonlinear partial differential equations (PDEs) by combining perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). Nonlinear PDEs with polynomial terms are decomposed into a sequence of linear subproblems, which are efficiently solved using a Multi-Head PINN. Once the latent representation of the linear operator is learned, solutions to new PDE instances with varying perturbations, forcing terms, or boundary/initial conditions can be obtained in closed form without retraining. We validate the method on KPP-Fisher and wave equations, achieving errors on the order of 1e-3 while adapting to new problem instances in under 0.2 seconds; comparable accuracy to classical solvers but with faster transfer. Sensitivity analyses show predictable error growth with epsilon and polynomial degree, clarifying the method's effective regime. Our contributions are: (i) extending one-shot transfer learning from nonlinear ODEs to PDEs, (ii) deriving a closed-form solution for adapting to new PDE instances, and (iii) demonstrating accuracy and efficiency on canonical nonlinear PDEs. We conclude by outlining extensions to derivative-dependent nonlinearities and higher-dimensional PDEs.

Paperid: 1211, https://arxiv.org/pdf/2511.09728.pdf

Abstract:
Due to its nonlinearity, bi-harmonic dissipation, and backward heat-like term in the absence of a divergence-free condition, the $2$-D/$3$-D Kuramoto-Sivashinsky equation poses significant challenges for both mathematical analysis and numerical approximation. These difficulties motivate the development of methods that blend classical analysis with numerical approximation approaches embodied in the framework of the physics-informed neural networks (PINNs). In addition, despite the extensive use of PINN frameworks for various linear and nonlinear PDEs, no study had previously established rigorous error estimates for the Kuramoto-Sivashinsky equation within a PINN setting. In this work, we overcome the inherent challenges, and establish several global regularity criteria based on space-time integrability conditions in Besov spaces. We then derive the first rigorous error estimates for the PINNs approximation of the Kuramoto-Sivashinsky equation and validate our theoretical error bounds through numerical simulations.

Paperid: 1212, https://arxiv.org/pdf/2511.09130.pdf

Abstract:
Flood mapping is crucial for assessing and mitigating flood impacts, yet traditional methods like numerical modeling and aerial photography face limitations in efficiency and reliability. To address these challenges, we propose PIFF, a physics-informed, flow-based generative neural network for near real-time flood depth estimation. Built on an image-to-image generative framework, it efficiently maps Digital Elevation Models (DEM) to flood depth predictions. The model is conditioned on a simplified inundation model (SPM) that embeds hydrodynamic priors into the training process. Additionally, a transformer-based rainfall encoder captures temporal dependencies in precipitation. Integrating physics-informed constraints with data-driven learning, PIFF captures the causal relationships between rainfall, topography, SPM, and flooding, replacing costly simulations with accurate, real-time flood maps. Using a 26 km study area in Tainan, Taiwan, with 182 rainfall scenarios ranging from 24 mm to 720 mm over 24 hours, our results demonstrate that PIFF offers an effective, data-driven alternative for flood prediction and response.

Paperid: 1213, https://arxiv.org/pdf/2511.08561.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving forward and inverse problems governed by differential equations. However, their reliability when used in ill-posed inverse problems remains poorly understood. In this study, we explore the fundamental limitations of PINNs using a simple illustrative case: RC low-pass filters. Showing that while PINNs can accurately predict system dynamics in forward problems, they fail to recover unique physical parameters when solving inverse problems when more than two parameters are approximated. Our findings provide grounds to understand the boundaries of PINNs applicability for parameter discovery in physical systems.

Paperid: 1214, https://arxiv.org/pdf/2511.08302.pdf

Abstract:
We address the inverse problem of identifying a time-dependent potential coefficient in a one-dimensional diffusion equation subject to Dirichlet boundary conditions and a nonlocal integral overdetermination constraint reflecting spatially averaged measurements. After establishing well-posedness for the forward problem and deriving an a priori estimate that ensures uniqueness and continuous dependence on the data, we prove existence and uniqueness for the inverse problem. To compute numerically the unknown coefficient, we propose and compare three numerical methods: an integration-based scheme, a Newton-Raphson iterative solver, and a physics-informed neural network (PINN). Numerical experiments on both exact and noisy data demonstrate the accuracy, robustness, and efficiency of each approach.

Paperid: 1215, https://arxiv.org/pdf/2511.07684.pdf

Abstract:
We propose a nonlinear, non-intrusive reduced basis method with online adaptation for efficient approximation of parametrized partial differential equations. The method combines neural networks with reduced-order modeling and physics-informed training to enhance both accuracy and efficiency. In the offline stage, reduced basis functions are obtained via nonlinear dimension reduction, and a neural surrogate is trained to map parameters to approximate solutions. The surrogate employs a nonlinear reconstruction of the solution from the basis functions, enabling more accurate representation of complex solution structures than linear mappings. The model is further refined during the online stage using lightweight physics-informed neural network training. This offline-online framework enables accurate prediction especially in complex scenarios or with limited snapshot data. We demonstrate the performance and effectiveness of the proposed method through numerical experiments.

Paperid: 1216, https://arxiv.org/pdf/2511.07262.pdf

Abstract:
Scientific Machine Learning (SciML) integrates data-driven inference with physical modeling to solve complex problems in science and engineering. However, the design of SciML architectures, loss formulations, and training strategies remains an expert-driven research process, requiring extensive experimentation and problem-specific insights. Here we introduce AgenticSciML, a collaborative multi-agent system in which over 10 specialized AI agents collaborate to propose, critique, and refine SciML solutions through structured reasoning and iterative evolution. The framework integrates structured debate, retrieval-augmented method memory, and ensemble-guided evolutionary search, enabling the agents to generate and assess new hypotheses about architectures and optimization procedures. Across physics-informed learning and operator learning tasks, the framework discovers solution methods that outperform single-agent and human-designed baselines by up to four orders of magnitude in error reduction. The agents produce novel strategies -- including adaptive mixture-of-expert architectures, decomposition-based PINNs, and physics-informed operator learning models -- that do not appear explicitly in the curated knowledge base. These results show that collaborative reasoning among AI agents can yield emergent methodological innovation, suggesting a path toward scalable, transparent, and autonomous discovery in scientific computing.

Paperid: 1217, https://arxiv.org/pdf/2511.06745.pdf

Abstract:
Self-supervised goal-conditioned reinforcement learning enables robots to autonomously acquire diverse skills without human supervision. However, a central challenge is the goal setting problem: robots must propose feasible and diverse goals that are achievable in their current environment. Existing methods like RIG (Visual Reinforcement Learning with Imagined Goals) use variational autoencoder (VAE) to generate goals in a learned latent space but have the limitation of producing physically implausible goals that hinder learning efficiency. We propose Physics-Informed RIG (PI-RIG), which integrates physical constraints directly into the VAE training process through a novel Enhanced Physics-Informed Variational Autoencoder (Enhanced p3-VAE), enabling the generation of physically consistent and achievable goals. Our key innovation is the explicit separation of the latent space into physics variables governing object dynamics and environmental factors capturing visual appearance, while enforcing physical consistency through differential equation constraints and conservation laws. This enables the generation of physically consistent and achievable goals that respect fundamental physical principles such as object permanence, collision constraints, and dynamic feasibility. Through extensive experiments, we demonstrate that this physics-informed goal generation significantly improves the quality of proposed goals, leading to more effective exploration and better skill acquisition in visual robotic manipulation tasks including reaching, pushing, and pick-and-place scenarios.

Paperid: 1218, https://arxiv.org/pdf/2511.04564.pdf

Abstract:
Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize physical systems. This framework enables data-driven understanding and prediction of complex physical phenomena. While coefficient functions in PIML are typically estimated on the basis of predictive performance, physics as a discipline does not rely solely on prediction accuracy to evaluate models. For example, Kepler's heliocentric model was favored owing to small discrepancies in planetary motion, despite its similar predictive accuracy to the geocentric model. This highlights the inherent uncertainties in data-driven model inference and the scientific importance of selecting physically meaningful solutions. In this paper, we propose a framework to quantify and analyze such uncertainties in the estimation of coefficient functions in PIML. We apply our framework to reduced model of magnetohydrodynamics and our framework shows that there are uncertainties, and unique identification is possible with geometric constraints. Finally, we confirm that we can estimate the reduced model uniquely by incorporating these constraints.

Paperid: 1219, https://arxiv.org/pdf/2511.03876.pdf

Abstract:
Background: Non-invasive imaging-based assessment of blood flow plays a critical role in evaluating heart function and structure. Computed Tomography (CT) is a widely-used imaging modality that can robustly evaluate cardiovascular anatomy and function, but direct methods to estimate blood flow velocity from movies of contrast evolution have not been developed. Purpose: This study evaluates the impact of CT imaging on Physics-Informed Neural Networks (PINN)-based flow estimation and proposes an improved framework, SinoFlow, which uses sinogram data directly to estimate blood flow. Methods: We generated pulsatile flow fields in an idealized 2D vessel bifurcation using computational fluid dynamics and simulated CT scans with varying gantry rotation speeds, tube currents, and pulse mode imaging settings. We compared the performance of PINN-based flow estimation using reconstructed images (ImageFlow) to SinoFlow. Results: SinoFlow significantly improved flow estimation performance by avoiding propagating errors introduced by filtered backprojection. SinoFlow was robust across all tested gantry rotation speeds and consistently produced lower mean squared error and velocity errors than ImageFlow. Additionally, SinoFlow was compatible with pulsed-mode imaging and maintained higher accuracy with shorter pulse widths. Conclusions: This study demonstrates the potential of SinoFlow for CT-based flow estimation, providing a more promising approach for non-invasive blood flow assessment. The findings aim to inform future applications of PINNs to CT images and provide a solution for image-based estimation, with reasonable acquisition parameters yielding accurate flow estimates.

Paperid: 1220, https://arxiv.org/pdf/2511.01804.pdf

Abstract:
Blood flow is sensitive to disease and provides insight into cardiac function, making flow field analysis valuable for diagnosis. However, while safer than radiation-based imaging and more suitable for patients with medical implants, ultrasound suffers from attenuation with depth, limiting the quality of the image. Despite advances in echocardiographic particle image velocimetry (EchoPIV), accurately measuring blood velocity remains challenging due to the technique's limitations and the complexity of blood flow dynamics. Physics-informed machine learning can enhance accuracy and robustness, particularly in scenarios where noisy or incomplete data challenge purely data-driven approaches. We present a physics-informed neural field model with multi-scale Fourier Feature encoding for estimating blood flow from sparse and noisy ultrasound data without requiring ground truth supervision. We demonstrate that this model achieves consistently low mean squared error in denoising and inpainting both synthetic and real datasets, verified against reference flow fields and ground truth flow rate measurements. While physics-informed neural fields have been widely used to reconstruct medical images, applications to medical flow reconstruction are mostly prominent in Flow MRI. In this work, we adapt methods that have proven effective in other imaging modalities to address the specific challenge of ultrasound-based flow reconstruction.

Paperid: 1221, https://arxiv.org/pdf/2511.00428.pdf

Abstract:
The analysis of speech production based on physical models of the vocal folds and vocal tract is essential for studies on vocal-fold behavior and linguistic research. This paper proposes a speech production analysis method using physics-informed neural networks (PINNs). The networks are trained directly on the governing equations of vocal-fold vibration and vocal-tract acoustics. Vocal-fold collisions introduce nondifferentiability and vanishing gradients, challenging phenomena for PINNs. We demonstrate, however, that introducing a differentiable approximation function enables the analysis of vocal-fold vibrations within the PINN framework. The period of self-excited vocal-fold vibration is generally unknown. We show that by treating the period as a learnable network parameter, a periodic solution can be obtained. Furthermore, by implementing the coupling between glottal flow and vocal-tract acoustics as a hard constraint, glottis-tract interaction is achieved without additional loss terms. We confirmed the method's validity through forward and inverse analyses, demonstrating that the glottal flow rate, vocal-fold vibratory state, and subglottal pressure can be simultaneously estimated from speech signals. Notably, the same network architecture can be applied to both forward and inverse analyses, highlighting the versatility of this approach. The proposed method inherits the advantages of PINNs, including mesh-free computation and the natural incorporation of nonlinearities, and thus holds promise for a wide range of applications.

Paperid: 1222, https://arxiv.org/pdf/2511.00418.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration. This paper introduces a \emph{structure-preserving PINN} framework for the nonlinear Korteweg--de Vries (KdV) equation, a prototypical model for nonlinear and dispersive wave propagation. The proposed method embeds the conservation of mass and Hamiltonian energy directly into the loss function, ensuring physically consistent and energy-stable evolution throughout training and prediction. Unlike standard \texttt{tanh}-based PINNs~\cite{raissi2019pinn,wang2022modifiedpinn}, our approach employs sinusoidal activation functions that enhance spectral expressiveness and accurately capture the oscillatory and dispersive nature of KdV solitons. Through representative case studies -- including single-soliton propagation (shape-preserving translation), two-soliton interaction (elastic collision with phase shift), and cosine-pulse initialization (nonlinear dispersive breakup) -- the model successfully reproduces hallmark behaviors of KdV dynamics while maintaining conserved invariants. Ablation studies demonstrate that combining invariant-constrained optimization with sinusoidal feature mappings accelerates convergence, improves long-term stability, and mitigates drift without multi-stage pretraining. These results highlight that computationally efficient, invariant-aware regularization coupled with sinusoidal representations yields robust, energy-consistent PINNs for Hamiltonian partial differential equations such as the KdV equation.

Paperid: 1223, https://arxiv.org/pdf/2510.27018.pdf

Abstract:
Approximating the solutions of boundary value problems governed by partial differential equations with neural networks is challenging, largely due to the difficult training process. This difficulty can be partly explained by the spectral bias, that is, the slower convergence of high-frequency components, and can be mitigated by localizing neural networks via (overlapping) domain decomposition. We combine this localization with the Gauss-Newton method as the optimizer to obtain faster convergence than gradient-based schemes such as Adam; this comes at the cost of solving an ill-conditioned linear system in each iteration. Domain decomposition induces a block-sparse structure in the otherwise dense Gauss-Newton system, reducing the computational cost per iteration. Our numerical results indicate that combining localization and Gauss-Newton optimization is promising for neural network-based solvers for partial differential equations.

Paperid: 1224, https://arxiv.org/pdf/2510.26959.pdf

Abstract:
Integrated energy systems (IES) are complex heterogeneous architectures that typically encompass power sources, hydrogen electrolyzers, energy storage, and heat exchangers. This integration is achieved through operating control strategy optimization. However, the lack of physical understanding as to how these systems evolve over time introduces uncertainties that hinder reliable application thereof. Techniques that can accommodate such uncertainties are fundamental for ensuring proper operation of these systems. Unfortunately, no unifying methodology exists for accommodating uncertainties in this regard. That being said, adaptive control (AC) is a discipline that may allow for accommodating such uncertainties in real-time. In the present work, we derive an AC formulation for linear systems in which all states are observable and apply it to the control of a glycol heat exchanger (GHX) in an IES. Based on prior research in which we quantified the uncertainties of the GHXs system dynamics, we introduced an error of 50% on four terms of the nominal model. In the case where a linear quadratic regulator is used as the nominal control for the reference system, we found that employing AC can reduce the mean absolute error and integral time absolute error by a factor of 30%-75%. This reduction is achieved with minimal computing overhead and control infrastructure, thus underscoring the strength of AC. However, the control effort induced is significant, therefore warranting further study in order to estimate its impact on a physical system. To address further challenges, including partially observable and non-linear dynamics, enhancements of the linear formulation are currently being developed.

Paperid: 1225, https://arxiv.org/pdf/2510.26586.pdf

Abstract:
In this study, we leverage a mixture model learning approach to identify defects in laser-based Additive Manufacturing (AM) processes. By incorporating physics based principles, we also ensure that the model is sensitive to meaningful physical parameter variations. The empirical evaluation was conducted by analyzing real-world data from two AM processes: Directed Energy Deposition and Laser Powder Bed Fusion. In addition, we also studied the performance of the developed framework over public datasets with different alloy type and experimental parameter information. The results show the potential of physics-guided mixture models to examine the underlying physical behavior of an AM system.

Paperid: 1226, https://arxiv.org/pdf/2510.26121.pdf

Abstract:
Physics-informed machine learning (PIML) integrates prior physical information, often in the form of differential equation constraints, into the process of fitting machine learning models to physical data. Popular PIML approaches, including neural operators, physics-informed neural networks, neural ordinary differential equations, and neural discrete equilibria, are typically fit to objectives that simultaneously include both data and physical constraints. However, the multi-objective nature of this approach creates ambiguity in the measurement of model quality. This is related to a poor understanding of epistemic uncertainty, and it can lead to surprising failure modes, even when existing statistical metrics suggest strong fits. Working within a Gaussian process regression framework, we introduce the Physics-Informed Log Evidence (PILE) score. Bypassing the ambiguities of test losses, the PILE score is a single, uncertainty-aware metric that provides a selection principle for hyperparameters of a PIML model. We show that PILE minimization yields excellent choices for a wide variety of model parameters, including kernel bandwidth, least squares regularization weights, and even kernel function selection. We also show that, even prior to data acquisition, a special 'data-free' case of the PILE score identifies a priori kernel choices that are 'well-adapted' to a given PDE. Beyond the kernel setting, we anticipate that the PILE score can be extended to PIML at large, and we outline approaches to do so.

Paperid: 1227, https://arxiv.org/pdf/2508.15394.pdf

Abstract:
We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can be optimized using a least squares (LS) solve, and the remaining hidden layer parameters are updated by means of gradient descent form. However, building the LS system for all possible combinations of branch and trunk inputs yields a prohibitively large linear problem that is infeasible to solve directly. To address this issue, our method decomposes the large LS system into two smaller, more manageable subproblems $\unicode{x2014}$ one for the branch network and one for the trunk network $\unicode{x2014}$ and solves them separately. This method is generalized to a broader type of $L^2$ loss with a regularization term for the last layer parameters, including the case of unsupervised learning with physics-informed loss.

Paperid: 1228, https://arxiv.org/pdf/2508.14127.pdf

Abstract:
Designing shape memory alloys (SMAs) that meet performance targets while remaining affordable and sustainable is a complex challenge. In this work, we focus on optimizing SMA compositions to achieve a desired martensitic start temperature (Ms) while minimizing cost. To do this, we use machine learning models as surrogate predictors and apply numerical optimization methods to search for suitable alloy combinations. We trained two types of machine learning models, a tree-based ensemble and a neural network, using a dataset of experimentally characterized alloys and physics-informed features. The tree-based model was used with a derivative-free optimizer (COBYLA), while the neural network, which provides gradient information, was paired with a gradient-based optimizer (TRUST-CONSTR). Our results show that while both models predict Ms with similar accuracy, the optimizer paired with the neural network finds better solutions more consistently. COBYLA often converged to suboptimal results, especially when the starting guess was far from the target. The TRUST-CONSTR method showed more stable behavior and was better at reaching alloy compositions that met both objectives. This study demonstrates a practical approach to exploring new SMA compositions by combining physics-informed data, machine learning models, and optimization algorithms. Although the scale of our dataset is smaller than simulation-based efforts, the use of experimental data improves the reliability of the predictions. The approach can be extended to other materials where design trade-offs must be made with limited data.

Paperid: 1229, https://arxiv.org/pdf/2508.13559.pdf

Abstract:
Origami-inspired structures provide unprecedented opportunities for creating lightweight, deployable systems with programmable mechanical responses. However, their design remains challenging due to complex nonlinear mechanics, multistability, and the need for precise control of deployment forces. Here, we present a physics-informed neural network (PINN) framework for both forward prediction and inverse design of conical Kresling origami (CKO) without requiring pre-collected training data. By embedding mechanical equilibrium equations directly into the learning process, the model predicts complete energy landscapes with high accuracy while minimizing non-physical artifacts. The inverse design routine specifies both target stable-state heights and separating energy barriers, enabling freeform programming of the entire energy curve. This capability is extended to hierarchical CKO assemblies, where sequential layer-by-layer deployment is achieved through programmed barrier magnitudes. Finite element simulations and experiments on physical prototypes validate the designed deployment sequences and barrier ratios, confirming the robustness of the approach. This work establishes a versatile, data-free route for programming complex mechanical energy landscapes in origami-inspired metamaterials, offering broad potential for deployable aerospace systems, morphing structures, and soft robotic actuators.

Paperid: 1230, https://arxiv.org/pdf/2508.13216.pdf

Abstract:
Physics-informed neural networks approach the approximation of differential equations by directly incorporating their structure and given conditions in a loss function. This enables conditions like, e.g., invariants to be easily added during the modelling phase. In addition, the approach can be considered as mesh free and can be utilised to compute solutions on arbitrary grids after the training phase. Therefore, physics-informed neural networks are emerging as a promising alternative to solving differential equations with methods from numerical mathematics. However, their performance highly depends on a large variety of factors. In this paper, we systematically investigate and evaluate a core component of the approach, namely the training point distribution. We test two ordinary and two partial differential equations with five strategies for training data generation and shallow network architectures, with one and two hidden layers. In addition to common distributions, we introduce sine-based training points, which are motivated by the construction of Chebyshev nodes. The results are challenged by using certain parameter combinations like, e.g., random and fixed-seed weight initialisation for reproducibility. The results show the impact of the training point distributions on the solution accuracy and we find evidence that they are connected to the characteristics of the differential equation.

Paperid: 1231, https://arxiv.org/pdf/2508.11528.pdf

Abstract:
We propose an unsupervised anomaly detection approach based on a physics-informed diffusion model for multivariate time series data. Over the past years, diffusion model has demonstrated its effectiveness in forecasting, imputation, generation, and anomaly detection in the time series domain. In this paper, we present a new approach for learning the physics-dependent temporal distribution of multivariate time series data using a weighted physics-informed loss during diffusion model training. A weighted physics-informed loss is constructed using a static weight schedule. This approach enables a diffusion model to accurately approximate underlying data distribution, which can influence the unsupervised anomaly detection performance. Our experiments on synthetic and real-world datasets show that physics-informed training improves the F1 score in anomaly detection; it generates better data diversity and log-likelihood. Our model outperforms baseline approaches, additionally, it surpasses prior physics-informed work and purely data-driven diffusion models on a synthetic dataset and one real-world dataset while remaining competitive on others.

Paperid: 1232, https://arxiv.org/pdf/2508.08002.pdf

Abstract:
Traffic state estimation (TSE) falls methodologically into three categories: model-driven, data-driven, and model-data dual-driven. Model-driven TSE relies on macroscopic traffic flow models originated from hydrodynamics. Data-driven TSE leverages historical sensing data and employs statistical models or machine learning methods to infer traffic state. Model-data dual-driven traffic state estimation attempts to harness the strengths of both aspects to achieve more accurate TSE. From the perspective of mathematical operator theory, TSE can be viewed as a type of operator that maps available measurements of inerested traffic state into unmeasured traffic state variables in real time. For the first time this paper proposes to study real-time freeway TSE in the idea of physics-informed deep operator network (PI-DeepONet), which is an operator-oriented architecture embedding traffic flow models based on deep neural networks. The paper has developed an extended architecture from the original PI-DeepONet. The extended architecture is featured with: (1) the acceptance of 2-D data input so as to support CNN-based computations; (2) the introduction of a nonlinear expansion layer, an attention mechanism, and a MIMO mechanism; (3) dedicated neural network design for adaptive identification of traffic flow model parameters. A traffic state estimator built on the basis of this extended PI-DeepONet architecture was evaluated with respect to a short freeway stretch of NGSIM and a large-scale urban expressway in China, along with other four baseline TSE methods. The evaluation results demonstrated that this novel TSE method outperformed the baseline methods with high-precision estimation results of flow and mean speed.

Paperid: 1233, https://arxiv.org/pdf/2508.07546.pdf

Abstract:
In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate unknown functions, then substituting the MWNN into PDEs and training the MWNN by least-squares algorithm. We apply the proposed method to various problems, including stationary/nonstationary advection, diffusion and advection-diffusion problems, and linear/nonlinear time-dependent problems. Numerical experiments show that the PIMWNN method can achieve higher accuracy and faster speed than Physics Informed Neural Networks (PINNs). Moreover, the PIMWNN method, being mesh-free, can handle different boundary conditions easily and solve the time-dependent problems efficiently. The proposed method is expected to solve the spectral bias problem in network training. These characteristics show the great potential of the PIMWNN method used in the field of numerical solving methods for PDEs.

Paperid: 1234, https://arxiv.org/pdf/2508.04595.pdf

Abstract:
Resistance spot welding is the dominant joining process for the body-in-white in the automotive industry, where the weld nugget diameter is the key quality metric. Its measurement requires destructive testing, limiting the potential for efficient quality control. Physics-informed neural networks were investigated as a promising tool to reconstruct internal process states from experimental data, enabling model-based and non-invasive quality assessment in aluminum spot welding. A major challenge is the integration of real-world data into the network due to competing optimization objectives. To address this, we introduce two novel training strategies. First, experimental losses for dynamic displacement and nugget diameter are progressively included using a fading-in function to prevent excessive optimization conflicts. We also implement a custom learning rate scheduler and early stopping based on a rolling window to counteract premature reduction due to increased loss magnitudes. Second, we introduce a conditional update of temperature-dependent material parameters via a look-up table, activated only after a loss threshold is reached to ensure physically meaningful temperatures. An axially symmetric two-dimensional model was selected to represent the welding process accurately while maintaining computational efficiency. To reduce computational burden, the training strategies and model components were first systematically evaluated in one dimension, enabling controlled analysis of loss design and contact models. The two-dimensional network predicts dynamic displacement and nugget growth within the experimental confidence interval, supports transferring welding stages from steel to aluminum, and demonstrates strong potential for fast, model-based quality control in industrial applications.

Paperid: 1235, https://arxiv.org/pdf/2508.04198.pdf

Abstract:
In this paper, we propose a computational framework for the optimal design of broadband absorbing materials composed of plasmonic nanoparticle arrays. This design problem poses several key challenges: (1) the complex multi-particle interactions and high-curvature geometries; (2) the requirement to achieve broadband frequency responses, including resonant regimes; (3) the complexity of shape derivative calculations; and (4) the non-convexity of the optimization landscape. To systematically address these challenges, we employ three sequential strategies. First, we introduce a parameterized integral equation formulation that circumvents traditional shape derivative computations. Second, we develop a shape-adaptive reduced basis method (RBM) that utilizes the eigenfunctions of the Neumann-PoincarÃ© operator for forward problems and their adjoint counterparts for adjoint problems, thereby addressing singularities and accelerating computations. Third, we propose a physics-informed initialization strategy that estimates nanoparticle configurations under weak coupling assumptions, thereby improving the performance of gradient-based optimization algorithms. The method's computational advantages are demonstrated through numerical experiments, which show accurate and efficient designs across various geometric configurations. Furthermore, the framework is flexible and extensible to other material systems and boundary conditions.

Paperid: 1236, https://arxiv.org/pdf/2508.03278.pdf

Abstract:
High throughput experimentation tools, machine learning (ML) methods, and open material databases are radically changing the way new materials are discovered. From the experimentally driven approach in the past, we are moving quickly towards the artificial intelligence (AI) driven approach, realizing the 'inverse design' capabilities that allow the discovery of new materials given the desired properties. This review aims to discuss different principles of AI-driven generative models that are applicable for materials discovery, including different materials representations available for this purpose. We will also highlight specific applications of generative models in designing new catalysts, semiconductors, polymers, or crystals while addressing challenges such as data scarcity, computational cost, interpretability, synthesizability, and dataset biases. Emerging approaches to overcome limitations and integrate AI with experimental workflows will be discussed, including multimodal models, physics informed architectures, and closed-loop discovery systems. This review aims to provide insights for researchers aiming to harness AI's transformative potential in accelerating materials discovery for sustainability, healthcare, and energy innovation.

Paperid: 1237, https://arxiv.org/pdf/2508.01951.pdf

Abstract:
This paper introduces OptiGridML, a machine learning framework for discrete topology optimization in power grids. The task involves selecting substation breaker configurations that maximize cross-region power exports, a problem typically formulated as a mixed-integer program (MIP) that is NP-hard and computationally intractable for large networks. OptiGridML replaces repeated MIP solves with a two-stage neural architecture: a line-graph neural network (LGNN) that approximates DC power flows for a given network topology, and a heterogeneous GNN (HeteroGNN) that predicts breaker states under structural and physical constraints. A physics-informed consistency loss connects these components by enforcing Kirchhoff's law on predicted flows. Experiments on synthetic networks with up to 1,000 breakers show that OptiGridML achieves power export improvements of up to 18% over baseline topologies, while reducing inference time from hours to milliseconds. These results demonstrate the potential of structured, flow-aware GNNs for accelerating combinatorial optimization in physical networked systems.

Paperid: 1238, https://arxiv.org/pdf/2508.01314.pdf

Abstract:
The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like computer vision and natural language processing, obtaining such datasets for engineering applications is prohibitively expensive. Physics-Informed Neural Networks (PINNs), a branch of Physics-Informed Machine Learning (PIML), tackle this challenge by embedding physical principles within neural network architectures. PINNs have been extensively explored for solving diverse forward and inverse problems in fluid mechanics. Nonetheless, there is limited research on employing PINNs for flow reconstruction from sparse data under constrained computational resources. Earlier studies were focused on forward problems with well-defined data. The present study attempts to develop models capable of reconstructing the flow field data from sparse datasets mirroring real-world scenarios. This study focuses on two cases: (a) two-dimensional (2D) unsteady laminar flow past a circular cylinder and (b) three-dimensional (3D) unsteady turbulent flow past an ultra-large container ship (ULCS). The first case compares the effectiveness of training methods like Standard PINN and Backward Compatible PINN (BC-PINN) and explores the performance enhancements through systematic relaxation of physics constraints and dynamic weighting of loss function components. The second case highlights the capability of PINN-based models to learn underlying physics from sparse data while accurately reconstructing the flow field for a highly turbulent flow.

Paperid: 1239, https://arxiv.org/pdf/2508.00855.pdf

Abstract:
Nonlinear partial differential equations (PDEs) are pivotal in modeling complex physical systems, yet traditional Physics-Informed Neural Networks (PINNs) often struggle with unresolved residuals in critical spatiotemporal regions and violations of temporal causality. To address these limitations, we propose a novel Residual Guided Training strategy for Physics-Informed Transformer via Generative Adversarial Networks (GAN). Our framework integrates a decoder-only Transformer to inherently capture temporal correlations through autoregressive processing, coupled with a residual-aware GAN that dynamically identifies and prioritizes high-residual regions. By introducing a causal penalty term and an adaptive sampling mechanism, the method enforces temporal causality while refining accuracy in problematic domains. Extensive numerical experiments on the Allen-Cahn, Klein-Gordon, and Navier-Stokes equations demonstrate significant improvements, achieving relative MSE reductions of up to three orders of magnitude compared to baseline methods. This work bridges the gap between deep learning and physics-driven modeling, offering a robust solution for multiscale and time-dependent PDE systems.

Paperid: 1240, https://arxiv.org/pdf/2507.21437.pdf

Abstract:
Physics-informed neural networks and Physics-informed DeepONet excel in solving partial differential equations; however, they often fail to converge for singularly perturbed problems. To address this, we propose two novel frameworks, Prandtl-Van Dyke neural network (PVD-Net) and its operator learning extension Prandtl-Van Dyke Deep Operator Network (PVD-ONet), which rely solely on governing equations without data. To address varying task-specific requirements, both PVD-Net and PVD-ONet are developed in two distinct versions, tailored respectively for stability-focused and high-accuracy modeling. The leading-order PVD-Net adopts a two-network architecture combined with Prandtl's matching condition, targeting stability-prioritized scenarios. The high-order PVD-Net employs a five-network design with Van Dyke's matching principle to capture fine-scale boundary layer structures, making it ideal for high-accuracy scenarios. PVD-ONet generalizes PVD-Net to the operator learning setting by assembling multiple DeepONet modules, directly mapping initial conditions to solution operators and enabling instant predictions for an entire family of boundary layer problems without retraining. Numerical experiments on various models show that our proposed methods consistently outperform existing baselines under various error metrics, thereby offering a powerful new approach for multi-scale problems.

Paperid: 1241, https://arxiv.org/pdf/2507.19522.pdf

Abstract:
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of a network for a given input by optimizing weights and biases. An inverse problem finds equation parameters or coefficients that effectively model the data. A Physics-Informed Neural Network (PINN) can solve both problems. PINNs inject prior analytical information about the data into the cost function to improve model performance outside the training set boundaries. This also allows PINNs to efficiently solve problems with sparse data without overfitting by extrapolating the model to fit larger trends in the data. The prior information we implement is in the form of differential equations. Residuals are the differences between the left-hand and right-hand sides of corresponding differential equations; PINNs minimize these residuals to effectively solve the differential equation and take advantage of prior knowledge. In this way, the solution and parameters are embedded into the loss function and optimized, allowing both the weights of the neural network and the model parameters to be found simultaneously, solving both the forward and inverse problems in the process. In this paper, we will create PINNs with residuals of varying complexity, beginning with linear and quadratic models and then expanding to fit models for the heat equation and other complex differential equations. We will mainly use Python as the computing language, using the PyTorch library to aid us in our research.

Paperid: 1242, https://arxiv.org/pdf/2507.18731.pdf

Abstract:
Phase-field equations, mostly solved numerically, are known for capturing the mesoscale microstructural evolution of a material. However, such numerical solvers are computationally expensive as it needs to generate fine mesh systems to solve the complex Partial Differential Equations(PDEs) with good accuracy. Therefore, we propose an alternative approach of predicting the microstructural evolution subjected to periodic boundary conditions using Physics informed Neural Operators (PINOs). In this study, we have demonstrated the capability of PINO to predict the growth of $Î¸^{\prime}$ precipitates in Al-Cu alloys by learning the operator as well as by solving three coupled physics equations simultaneously. The coupling is of two second-order Allen-Cahn equation and one fourth-order Cahn-Hilliard equation. We also found that using Fourier derivatives(pseudo-spectral method and Fourier extension) instead of Finite Difference Method improved the Cahn-Hilliard equation loss by twelve orders of magnitude. Moreover, since differentiation is equivalent to multiplication in the Fourier domain, unlike Physics informed Neural Networks(PINNs), we can easily compute the fourth derivative of Cahn-Hilliard equation without converting it to coupled second order derivative.

Paperid: 1243, https://arxiv.org/pdf/2507.16571.pdf

Abstract:
We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid methodologies to unstructured meshes through a modified DeepONet architecture that incorporates local geometry in the neural network. The architecture employs local mesh topology to ensure rotation invariance, while also ensuring first-order constraint on the learned operator. The training methodology incorporates physics-informed regularization through entropy penalization, total variation diminishing penalization, and parameter regularization to ensure physically consistent solutions, particularly in shock-dominated regions. The model is trained on high-fidelity datasets solutions derived from sine waves and randomized piecewise constant initial conditions with periodic boundary conditions, enabling robust generalization to complex flow configurations or geometries. Validation test cases from the literature, including challenging geometry configuration, demonstrates substantial improvements in accuracy compared to traditional second-order finite volume schemes. The method achieves gains of 20-60% in solution accuracy while enhancing computational efficiency. A convergence study has been conveyed and reveal improved mesh convergence rates compared to the conventional solver. The proposed algorithm is faster and more accurate than the traditional second-order finite volume solver, enabling high-fidelity simulations on coarser grids while preserving the stability and conservation properties essential for hyperbolic conservation laws. This work is a part of a new generation of solvers that are built by combining Machine-Learning (ML) tools with traditional numerical schemes, all while ensuring physical constraint on the results.

Paperid: 1244, https://arxiv.org/pdf/2507.16380.pdf

Abstract:
This work focuses on the behavior of stochastic gradient descent (SGD) in solving least-squares regression with physics-informed neural networks (PINNs). Past work on this topic has been based on the over-parameterization regime, whose convergence may require the network width to increase vastly with the number of training samples. So, the theory derived from over-parameterization may incur prohibitive computational costs and is far from practical experiments. We perform new optimization and generalization analysis for SGD in training two-layer PINNs, making certain assumptions about the target function to avoid over-parameterization. Given $Îµ>0$, we show that if the network width exceeds a threshold that depends only on $Îµ$ and the problem, then the training loss and expected loss will decrease below $O(Îµ)$.

Paperid: 1245, https://arxiv.org/pdf/2507.15455.pdf

Abstract:
We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic differential games and robust control. The method alternates between solving linear second-order PDEs under fixed feedback policies and updating the controls via pointwise minimax optimization using automatic differentiation. Under standard Lipschitz and uniform ellipticity assumptions, we prove that the value function iterates converge locally uniformly to the unique viscosity solution of the HJI equation. The analysis establishes equi-Lipschitz regularity of the iterates, enabling provable stability and convergence without requiring convexity of the Hamiltonian. Numerical experiments demonstrate the accuracy and scalability of the method. In a two-dimensional stochastic path-planning game with a moving obstacle, our method matches finite-difference benchmarks with relative $L^2$-errors below %10^{-2}%. In five- and ten-dimensional publisher-subscriber differential games with anisotropic noise, the proposed approach consistently outperforms direct PINN solvers, yielding smoother value functions and lower residuals. Our results suggest that integrating PINNs with policy iteration is a practical and theoretically grounded method for solving high-dimensional, nonconvex HJI equations, with potential applications in robotics, finance, and multi-agent reinforcement learning.

Paperid: 1246, https://arxiv.org/pdf/2507.15021.pdf

Abstract:
Coastal communities increasingly face compound floods, where multiple drivers like storm surge, high tide, heavy rainfall, and river discharge occur together or in sequence to produce impacts far greater than any single driver alone. Traditional hydrodynamic models can provide accurate physics-based simulations but require substantial computational resources for real-time applications or risk assessments, while machine learning alternatives often sacrifice physical consistency for speed, producing unrealistic predictions during extreme events. This study addresses these challenges by developing ALPINE (All-in-one Physics Informed Neural Emulator), a physics-informed neural network (PINN) framework to enforce complete shallow water dynamics in compound flood modeling. Unlike previous approaches that implement partial constraints, our framework simultaneously enforces mass conservation and both momentum equations, ensuring full adherence to Newton's laws throughout the prediction process. The model integrates a convolutional encoder-decoder architecture with ConvLSTM temporal processing, trained using a composite loss function that balances data fidelity with physics-based residuals. Using six historical storm events (four for training, one for validation, and one held-out for unseen testing), we observe substantial improvements over baseline neural networks. ALPINE reduces domain-averaged prediction errors and improves model skill metrics for water surface elevation and velocity components. Physics-informed constraints prove most valuable during peak storm intensity, when multiple flood drivers interact and reliable predictions matter most. This approach yields a physically consistent emulator capable of supporting compound-flood forecasting and large-scale risk analyses while preserving physical realism essential for coastal emergency management.

Paperid: 1247, https://arxiv.org/pdf/2507.13542.pdf

Abstract:
Traditional echocardiographic parameters such as ejection fraction (EF) and global longitudinal strain (GLS) have limitations in the early detection of cardiac dysfunction. EF often remains normal despite underlying pathology, and GLS is influenced by load conditions and vendor variability. There is a growing need for reproducible, interpretable, and operator-independent parameters that capture subtle and global cardiac functional alterations. We introduce the Acoustic Index, a novel AI-derived echocardiographic parameter designed to quantify cardiac dysfunction from standard ultrasound views. The model combines Extended Dynamic Mode Decomposition (EDMD) based on Koopman operator theory with a hybrid neural network that incorporates clinical metadata. Spatiotemporal dynamics are extracted from echocardiographic sequences to identify coherent motion patterns. These are weighted via attention mechanisms and fused with clinical data using manifold learning, resulting in a continuous score from 0 (low risk) to 1 (high risk). In a prospective cohort of 736 patients, encompassing various cardiac pathologies and normal controls, the Acoustic Index achieved an area under the curve (AUC) of 0.89 in an independent test set. Cross-validation across five folds confirmed the robustness of the model, showing that both sensitivity and specificity exceeded 0.8 when evaluated on independent data. Threshold-based analysis demonstrated stable trade-offs between sensitivity and specificity, with optimal discrimination near this threshold. The Acoustic Index represents a physics-informed, interpretable AI biomarker for cardiac function. It shows promise as a scalable, vendor-independent tool for early detection, triage, and longitudinal monitoring. Future directions include external validation, longitudinal studies, and adaptation to disease-specific classifiers.

Paperid: 1248, https://arxiv.org/pdf/2507.13376.pdf

Abstract:
Physics-guided approaches offer a promising path toward accurate and generalisable impact identification in composite structures, especially when experimental data are sparse. This paper presents a hybrid framework for impact localisation and force estimation in composite plates, combining a data-driven implementation of First-Order Shear Deformation Theory (FSDT) with machine learning and uncertainty quantification. The structural configuration and material properties are inferred from dispersion relations, while boundary conditions are identified via modal characteristics to construct a low-fidelity but physically consistent FSDT model. This model enables physics-informed data augmentation for extrapolative localisation using supervised learning. Simultaneously, an adaptive regularisation scheme derived from the same model improves the robustness of impact force reconstruction. The framework also accounts for uncertainty by propagating localisation uncertainty through the force estimation process, producing probabilistic outputs. Validation on composite plate experiments confirms the framework's accuracy, robustness, and efficiency in reducing dependence on large training datasets. The proposed method offers a scalable and transferable solution for impact monitoring and structural health management in composite aerostructures.

Paperid: 1249, https://arxiv.org/pdf/2507.12600.pdf

Abstract:
Simulating hair dynamics that generalize across arbitrary hairstyles, body shapes, and motions is a critical challenge. Our novel two-stage neural solution is the first to leverage Transformer-based architectures for such a broad generalization. We propose a Transformer-powered static network that predicts static draped shapes for any hairstyle, effectively resolving hair-body penetrations and preserving hair fidelity. Subsequently, a dynamic network with a novel cross-attention mechanism fuses static hair features with kinematic input to generate expressive dynamics and complex secondary motions. This dynamic network also allows for efficient fine-tuning of challenging motion sequences, such as abrupt head movements. Our method offers real-time inference for both static single-frame drapes and dynamic drapes over pose sequences. Our method demonstrates high-fidelity and generalizable dynamic hair across various styles, guided by physics-informed losses, and can resolve penetrations even for complex, unseen long hairstyles, highlighting its broad generalization.

Paperid: 1250, https://arxiv.org/pdf/2507.10983.pdf

Abstract:
Semiconductor manufacturing relies heavily on film deposition processes, such as Chemical Vapor Deposition and Physical Vapor Deposition. These complex processes require precise control to achieve film uniformity, proper adhesion, and desired functionality. Recent advancements in Physics-Informed Neural Networks (PINNs), an innovative machine learning (ML) approach, have shown significant promise in addressing challenges related to process control, quality assurance, and predictive modeling within semiconductor film deposition and other manufacturing domains. This paper provides a comprehensive review of ML applications targeted at semiconductor film deposition processes. Through a thematic analysis, we identify key trends, existing limitations, and research gaps, offering insights into both the advantages and constraints of current methodologies. Our structured analysis aims to highlight the potential integration of these ML techniques to enhance interpretability, accuracy, and robustness in film deposition processes. Additionally, we examine state-of-the-art PINN methods, discussing strategies for embedding physical knowledge, governing laws, and partial differential equations into advanced neural network architectures tailored for semiconductor manufacturing. Based on this detailed review, we propose novel research directions that integrate the strengths of PINNs to significantly advance film deposition processes. The contributions of this study include establishing a clear pathway for future research in integrating physics-informed ML frameworks, addressing existing methodological gaps, and ultimately improving precision, scalability, and operational efficiency within semiconductor manufacturing.

Paperid: 1251, https://arxiv.org/pdf/2507.09766.pdf

Abstract:
Accurate estimation of Remaining Useful Life (RUL) and State of Health (SOH) is essential for Prognostics and Health Management (PHM) across a wide range of industrial applications. We propose a novel framework -- Reinforced Graph-Based Physics-Informed Neural Networks Enhanced with Dynamic Weights (RGPD) -- that combines physics-based supervision with advanced spatio-temporal learning. Graph Convolutional Recurrent Networks (GCRNs) embed graph-convolutional filters within recurrent units to capture how node representations evolve over time. Graph Attention Convolution (GATConv) leverages a self-attention mechanism to compute learnable, edge-wise attention coefficients, dynamically weighting neighbor contributions for adaptive spatial aggregation. A Soft Actor-Critic (SAC) module is positioned between the Temporal Attention Unit (TAU) and GCRN to further improve the spatio-temporal learning. This module improves attention and prediction accuracy by dynamically scaling hidden representations to minimize noise and highlight informative features. To identify the most relevant physical constraints in each area, Q-learning agents dynamically assign weights to physics-informed loss terms, improving generalization across real-time industrial systems and reducing the need for manual tuning. In both RUL and SOH estimation tasks, the proposed method consistently outperforms state-of-the-art models, demonstrating strong robustness and predictive accuracy across varied degradation patterns across three diverse industrial benchmark datasets.

Paperid: 1252, https://arxiv.org/pdf/2507.09591.pdf

Abstract:
Wire-arc directed energy deposition (DED) has emerged as a promising additive manufacturing (AM) technology for large-scale structural engineering applications. However, the complex thermal dynamics inherent to the process present challenges in ensuring structural integrity and mechanical properties of fabricated thick walls and plates. While finite element method (FEM) simulations have been conventionally employed to predict thermal history during deposition, their computational demand remains prohibitively high for actual large-scale applications. Given the necessity of multiple repetitive simulations for heat management and the determination of an optimal printing strategy, FEM simulation quickly becomes entirely infeasible. Instead, advancements have been made in using trained neural networks as surrogate models for rapid prediction. However, traditional data-driven approaches necessitate large amounts of relevant and verifiable external data, during the training and validation of the neural network. Regarding large-scale wire-arc DED, none of these data sources are readily available in quantities sufficient for an accurate surrogate. The introduction of physics-informed neural networks (PINNs) has opened up an alternative simulation strategy by leveraging the existing physical knowledge of the phenomena with advanced machine learning methods. Despite their theoretical advantages, PINNs have seen limited application in the context of large-scale wire-arc DED for structural engineering. This study investigates the scalability of PINNs, focusing on efficient collocation points sampling, a critical factor controlling both the training time and model performance. Results show PINNs can reduce computational time and effort by up to 98.6%, while maintaining the desired accuracy and offering "super-resolution". Future directions for enhancing PINN performance in metal AM are discussed.

Paperid: 1253, https://arxiv.org/pdf/2507.06967.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are increasingly used to approximate solutions of partial differential equations (PDEs), especially in high dimensions. In real-world applications, data samples are noisy, so it is important to know when a predictor can still achieve low empirical risk. However, little is known about the conditions under which a PINN can do so effectively. We prove a lower bound on the size of neural networks required for the supervised PINN empirical risk to fall below the variance of noisy supervision labels. Specifically, if a predictor achieves an empirical risk $O(Î·)$ below $Ï^2$ (variance of supervision data), then necessarily $d_N\log d_N\gtrsim N_s Î·^2$, where $N_s$ is the number of samples and $d_N$ is the number of trainable parameters of the PINN. A similar constraint applies to the fully unsupervised PINN setting when boundary labels are sampled noisily. Consequently, increasing the number of noisy supervision labels alone does not provide a ``free lunch'' in reducing empirical risk. We also show empirically that PINNs can indeed achieve empirical risks below $Ï^2$ under such conditions. As a case study, we investigate PINNs applied to the Hamilton--Jacobi--Bellman (HJB) PDE. Our findings lay the groundwork for quantitatively understanding the parameter requirements for training PINNs in the presence of noise.

Paperid: 1254, https://arxiv.org/pdf/2507.05291.pdf

Abstract:
We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress values. This method is based in representing a periodic micro-structure as a graph, combined with a message passing graph neural network. We are able to retrieve local stress field distributions, providing average stress values produced by a mean field reduced order model (ROM) or Finite Element (FE) simulation at the macro-scale. The prediction of local stress fields are of utmost importance considering fracture analysis or the definition of local fatigue criteria. Our model incorporates physical constraints during training to constraint local stress field equilibrium state and employs a periodic graph representation to enforce periodic boundary conditions. The benefits of the proposed physics-informed GNN are evaluated considering linear and non linear hyperelastic responses applied to varying geometries. In the non-linear hyperelastic case, the proposed method achieves significant computational speed-ups compared to FE simulation, making it particularly attractive for large-scale applications.

Paperid: 1255, https://arxiv.org/pdf/2507.04153.pdf

Abstract:
Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from a mask are presented. A novel hybrid Waveguide Neural Operator (WGNO) is introduced, which is based on a waveguide method with its most computationally expensive part replaced by a neural network. Numerical experiments on realistic 2D and 3D masks show that the WGNO achieves state-of-the-art accuracy and inference time, providing a highly efficient solution for accelerating the design workflows of lithography masks.

Paperid: 1256, https://arxiv.org/pdf/2507.01047.pdf

Abstract:
While digital twins (DT) hold promise for providing real-time insights into complex energy assets, much of the current literature either does not offer a clear framework for information exchange between the model and the asset, lacks key features needed for real-time implementation, or gives limited attention to model uncertainty. Here, we aim to solve these gaps by proposing a variational digital twin (VDT) framework that augments standard neural architectures with a single Bayesian output layer. This lightweight addition, along with a novel VDT updating algorithm, lets a twin update in seconds on commodity GPUs while producing calibrated uncertainty bounds that can inform experiment design, control algorithms, and model reliability. The VDT is evaluated on four energy-sector problems. For critical-heat-flux prediction, uncertainty-driven active learning reaches R2 = 0.98 using 47 % fewer experiments and one-third the training time of random sampling. A three-year renewable-generation twin maintains R2 > 0.95 for solar output and curbs error growth for volatile wind forecasts via monthly updates that process only one month of data at a time. A nuclear reactor transient cooldown twin reconstructs thermocouple signals with R2 > 0.99 and preserves accuracy after 50 % sensor loss, demonstrating robustness to degraded instrumentation. Finally, a physics-informed Li-ion battery twin, retrained after every ten discharges, lowers voltage mean-squared error by an order of magnitude relative to the best static model while adapting its credible intervals as the cell approaches end-of-life. These results demonstrate that combining modest Bayesian augmentation with efficient update schemes turns conventional surrogates into uncertainty-aware, data-efficient, and computationally tractable DTs, paving the way for dependable models across industrial and scientific energy systems.

Paperid: 1257, https://arxiv.org/pdf/2507.00816.pdf

Abstract:
Accurate dynamics modeling is essential for quadrotors to achieve precise trajectory tracking in various applications. Traditional physical knowledge-driven modeling methods face substantial limitations in unknown environments characterized by variable payloads, wind disturbances, and external perturbations. On the other hand, data-driven modeling methods suffer from poor generalization when handling out-of-distribution (OoD) data, restricting their effectiveness in unknown scenarios. To address these challenges, we introduce the Physics-Informed Wind-Adaptive Network (PI-WAN), which combines knowledge-driven and data-driven modeling methods by embedding physical constraints directly into the training process for robust quadrotor dynamics learning. Specifically, PI-WAN employs a Temporal Convolutional Network (TCN) architecture that efficiently captures temporal dependencies from historical flight data, while a physics-informed loss function applies physical principles to improve model generalization and robustness across previously unseen conditions. By incorporating real-time prediction results into a model predictive control (MPC) framework, we achieve improvements in closed-loop tracking performance. Comprehensive simulations and real-world flight experiments demonstrate that our approach outperforms baseline methods in terms of prediction accuracy, tracking precision, and robustness to unknown environments.

Paperid: 1258, https://arxiv.org/pdf/2506.22437.pdf

Abstract:
Accurate image alignment is essential for monitoring crack evolution in structural health monitoring (SHM), particularly under real-world conditions involving perspective distortion, occlusion, and low contrast. However, traditional feature detectors such as SIFT and SURF, which rely on Gaussian-based scale spaces, tend to suppress high-frequency edges, making them unsuitable for thin crack localization. Lightweight binary alternatives like ORB and BRISK, while computationally efficient, often suffer from poor keypoint repeatability on textured or shadowed surfaces. This study presents a physics-informed alignment framework that adapts the open KAZE architecture to SHM-specific challenges. By utilizing nonlinear anisotropic diffusion to construct a crack-preserving scale space, and integrating RANSAC-based homography estimation, the framework enables accurate geometric correction without the need for training, parameter tuning, or prior calibration. The method is validated on time-lapse images of masonry and concrete acquired via handheld smartphone under varied field conditions, including shadow interference, cropping, oblique viewing angles, and surface clutter. Compared to classical detectors, the proposed framework reduces crack area and spine length errors by up to 70 percent and 90 percent, respectively, while maintaining sub-5 percent alignment error in key metrics. Unsupervised, interpretable, and computationally lightweight, this approach supports scalable deployment via UAVs and mobile platforms. By tailoring nonlinear scale-space modeling to SHM image alignment, this work offers a robust and physically grounded alternative to conventional techniques for tracking real-world crack evolution.

Paperid: 1259, https://arxiv.org/pdf/2506.22413.pdf

Abstract:
In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture shocks and other discontinuities in compressible flows. Conversely, utilizing non-conservative forms often introduces significant errors near these discontinuities or results in smeared shocks. This dependency poses a considerable limitation, particularly as many PDEs encountered in complex physical phenomena, such as multi-phase flows, are inherently non-conservative. This inherent non-conservativity restricts the direct applicability of standard numerical solvers designed for conservative forms. This work aims to thoroughly investigate the sensitivity of Physics-Informed Neural Networks (PINNs) to the choice of PDE formulation (conservative vs. non-conservative) when solving problems involving shocks and discontinuities. We have conducted this investigation across a range of benchmark problems, specifically the Burgers equation and both steady and unsteady Euler equations, to provide a comprehensive understanding of PINNs capabilities in this critical area.

Paperid: 1260, https://arxiv.org/pdf/2506.21952.pdf

Abstract:
Distributed acoustic sensing (DAS) has attracted considerable attention across various fields and artificial intelligence (AI) technology plays an important role in DAS applications to realize event recognition and denoising. Existing AI models require real-world data (RWD), whether labeled or not, for training, which is contradictory to the fact of limited available event data in real-world scenarios. Here, a physics-informed DAS neural network paradigm is proposed, which does not need real-world events data for training. By physically modeling target events and the constraints of real world and DAS system, physical functions are derived to train a generative network for generation of DAS events data. DAS debackground net is trained by using the generated DAS events data to eliminate background noise in DAS data. The effectiveness of the proposed paradigm is verified in event identification application based on a public dataset of DAS spatiotemporal data and in belt conveyor fault monitoring application based on DAS time-frequency data, and achieved comparable or better performance than data-driven networks trained with RWD. Owing to the introduction of physical information and capability of background noise removal, the paradigm demonstrates generalization in same application on different sites. A fault diagnosis accuracy of 91.8% is achieved in belt conveyor field with networks which transferred from simulation test site without any fault events data of test site and field for training. The proposed paradigm is a prospective solution to address significant obstacles of data acquisition and intense noise in practical DAS applications and explore more potential fields for DAS.

Paperid: 1261, https://arxiv.org/pdf/2506.19178.pdf

Abstract:
The growing reliance on power electronics introduces new challenges requiring detailed time-domain analyses with fast and accurate circuit simulation tools. Currently, commercial time-domain simulation software are mainly relying on physics-based methods to simulate power electronics. Recent work showed that data-driven and physics-informed learning methods can increase simulation speed with limited compromise on accuracy, but many challenges remain before deployment in commercial tools can be possible. In this paper, we propose a physics-informed bidirectional long-short term memory neural network (BiLSTM-PINN) model to simulate the time-domain response of a closed-loop dc-dc boost converter for various operating points, parameters, and perturbations. A physics-informed fully-connected neural network (FCNN) and a BiLSTM are also trained to establish a comparison. The three methods are then compared using step-response tests to assess their performance and limitations in terms of accuracy. The results show that the BiLSTM-PINN and BiLSTM models outperform the FCNN model by more than 9 and 4.5 times, respectively, in terms of median RMSE. Their standard deviation values are more than 2.6 and 1.7 smaller than the FCNN's, making them also more consistent. Those results illustrate that the proposed BiLSTM-PINN is a potential alternative to other physics-based or data-driven methods for power electronics simulations.

Paperid: 1262, https://arxiv.org/pdf/2506.17726.pdf

Abstract:
In this paper, the physics informed neural networks (PINNs) is employed for the numerical simulation of heat transfer involving a moving source. To reduce the computational effort, a new training method is proposed that uses a continuous time-stepping through transfer learning. Within this, the time interval is divided into smaller intervals and a single network is initialized. On this single network each time interval is trained with the initial condition for (n+1)th as the solution obtained at nth time increment. Thus, this framework enables the computation of large temporal intervals without increasing the complexity of the network itself. The proposed framework is used to estimate the temperature distribution in a homogeneous medium with a moving heat source. The results from the proposed framework is compared with traditional finite element method and a good agreement is seen.

Paperid: 1263, https://arxiv.org/pdf/2506.13369.pdf

Abstract:
We present a dual-guided framework for reconstructing unsteady incompressible flow fields using sparse observations. The approach combines optimized sensor placement with a physics-informed guided generative model. Sensor locations are selected using mutual information theory applied to a reduced-order model of the flow, enabling efficient identification of high-information observation points with minimal computational cost. These sensors, once selected, provide targeted observations that guide a denoising diffusion probabilistic model conditioned by physical constraints. Extensive experiments on 2D laminar cylinder wake flows demonstrate that under sparse sensing conditions, the structured sensor layouts fail to capture key flow dynamics, yielding high reconstruction errors. In contrast, our optimized sensor placement strategy achieves accurate reconstructions with L2 errors as low as 0.05, even with a limited number of sensors, confirming the effectiveness of the proposed approach in data-limited regimes. When the number of sensors is higher than a threshold, however, both methods perform comparably. Our dual-guided approach bridges reduced order model-based sensor position optimization with modern generative modeling, providing accurate, physics-consistent reconstruction from sparse data for scientific machine-learning problems.

Paperid: 1264, https://arxiv.org/pdf/2506.12922.pdf

Abstract:
In this work, a physics-informed neural networks (PINNs) based algorithm is used for simulation of nonlinear 1D and 2D Burgers' type models. This scheme relies on a neural network built to approximate the problem solution and use a trial function that meets the initial data and boundary criteria. First of all, a brief mathematical formulation of the problem and the structure of PINNs, including the neural network architecture, loss construction, and training methodology is described. Finally, the algorithm is demonstrated with five test problems involving variations of the 1D coupled, 2D single and 2D coupled Burgers' models. We compare the PINN-based solutions with exact results to assess accuracy and convergence of the developed algorithm. The results demonstrate that PINNs may faithfully replicate nonlinear PDE solutions and offer competitive performance in terms of inaccuracy and flexibility. This work demonstrates the potential of PINNs as a reliable approach to solving complex time-dependent PDEs.

Paperid: 1265, https://arxiv.org/pdf/2506.11625.pdf

Abstract:
The relative balance between physics and data within any physics-informed machine learner is an important modelling consideration to ensure that the benefits of both physics and data-based approaches are maximised. An over reliance on physical knowledge can be detrimental, particularly when the physics-based component of a model may not accurately represent the true underlying system. An underutilisation of physical knowledge potentially wastes a valuable resource, along with benefits in model interpretability and reduced demand for expensive data collection. Achieving an optimal physics-data balance is a challenging aspect of model design, particularly if the level varies through time; for example, one might have a physical approximation, only valid within particular regimes, or a physical phenomenon may be known to only occur when given conditions are met (e.g. at high temperatures). This paper develops novel, physically-informed, change-point kernels for Gaussian processes, capable of dynamically varying the reliance upon available physical knowledge. A high level of control is granted to a user, allowing for the definition of conditions in which they believe a phenomena should occur and the rate at which the knowledge should be phased in and out of a model. In circumstances where users may be less certain, the switching reliance upon physical knowledge may be automatically learned and recovered from the model in an interpretable and intuitive manner. Variation of the modelled noise based on the physical phenomena occurring is also implemented to provide a more representative capture of uncertainty alongside predictions. The capabilities of the new kernel structures are explored through the use of two engineering case studies: the directional wind loading of a cable-stayed bridge and the prediction of aircraft wing strain during in-flight manoeuvring.

Paperid: 1266, https://arxiv.org/pdf/2506.11395.pdf

Abstract:
Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the time-harmonic wave field using the Helmholtz equation. Compared to existing numerical models, the physics-informed neural networks forward problem has to overcome several topics related to the convergence of the optimization toward the "true" solution. The topics reach from considering the physical dimensionality (from 2D to 3D), the modeling of realistic sources (from a self-similar source to a realistic confined point source), the modeling of sound-hard (Neumann) boundary conditions, and the modeling of the full wave field by considering the complex solution quantities. Within this contribution, we study 3D room acoustic cases at low frequency, varying the source definition and the number of boundary condition sets and using a complex speed of sound model to account for some degree of absorption. We assess the convergence behavior by looking at the loss landscape of the PINN architecture, the $L^2$ error compared to a finite element reference simulation for each network architecture and configuration. The convergence studies showed that at least six training points per wavelength are necessary for accurate training and subsequent predictions of the PINN. The developments are part of an initiative aiming to model the low-frequency behavior of room acoustics, including absorbers.

Paperid: 1267, https://arxiv.org/pdf/2506.07929.pdf

Abstract:
Accurate driving cycle construction is crucial for vehicle design, fuel economy analysis, and environmental impact assessments. A generative Physics-Informed Expected SARSA-Monte Carlo (PIESMC) approach that constructs representative driving cycles by capturing transient dynamics, acceleration, deceleration, idling, and road grade transitions while ensuring model fidelity is introduced. Leveraging a physics-informed reinforcement learning framework with Monte Carlo sampling, PIESMC delivers efficient cycle construction with reduced computational cost. Experimental evaluations on two real-world datasets demonstrate that PIESMC replicates key kinematic and energy metrics, achieving up to a 57.3% reduction in cumulative kinematic fragment errors compared to the Micro-trip-based (MTB) method and a 10.5% reduction relative to the Markov-chain-based (MCB) method. Moreover, it is nearly an order of magnitude faster than conventional techniques. Analyses of vehicle-specific power distributions and wavelet-transformed frequency content further confirm its ability to reproduce experimental central tendencies and variability.

Paperid: 1268, https://arxiv.org/pdf/2506.06300.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a powerful meshless tool for topology optimization, capable of simultaneously determining optimal topologies and physical solutions. However, conventional PINNs rely on density-based topology descriptions, which necessitate manual interpolation and limit their applicability to complex geometries. To address this, we propose Lagrangian topology-conscious PINNs (LT-PINNs), a novel framework for boundary-focused engineering optimization. By parameterizing the control variables of topology boundary curves as learnable parameters, LT-PINNs eliminate the need for manual interpolation and enable precise boundary determination. We further introduce specialized boundary condition loss function and topology loss function to ensure sharp and accurate boundary representations, even for intricate topologies. The accuracy and robustness of LT-PINNs are validated via two types of partial differential equations (PDEs), including elastic equation with Dirichlet boundary conditions and Laplace's equation with Neumann boundary conditions. Furthermore, we demonstrate effectiveness of LT-PINNs on more complex time-dependent and time-independent flow problems without relying on measurement data, and showcase their engineering application potential in flow velocity rearrangement, transforming a uniform upstream velocity into a sine-shaped downstream profile. The results demonstrate (1) LT-PINNs achieve substantial reductions in relative L2 errors compared with the state-of-art density topology-oriented PINNs (DT-PINNs), (2) LT-PINNs can handle arbitrary boundary conditions, making them suitable for a wide range of PDEs, and (3) LT-PINNs can infer clear topology boundaries without manual interpolation, especially for complex topologies.

Paperid: 1269, https://arxiv.org/pdf/2506.05918.pdf

Abstract:
Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws directly into the training of neural networks. However, when dealing with complex problems, the accuracy of PINNs still has room for improvement. To address this issue, we introduce the Over-PINNs framework, which leverages automatic differentiation (AD) to generate higher-order auxiliary equations that impose additional physical constraints. These equations are incorporated as extra loss terms in the training process, effectively enhancing the model's ability to capture physical information through an "overdetermined" approach. Numerical results illustrate that this method exhibits strong versatility in solving various types of PDEs. It achieves a significant improvement in solution accuracy without incurring substantial additional computational costs.

Paperid: 1270, https://arxiv.org/pdf/2506.02168.pdf

Abstract:
A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that $f(x) \approx y$ for any $(x, y)$ drawn from the same distribution. Neural networks and kernel-based methods are commonly employed for this task due to their capacity for fast and parallel computation. The approximation capabilities, or expressive power, of these methods have been extensively studied over the past 35 years. In this paper, we will present examples of key ideas in this area found in the literature. We will discuss emerging trends in machine learning including the role of shallow/deep networks, approximation on manifolds, physics-informed neural surrogates, neural operators, and transformer architectures. Despite function approximation being a fundamental problem in machine learning, approximation theory does not play a central role in the theoretical foundations of the field. One unfortunate consequence of this disconnect is that it is often unclear how well trained models will generalize to unseen or unlabeled data. In this review, we examine some of the shortcomings of the current machine learning framework and explore the reasons for the gap between approximation theory and machine learning practice. We will then introduce our novel research to achieve function approximation on unknown manifolds without the need to learn specific manifold features, such as the eigen-decomposition of the Laplace-Beltrami operator or atlas construction. In many machine learning problems, particularly classification tasks, the labels $y_j$ are drawn from a finite set of values.

Paperid: 1271, https://arxiv.org/pdf/2505.22377.pdf

Abstract:
Fractional physics-informed neural networks (fPINNs) have been successfully introduced in [Pang, Lu and Karniadakis, SIAM J. Sci. Comput. 41 (2019) A2603-A2626], which observe relative errors of $10^{-3} \, \sim \, 10^{-4}$ for the subdiffusion equations. However their high-precision (multiprecision) numerical solution remains challenging, due to the limited regularity of the subdiffusion model caused by the nonlocal operator. To fill in the gap, we present the multistage fPINNs based on traditional multistage PINNs [Wang and Lai, J. Comput. Phys. 504 (2024) 112865]. Numerical experiments show that the relative errors improve to $10^{-7} \, \sim \, 10^{-8}$ for the subdiffusion equations on uniform or nouniform meshes.

Paperid: 1272, https://arxiv.org/pdf/2505.21723.pdf

Abstract:
In the era of AI, neural networks have become increasingly popular for modeling, inference, and prediction, largely due to their potential for universal approximation. With the proliferation of such deep learning models, a question arises: are leaner statistical methods still relevant? To shed insight on this question, we employ the mechanistic nonlinear ordinary differential equation (ODE) inverse problem as a testbed, using physics-informed neural network (PINN) as a representative of the deep learning paradigm and manifold-constrained Gaussian process inference (MAGI) as a representative of statistically principled methods. Through case studies involving the SEIR model from epidemiology and the Lorenz model from chaotic dynamics, we demonstrate that statistical methods are far from obsolete, especially when working with sparse and noisy observations. On tasks such as parameter inference and trajectory reconstruction, statistically principled methods consistently achieve lower bias and variance, while using far fewer parameters and requiring less hyperparameter tuning. Statistical methods can also decisively outperform deep learning models on out-of-sample future prediction, where the absence of relevant data often leads overparameterized models astray. Additionally, we find that statistically principled approaches are more robust to accumulation of numerical imprecision and can represent the underlying system more faithful to the true governing ODEs.

Paperid: 1273, https://arxiv.org/pdf/2505.21421.pdf

Abstract:
In compressible fluid flow, reconstructing shocks, discontinuities, rarefactions, and their interactions from sparse measurements is an important inverse problem with practical applications. Moreover, physics-informed machine learning has recently become an increasingly popular approach for performing reconstructions tasks. In this work we explore a machine learning recipe, known as GraphGPS, for reconstructing canonical compressible flows known as 3D Riemann problems from sparse observations, in a physics-informed manner. The GraphGPS framework combines the benefits of positional encodings, local message-passing of graphs, and global contextual awareness, and we explore the latter two components through an ablation study. Furthermore, we modify the aggregation step of message-passing such that it is aware of shocks and discontinuities, resulting in sharper reconstructions of these features. Additionally, we modify message-passing such that information flows strictly from known nodes only, which results in computational savings, better training convergence, and no degradation of reconstruction accuracy. We also show that the GraphGPS framework outperforms numerous machine learning benchmarks.

Paperid: 1274, https://arxiv.org/pdf/2505.20361.pdf

Abstract:
Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose Separation-Transfer Physics Informed Neural Networks (ST-PINNs) to address such problems. By sequentially resolving discontinuities from strong to weak and leveraging transfer learning during training, ST-PINNs significantly reduce the problem complexity and enhance solution accuracy. To the best of our knowledge, this is the first study to apply a PINNs-based approach to the two-dimensional unsteady planar shock refraction problem, offering new insights into the application of PINNs to complex shock-interface interactions. Numerical experiments demonstrate that ST-PINNs more accurately capture sharp discontinuities and substantially reduce solution errors in hydrodynamic problems involving multiple discontinuities.

Paperid: 1275, https://arxiv.org/pdf/2505.13501.pdf

Abstract:
The data-driven discovery of long-time macroscopic dynamics and thermodynamics of dissipative systems with particle fidelity is hampered by significant obstacles. These include the strong time-scale limitations inherent to particle simulations, the non-uniqueness of the thermodynamic potentials and operators from given macroscopic dynamics, and the need for efficient uncertainty quantification. This paper introduces Statistical-Physics Informed Epistemic Diffusion Models (SPIEDiff), a machine learning framework designed to overcome these limitations in the context of purely dissipative systems by leveraging statistical physics, conditional diffusion models, and epinets. We evaluate the proposed framework on stochastic Arrhenius particle processes and demonstrate that SPIEDiff can accurately uncover both thermodynamics and kinetics, while enabling reliable long-time macroscopic predictions using only short-time particle simulation data. SPIEDiff can deliver accurate predictions with quantified uncertainty in minutes, drastically reducing the computational demand compared to direct particle simulations, which would take days or years in the examples considered. Overall, SPIEDiff offers a robust and trustworthy pathway for the data-driven discovery of thermodynamic models.

Paperid: 1276, https://arxiv.org/pdf/2505.12557.pdf

Abstract:
This study investigates the application of Physics-Informed Neural Networks (PINNs) to inverse problems in acoustic tube analysis, focusing on reconstructing acoustic fields from noisy and limited observation data. Specifically, we address scenarios where the radiation model is unknown, and pressure data is only available at the tube's radiation end. A PINNs framework is proposed to reconstruct the acoustic field, along with the PINN Fine-Tuning Method (PINN-FTM) and a traditional optimization method (TOM) for predicting radiation model coefficients. The results demonstrate that PINNs can effectively reconstruct the tube's acoustic field under noisy conditions, even with unknown radiation parameters. PINN-FTM outperforms TOM by delivering balanced and reliable predictions and exhibiting robust noise-tolerance capabilities.

Paperid: 1277, https://arxiv.org/pdf/2505.12360.pdf

Abstract:
Accelerating the solution of nonlinear partial differential equations (PDEs) while maintaining accuracy at coarse spatiotemporal resolution remains a key challenge in scientific computing. Physics-informed machine learning (ML) methods such as Physics-Informed Neural Networks (PINNs) introduce prior knowledge through loss functions to ensure physical consistency, but their "soft constraints" are usually not strictly satisfied. Here, we propose LaPON, an operator network inspired by the Lagrange's mean value theorem, which embeds prior knowledge directly into the neural network architecture instead of the loss function, making the neural network naturally satisfy the given constraints. This is a hybrid framework that combines neural operators with traditional numerical methods, where neural operators are used to compensate for the effect of discretization errors on the analytical scale in under-resolution simulations. As evaluated on turbulence problem modeled by the Navier-Stokes equations (NSE), the multiple time step extrapolation accuracy and stability of LaPON exceed the direct numerical simulation baseline at 8x coarser grids and 8x larger time steps, while achieving a vorticity correlation of more than 0.98 with the ground truth. It is worth noting that the model can be well generalized to unseen flow states, such as turbulence with different forcing, without retraining. In addition, with the same training data, LaPON's comprehensive metrics on the out-of-distribution test set are at least approximately twice as good as two popular ML baseline methods. By combining numerical computing with machine learning, LaPON provides a scalable and reliable solution for high-fidelity fluid dynamics simulation, showing the potential for wide application in fields such as weather forecasting and engineering design.

Paperid: 1278, https://arxiv.org/pdf/2505.11682.pdf

Abstract:
Parameter estimation in inverse problems involving partial differential equations (PDEs) underpins modeling across scientific disciplines, especially when parameters vary in space or time. Physics-informed Machine Learning (PhiML) integrates PDE constraints into deep learning, but prevailing approaches depend on recursive automatic differentiation (autodiff), which produces inaccurate high-order derivatives, inflates memory usage, and underperforms in noisy settings. We propose Mollifier Layers, a lightweight, architecture-agnostic module that replaces autodiff with convolutional operations using analytically defined mollifiers. This reframing of derivative computation as smoothing integration enables efficient, noise-robust estimation of high-order derivatives directly from network outputs. Mollifier Layers attach at the output layer and require no architectural modifications. We compare them with three distinct architectures and benchmark performance across first-, second-, and fourth-order PDEs -- including Langevin dynamics, heat diffusion, and reaction-diffusion systems -- observing significant improvements in memory efficiency, training time and accuracy for parameter recovery across tasks. To demonstrate practical relevance, we apply Mollifier Layers to infer spatially varying epigenetic reaction rates from super-resolution chromatin imaging data -- a real-world inverse problem with biomedical significance. Our results establish Mollifier Layers as an efficient and scalable tool for physics-constrained learning.

Paperid: 1279, https://arxiv.org/pdf/2505.10393.pdf

Abstract:
We investigate the efficient learning of magnetic phases using artificial neural networks trained on synthetic data, combining computational simplicity with physics-informed strategies. Focusing on the diluted Ising model, which lacks an exact analytical solution, we explore two complementary approaches: a supervised classification using simple dense neural networks, and an unsupervised detection of phase transitions using convolutional autoencoders trained solely on idealized spin configurations. To enhance model performance, we incorporate two key forms of physics-informed guidance. First, we exploit architectural biases which preferentially amplify features related to symmetry breaking. Second, we include training configurations that explicitly break $\mathbb{Z}_2$ symmetry, reinforcing the network's ability to detect ordered phases. These mechanisms, acting in tandem, increase the network's sensitivity to phase structure even in the absence of explicit labels. We validate the machine learning predictions through comparison with direct numerical estimates of critical temperatures and percolation thresholds. Our results show that synthetic, structured, and computationally efficient training schemes can reveal physically meaningful phase boundaries, even in complex systems. This framework offers a low-cost and robust alternative to conventional methods, with potential applications in broader condensed matter and statistical physics contexts.

Paperid: 1280, https://arxiv.org/pdf/2505.06459.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some work has been done to quantify the different uncertainties that arise when dealing with PINNs. In this paper, we use a two-step procedure to train Bayesian Neural Networks that provide uncertainties over the solutions to differential equation systems provided by PINNs. We use available error bounds over PINNs to formulate a heteroscedastic variance that improves the uncertainty estimation. Furthermore, we solve forward problems and utilize the obtained uncertainties when doing parameter estimation in inverse problems in cosmology.

Paperid: 1281, https://arxiv.org/pdf/2505.03806.pdf

Abstract:
This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential equations. Moreover, PrINNs extend the concept of Physics-Informed Neural Networks (PINNs) and their variants, offering a platform for the integration of diverse forms of perception precisiation, including singular, probability distribution, possibility distribution, interval, and fuzzy graph. In fact, PrINNs allow neural networks to model dynamical systems by integrating expert knowledge and perception-based information through loss functions, enabling the creation of modern data-driven models. Some of the key contributions include Mixture of Experts Informed Neural Networks (MOEINNs), which combine heterogeneous expert knowledge into the network, and Transformed-Knowledge Informed Neural Networks (TKINNs), which facilitate the incorporation of meta-information for enhanced model performance. Additionally, Fuzzy-Informed Neural Networks (FINNs) as a modern class of fuzzy deep neural networks leverage fuzzy logic constraints within a deep learning architecture, allowing online training without pre-training and eliminating the need for defuzzification. PrINNs represent a significant step forward in bridging the gap between traditional physics-based modeling and modern data-driven approaches, enabling neural networks to learn from both structured physics laws and flexible perception-based rules. This approach empowers neural networks to operate in uncertain environments, model complex systems, and discover new forms of differential equations, making PrINNs a powerful tool for advancing computational science and engineering.

Paperid: 1282, https://arxiv.org/pdf/2505.02258.pdf

Abstract:
Dielectric response (DR) of insulating materials is key input information for designing electrical insulation systems and defining safe operating conditions of various HV devices. In dielectric materials, different polarization and conduction processes occur at different time scales, making it challenging to physically interpret raw measured data. To analyze DR measurement results, equivalent circuit models (ECMs) are commonly used, reducing the complexity of the physical system to a number of circuit elements that capture the dominant response. This paper examines the use of physics-informed neural networks (PINNs) for inverse modeling of DR in time domain using parallel RC circuits. To assess their performance, we test PINNs on synthetic data generated from analytical solutions of corresponding ECMs, incorporating Gaussian noise to simulate measurement errors. Our results show that PINNs are highly effective at solving well-conditioned inverse problems, accurately estimating up to five unknown RC parameters with minimal requirements on neural network size, training duration, and hyperparameter tuning. Furthermore, we extend the ECMs to incorporate temperature dependence and demonstrate that PINNs can accurately recover embedded, nonlinear temperature functions from noisy DR data sampled at different temperatures. This case study in modeling DR in time domain presents a solution with wide-ranging potential applications in disciplines relying on ECMs, utilizing the latest technology in machine learning for scientific computation.

Paperid: 1283, https://arxiv.org/pdf/2505.01569.pdf

Abstract:
Passivity-based control ensures system stability by leveraging dissipative properties and is widely applied in electrical and mechanical systems. Port-Hamiltonian systems (PHS), in particular, are well-suited for interconnection and damping assignment passivity-based control (IDA-PBC) due to their structured, energy-centric modeling approach. However, current IDA-PBC faces two key challenges: (i) it requires precise system knowledge, which is often unavailable due to model uncertainties, and (ii) it is typically limited to set-point control. To address these limitations, we propose a data-driven tracking control approach based on a physics-informed model, namely Gaussian process Port-Hamiltonian systems, along with the modified matching equation. By leveraging the Bayesian nature of the model, we establish probabilistic stability and passivity guarantees. A simulation demonstrates the effectiveness of our approach.

Paperid: 1284, https://arxiv.org/pdf/2504.21328.pdf

Abstract:
Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the physics of laws for versatile applications, PINNs still struggle with the challenging problems which are stiff to be solved and/or have high-frequency components in the solutions, resulting in accuracy and convergence issues. It may not only increase computational costs, but also lead to accuracy loss or solution divergence. In this study, an alternative approach is proposed to mitigate the above-mentioned problems. Inspired by the multi-grid method in CFD community, the underlying idea of the current approach is to efficiently remove different frequency errors via training with different levels of training samples, resulting in a simpler way to improve the training accuracy without spending time in fine-tuning of neural network structures, loss weights as well as hyperparameters. To demonstrate the efficacy of current approach, we first investigate canonical 1D ODE with high-frequency component and 2D convection-diffusion equation with V-cycle training strategy. Finally, the current method is employed for the classical benchmark problem of steady Lid-driven cavity flows at different Reynolds numbers, to investigate the applicability and efficacy for the problem involved multiple modes of high and low frequency. By virtue of various training sequence modes, improvement through predictions lead to 30% to 60% accuracy improvement. We also investigate the synergies between current method and transfer learning techniques for more challenging problems (i.e., higher Re). From the present results, it also revealed that the current framework can produce good predictions even for the case of Re=5000, demonstrating the ability to solve complex high-frequency PDEs.

Paperid: 1285, https://arxiv.org/pdf/2504.21155.pdf

Abstract:
Our contributions are motivated by fusion reactors that rely on maintaining magnetohydrodynamic (MHD) equilibrium, where the balance between plasma pressure and confining magnetic fields is required for stable operation. In axisymmetric tokamak reactors in particular, and under the assumption of toroidal symmetry, this equilibrium can be mathematically modelled using the Grad-Shafranov Equation (GSE). Recent works have demonstrated the potential of using Physics-Informed Neural Networks (PINNs) to model the GSE. Existing studies did not examine realistic scenarios in which a single network generalizes to a variety of boundary conditions. Addressing that limitation, we evaluate a PINN architecture that incorporates boundary points as network inputs. Additionally, we compare PINN model accuracy and inference speeds with a Fourier Neural Operator (FNO) model. Finding the PINN model to be the most performant, and accurate in our setting, we use the network verification tool Marabou to perform a range of verification tasks. Although we find some discrepancies between evaluations of the networks natively in PyTorch, compared to via Marabou, we are able to demonstrate useful and practical verification workflows. Our study is the first investigation of verification of such networks.

Paperid: 1286, https://arxiv.org/pdf/2504.17945.pdf

Abstract:
Accurate myocardial image registration is essential for cardiac strain analysis and disease diagnosis. However, spectral bias in neural networks impedes modeling high-frequency deformations, producing inaccurate, biomechanically implausible results, particularly in pathological data. This paper addresses spectral bias in physics-informed neural networks (PINNs) by integrating Fourier Feature mappings and introducing modulation strategies into a PINN framework. Experiments on two distinct datasets demonstrate that the proposed methods enhance the PINN's ability to capture complex, high-frequency deformations in cardiomyopathies, achieving superior registration accuracy while maintaining biomechanical plausibility - thus providing a foundation for scalable cardiac image registration and generalization across multiple patients and pathologies.

Paperid: 1287, https://arxiv.org/pdf/2504.14156.pdf

Abstract:
We present a parameter-decoupled superresolution framework for estimating sub-wavelength separations of passive two-point sources without requiring prior knowledge or control of the source. Our theoretical foundation circumvents the need to estimate multiple challenging parameters such as partial coherence, brightness imbalance, random relative phase, and photon statistics. A physics-informed machine learning (ML) model (trained with a standard desktop workstation), synergistically integrating this theory, further addresses practical imperfections including background noise, photon loss, and centroid/orientation misalignment. The integrated parameter-decoupling superresolution method achieves resolution 14 and more times below the diffraction limit (corresponding to ~ 13.5 nm in optical microscopy) on experimentally generated realistic images with >82% fidelity, performance rivaling state-of-the-art techniques for actively controllable sources. Critically, our method's robustness against source parameter variability and source-independent noises enables potential applications in realistic scenarios where source control is infeasible, such as astrophysical imaging, live-cell microscopy, and quantum metrology. This work bridges a critical gap between theoretical superresolution limits and practical implementations for passive systems.

Paperid: 1288, https://arxiv.org/pdf/2504.13797.pdf

Abstract:
Predicting the remaining useful life (RUL) of rotating machinery is critical for industrial safety and maintenance, but existing methods struggle with scarce target-domain data and unclear degradation dynamics. We propose a Meta-Learning and Knowledge Discovery-based Physics-Informed Neural Network (MKDPINN) to address these challenges. The method first maps noisy sensor data to a low-dimensional hidden state space via a Hidden State Mapper (HSM). A Physics-Guided Regulator (PGR) then learns unknown nonlinear PDEs governing degradation evolution, embedding these physical constraints into the PINN framework. This integrates data-driven and physics-based approaches. The framework uses meta-learning, optimizing across source-domain meta-tasks to enable few-shot adaptation to new target tasks. Experiments on industrial data and the C-MAPSS benchmark show MKDPINN outperforms baselines in generalization and accuracy, proving its effectiveness for RUL prediction under data scarcity

Paperid: 1289, https://arxiv.org/pdf/2504.11140.pdf

Abstract:
Solving partial differential equations (PDEs) has been indispensable in scientific and engineering applications. Recently, deep learning methods have been widely used to solve high-dimensional problems, one of which is the physics-informed neural network (PINN). Typically, a deep learning method has three main components: a neural network, a loss function, and an optimizer. While the construction of the loss function is rooted in the definition of solution space, how to choose a optimal neural network is somewhat ad hoc, leaving much room for improvement. In the framework of PINN, we propose an unsupervised network architecture search method for solving PDEs, termed PINN-DARTS, which applies the differentiable architecture search (DARTS) to find the optimal network architecture structure in a given set of neural networks. In this set, the number of layers and the number of neurons in each layer can change. In the searching phase, both network and architecture parameters are updated simultaneously, so the running time is close to that of PINN with a pre-determined network structure. Unlike available works, our approach is unsupervised and purely based on the PDE residual without any prior usage of solutions. PINN-DARTS outputs the optimal network structure as well as the associated numerical solution. The performance of PINN-DARTS is verified on several benchmark PDEs, including elliptic, parabolic, wave, and Burgers' equations. Compared to traditional architecture search methods, PINN-DARTS achieves significantly higher architectural accuracy. Another interesting observation is that both the solution complexity and the PDE type have a prominent impact on the optimal network architecture. Our study suggests that architectures with uneven widths from layer to layer may have superior performance across different solution complexities and different PDE types.

Paperid: 1290, https://arxiv.org/pdf/2504.10395.pdf

Abstract:
Estimating forest height from Synthetic Aperture Radar (SAR) images often relies on traditional physical models, which, while interpretable and data-efficient, can struggle with generalization. In contrast, Deep Learning (DL) approaches lack physical insight. To address this, we propose CoHNet - an end-to-end framework that combines the best of both worlds: DL optimized with physics-informed constraints. We leverage a pre-trained neural surrogate model to enforce physical plausibility through a unique training loss. Our experiments show that this approach not only improves forest height estimation accuracy but also produces meaningful features that enhance the reliability of predictions.

Paperid: 1291, https://arxiv.org/pdf/2504.05282.pdf

Abstract:
Heat exchangers (HEXs) play a central role in process industries for thermal energy transfer. Fouling, the gradual accumulation of solids on heat transfer surfaces, causes a time-varying decrease in the overall heat transfer coefficient (U(t)), significantly impacting the efficiency of heat transfer. Good estimation and modeling of fouling (the heat transfer coefficient) will lead to better fouling mitigation strategies. This study investigates the identifiability of the time-varying $U(t)$ in HEXs from closed-loop operational data, without external excitation of reference signals or knowledge of the controller parameters. We establish that while the complete system model cannot be identified under these given constraints, the time-varying heat transfer coefficient $U(t)$ remains identifiable. Further, we propose a neural network based architecture, called (Per-PINN), for estimation and modeling the heat transfer coefficient from the closed-loop system data. This Per-PINN model is shown to perform better than the existing Physics-Informed Neural Networks (PINN) based models for inverse parameter learning as it inherently fixes the underlying physical equations and learns only the time-varying parameter U(t).

Paperid: 1292, https://arxiv.org/pdf/2504.05248.pdf

Abstract:
Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially with sparse measurements and incomplete system information. However, PINNs face convergence issues, stability problems, overfitting, and complex loss function design. Here we introduce PINNverse, a training paradigm that addresses these limitations by reformulating the learning process as a constrained differential optimization problem. This approach achieves a dynamic balance between data loss and differential equation residual loss during training while preventing overfitting. PINNverse combines the advantages of PINNs with the Modified Differential Method of Multipliers to enable convergence on any point on the Pareto front. We demonstrate robust and accurate parameter estimation from noisy data in four classical ODE and PDE models from physics and biology. Our method enables accurate parameter inference also when the forward problem is expensive to solve.

Paperid: 1293, https://arxiv.org/pdf/2504.03914.pdf

Abstract:
We propose an adaptive randomized truncation estimator for Krylov subspace methods that optimizes the trade-off between the solution variance and the computational cost, while remaining unbiased. The estimator solves a constrained optimization problem to compute the truncation probabilities on the fly, with minimal computational overhead. The problem has a closed-form solution when the improvement of the deterministic algorithm satisfies a diminishing returns property. We prove that obtaining the optimal adaptive truncation distribution is impossible in the general case. Without the diminishing return condition, our estimator provides a suboptimal but still unbiased solution. We present experimental results in GP hyperparameter training and competitive physics-informed neural networks problem to demonstrate the effectiveness of our approach.

Paperid: 1294, https://arxiv.org/pdf/2504.03469.pdf

Abstract:
The unprecedented X-ray flux density provided by modern X-ray sources offers new spatiotemporal possibilities for X-ray imaging of fast dynamic processes. Approaches to exploit such possibilities often result in either i) a limited number of projections or spatial information due to limited scanning speed, as in time-resolved tomography, or ii) a limited number of time points, as in stroboscopic imaging, making the reconstruction problem ill-posed and unlikely to be solved by classical reconstruction approaches. 4D reconstruction from such data requires sample priors, which can be included via deep learning (DL). State-of-the-art 4D reconstruction methods for X-ray imaging combine the power of AI and the physics of X-ray propagation to tackle the challenge of sparse views. However, most approaches do not constrain the physics of the studied process, i.e., a full physical model. Here we present 4D physics-informed optimized neural implicit X-ray imaging (4D-PIONIX), a novel physics-informed 4D X-ray image reconstruction method combining the full physical model and a state-of-the-art DL-based reconstruction method for 4D X-ray imaging from sparse views. We demonstrate and evaluate the potential of our approach by retrieving 4D information from ultra-sparse spatiotemporal acquisitions of simulated binary droplet collisions, a relevant fluid dynamic process. We envision that this work will open new spatiotemporal possibilities for various 4D X-ray imaging modalities, such as time-resolved X-ray tomography and more novel sparse acquisition approaches like X-ray multi-projection imaging, which will pave the way for investigations of various rapid 4D dynamics, such as fluid dynamics and composite testing.

Paperid: 1295, https://arxiv.org/pdf/2504.01169.pdf

Abstract:
This paper presents a novel approach for accelerating n-body simulations by integrating a physics-informed graph neural networks (GNN) with traditional numerical methods. Our method implements a leapfrog-based simulation engine to generate datasets from diverse astrophysical scenarios which are then transformed into graph representations. A custom-designed GNN is trained to predict particle accelerations with high precision. Experiments, conducted on 60 training and 6 testing simulations spanning from 3 to 500 bodies over 1000 time steps, demonstrate that the proposed model achieves extremely low prediction errors-loss values while maintaining robust long-term stability, with accumulated errors in position, velocity, and acceleration remaining insignificant. Furthermore, our method yields a modest speedup of approximately 17% over conventional simulation techniques. These results indicate that the integration of deep learning with traditional physical simulation methods offers a promising pathway to significantly enhance computational efficiency without compromising accuracy.

Paperid: 1296, https://arxiv.org/pdf/2504.00249.pdf

Abstract:
In this paper, we introduce a formulation of Physics-Informed Neural Networks (PINNs), based on learning the form of the Fourier decomposition, and a training methodology based on a spread of randomly chosen boundary conditions. By training in this way we produce a PINN that generalises; after training it can be used to correctly predict the solution for an arbitrary set of boundary conditions and interpolate this solution between the samples that spanned the training domain. We demonstrate for a toy system of two coupled oscillators that this gives the PINN formulation genuine predictive capability owing to an effective reduction of the training to evaluation times ratio due to this decoupling of the solution from specific boundary conditions.

Paperid: 1297, https://arxiv.org/pdf/2503.24074.pdf

Abstract:
Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework designed to infer the presence, shape, and motion of static or moving solid boundaries within a flow field. By integrating a body fraction parameter into the governing equations, the model enforces no-slip/no-penetration boundary conditions in solid regions while preserving conservation laws of fluid dynamics. Using partial flow field data, the method simultaneously reconstructs the unknown flow field and infers the body fraction distribution, thereby revealing solid boundaries. The framework is validated across diverse scenarios, including incompressible Navier-Stokes and compressible Euler flows, such as steady flow past a fixed cylinder, an inline oscillating cylinder, and subsonic flow over an airfoil. The results demonstrate accurate detection of hidden boundaries, reconstruction of missing flow data, and estimation of trajectories and velocities of a moving body. Further analysis examines the effects of data sparsity, velocity-only measurements, and noise on inference accuracy. The proposed method exhibits robustness and versatility, highlighting its potential for applications when only limited experimental or numerical data are available.

Paperid: 1298, https://arxiv.org/pdf/2503.23396.pdf

Abstract:
Koopman operator has been recognized as an ongoing data-driven modeling method for vehicle dynamics which lifts the original state space into a high-dimensional linear state space. The deep neural networks (DNNs) are verified to be useful for the approximation of Koopman operator. To further improve the accuracy of Koopman operator approximation, this paper introduces a physical loss function term from the concept of physics-informed neural networks (PINNs), i.e., the acceleration loss between neural network output and sensor measurements, to improve the efficiency of network learning and its interpretability. Moreover, we utilize the sliding window least squares (SWLS) to update the system matrix and input matrix online in the lifted space, therefore enabling the deep Koopman operator to adapt to the rapid dynamics of autonomous vehicles in real events. The data collection and validation are conducted on CarSim/Simlink co-simulation platform. With comparison to other physics-based and data-driven approaches on various scenarios, the results reveal that the acceleration loss-informed network refines the accuracy of Koopman operator approximation and renders it with inherent generalization, and the SWLS enforces the deep Koopman operator's capability to cope with changes in vehicle parameters, road conditions, and rapid maneuvers. This indicates the proposed physics-informed adaptive deep Koopman operator is a performant and efficient data-driven modeling tool.

Paperid: 1299, https://arxiv.org/pdf/2503.23289.pdf

Abstract:
Neural networks have emerged as powerful tools for modeling complex physical systems, yet balancing high accuracy with computational efficiency remains a critical challenge in their convergence behavior. In this work, we propose the Hybrid Parallel Kolmogorov-Arnold Network (KAN) and Multi-Layer Perceptron (MLP) Physics-Informed Neural Network (HPKM-PINN), a novel architecture that synergistically integrates parallelized KAN and MLP branches within a unified PINN framework. The HPKM-PINN introduces a scaling factor Î¾, to optimally balance the complementary strengths of KAN's interpretable function approximation and MLP's nonlinear feature learning, thereby enhancing predictive performance through a weighted fusion of their outputs. Through systematic numerical evaluations, we elucidate the impact of the scaling factor Î¾ on the model's performance in both function approximation and partial differential equation (PDE) solving tasks. Benchmark experiments across canonical PDEs, such as the Poisson and Advection equations, demonstrate that HPKM-PINN achieves a marked decrease in loss values (reducing relative error by two orders of magnitude) compared to standalone KAN or MLP models. Furthermore, the framework exhibits numerical stability and robustness when applied to various physical systems. These findings highlight the HPKM-PINN's ability to leverage KAN's interpretability and MLP's expressivity, positioning it as a versatile and scalable tool for solving complex PDE-driven problems in computational science and engineering.

Paperid: 1300, https://arxiv.org/pdf/2503.22386.pdf

Abstract:
The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects. This paper introduces a novel scientific machine learning approach for solving parametric time-fractional differential equations by combining traditional spectral methods with neural networks. Instead of relying on automatic differentiation techniques, commonly used in traditional Physics-Informed Neural Networks (PINNs), we propose a more efficient global discretization method based on Legendre polynomials. This approach eliminates the need to simulate the parametric fractional differential equations across multiple parameter values. By applying the Legendre-Galerkin weak formulation to the differential equation, we construct a loss function for training the neural network. The trial solutions are represented as linear combinations of Legendre polynomials, with the coefficients learned by the neural network. The convergence of this method is theoretically established, and the theoretical results are validated through numerical experiments on several well-known differential equations.

Paperid: 1301, https://arxiv.org/pdf/2503.21529.pdf

Abstract:
Grid-forming converters (GFCs) are crucial for frequency and voltage stability in modern power systems. However, their performance under overload conditions remains a challenge. This paper highlights the limitations of existing approaches in managing DC source saturation and AC current limits, emphasizing the need for improved control strategies to ensure system stability. This paper proposes a control strategy based on a physics-informed neural network (PINN) to improve GFC performance under overloaded conditions, effectively preventing switch failures and mitigating DC source saturation. This approach outperforms conventional methods by maintaining stable voltage and frequency, even under significant load increase where traditional droop control alone proves inadequate. The post-disturbance operating point of GFCs remains unchanged using PINN-based control with an improvement of 0.245 Hz in frequency and 0.03 p.u. in active power when compared to an already existing current limitation strategy. Additionally, it reduces peak voltage deviations during transients by 24.14\%, lowers the rate of change of frequency (ROCOF) from 0.02 Hz/s to 0.005 Hz/s, and improves the rate of change of voltage (ROCOV), keeping both within acceptable limits. These improvements significantly enhance system resilience, especially in inertia-less power networks.

Paperid: 1302, https://arxiv.org/pdf/2503.18849.pdf

Abstract:
This paper investigates the application of Physics-Informed Neural Networks (PINNs) for solving the inverse advection-diffusion problem to localize pollution sources. The study focuses on optimizing neural network architectures to accurately model pollutant dispersion dynamics under diverse conditions, including scenarios with weak and strong winds and multiple pollution sources. Various PINN configurations are evaluated, showing the strong dependence of solution accuracy on hyperparameter selection. Recommendations for efficient PINN configurations are provided based on these comparisons. The approach is tested across multiple scenarios and validated using real-world data that accounts for atmospheric variability. The results demonstrate that the proposed methodology achieves high accuracy in source localization, showcasing the stability and potential of PINNs for addressing environmental monitoring and pollution management challenges under complex weather conditions.

Paperid: 1303, https://arxiv.org/pdf/2503.18181.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability. However, limitations related to convergence and the need for re-optimization with each change in PDE parameters hinder their widespread adoption across scientific and engineering applications. This survey reviews existing research that addresses these limitations through transfer learning and meta-learning. The covered methods improve the training efficiency, allowing faster adaptation to new PDEs with fewer data and computational resources. While traditional numerical methods solve systems of differential equations directly, neural networks learn solutions implicitly by adjusting their parameters. One notable advantage of neural networks is their ability to abstract away from specific problem domains, allowing them to retain, discard, or adapt learned representations to efficiently address similar problems. By exploring the application of these techniques to PINNs, this survey identifies promising directions for future research to facilitate the broader adoption of PINNs in a wide range of scientific and engineering applications.

Paperid: 1304, https://arxiv.org/pdf/2503.17704.pdf

Abstract:
Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to engineering turbulence problems. This study proposes a framework that enhances the ability of PINNs to solve parametric turbulence problems without training datasets from experiments or CFD-Parametric Turbulence PINNs (PT-PINNs)). Two key methods are introduced to improve the accuracy and robustness of this framework. The first is a soft constraint method for turbulent viscosity calculation. The second is a pre-training method based on the conservation of flow rate in the flow field. The effectiveness of PT-PINNs is validated using a three-dimensional backward-facing step (BFS) turbulence problem with two varying parameters (Re = 3000-200000, ER = 1.1-1.5). PT-PINNs produce predictions that closely match experimental data and computational fluid dynamics (CFD) results across various conditions. Moreover, PT-PINNs offer a computational efficiency advantage over traditional CFD methods. The total time required to construct the parametric BFS turbulence model is 39 hours, one-sixteenth of the time required by traditional numerical methods. The inference time for a single-condition prediction is just 40 seconds-only 0.5% of a single CFD computation. These findings highlight the potential of PT-PINNs for future applications in engineering turbulence optimization problems.

Paperid: 1305, https://arxiv.org/pdf/2503.17402.pdf

Abstract:
Due to the limited accuracy of 4D Magnetic Resonance Imaging (MRI) in identifying hemodynamics in cardiovascular diseases, the challenges in obtaining patient-specific flow boundary conditions, and the computationally demanding and time-consuming nature of Computational Fluid Dynamics (CFD) simulations, it is crucial to explore new data assimilation algorithms that offer possible alternatives to these limitations. In the present work, we study Physics-Informed Neural Networks (PINNs), Deep Operator Networks (DeepONets), and their Physics-Informed extensions (PI-DeepONets) in predicting vascular flow simulations in the context of a 3D Abdominal Aortic Aneurysm (AAA) idealized model. PINN is a technique that combines deep neural networks with the fundamental principles of physics, incorporating the physics laws, which are given as partial differential equations, directly into loss functions used during the training process. On the other hand, DeepONet is designed to learn nonlinear operators from data and is particularly useful in studying parametric partial differential equations (PDEs), e.g., families of PDEs with different source terms, boundary conditions, or initial conditions. Here, we adapt the approaches to address the particular use case of AAA by integrating the 3D Navier-Stokes equations (NSE) as the physical laws governing fluid dynamics. In addition, we follow best practices to enhance the capabilities of the models by effectively capturing the underlying physics of the problem under study. The advantages and limitations of each approach are highlighted through a series of relevant application cases. We validate our results by comparing them with CFD simulations for benchmark datasets, demonstrating good agreements and emphasizing those cases where improvements in computational efficiency are observed.

Paperid: 1306, https://arxiv.org/pdf/2503.16323.pdf

Abstract:
NeuralFoil is an open-source Python-based tool for rapid aerodynamics analysis of airfoils, similar in purpose to XFoil. Speedups ranging from 8x to 1,000x over XFoil are demonstrated, after controlling for equivalent accuracy. NeuralFoil computes both global and local quantities (lift, drag, velocity distribution, etc.) over a broad input space, including: an 18-dimensional space of airfoil shapes, possibly including control deflections; a 360 degree range of angles of attack; Reynolds numbers from $10^2$ to $10^{10}$; subsonic flows up to the transonic drag rise; and with varying turbulence parameters. Results match those of XFoil closely: the mean relative error of drag is 0.37% on simple cases, and remains as low as 2.0% on a test dataset with numerous post-stall and transitional cases. NeuralFoil facilitates gradient-based design optimization, due to its $C^\infty$-continuous solutions, automatic-differentiation-compatibility, and bounded computational cost without non-convergence issues. NeuralFoil is a hybrid of physics-informed machine learning techniques and analytical models. Here, physics information includes symmetries that are structurally embedded into the model architecture, feature engineering using domain knowledge, and guaranteed extrapolation to known limit cases. This work also introduces a new approach for surrogate model uncertainty quantification that enables robust design optimization. This work discusses the methodology and performance of NeuralFoil with several case studies, including a practical airfoil design optimization study including both aerodynamic and non-aerodynamic constraints. Here, NeuralFoil optimization is able to produce airfoils nearly identical in performance and shape to expert-designed airfoils within seconds; these computationally-optimized airfoils provide a useful starting point for further expert refinement.

Paperid: 1307, https://arxiv.org/pdf/2503.14342.pdf

Abstract:
We introduce a novel approach for end-to-end black-box optimization of high energy physics (HEP) detectors using local deep learning (DL) surrogates. These surrogates approximate a scalar objective function that encapsulates the complex interplay of particle-matter interactions and physics analysis goals. In addition to a standard reconstruction-based metric commonly used in the field, we investigate the information-theoretic metric of mutual information. Unlike traditional methods, mutual information is inherently task-agnostic, offering a broader optimization paradigm that is less constrained by predefined targets. We demonstrate the effectiveness of our method in a realistic physics analysis scenario: optimizing the thicknesses of calorimeter detector layers based on simulated particle interactions. The surrogate model learns to approximate objective gradients, enabling efficient optimization with respect to energy resolution. Our findings reveal three key insights: (1) end-to-end black-box optimization using local surrogates is a practical and compelling approach for detector design, providing direct optimization of detector parameters in alignment with physics analysis goals; (2) mutual information-based optimization yields design choices that closely match those from state-of-the-art physics-informed methods, indicating that these approaches operate near optimality and reinforcing their reliability in HEP detector design; and (3) information-theoretic methods provide a powerful, generalizable framework for optimizing scientific instruments. By reframing the optimization process through an information-theoretic lens rather than domain-specific heuristics, mutual information enables the exploration of new avenues for discovery beyond conventional approaches.

Paperid: 1308, https://arxiv.org/pdf/2503.10708.pdf

Abstract:
Accurate forecasting of viral disease outbreaks is crucial for guiding public health responses and preventing widespread loss of life. In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a promising framework that can capture the intricate dynamics of viral infection and reliably predict its future progression. However, despite notable advances, the application of PINNs in disease modeling remains limited. Standard PINNs are effective in simulating disease dynamics through forward modeling but often face challenges in estimating key biological parameters from sparse or noisy experimental data when applied in an inverse framework. To overcome these limitations, a recent extension known as Disease Informed Neural Networks (DINNs) has emerged, offering a more robust approach to parameter estimation tasks. In this work, we apply this DINNs technique on a recently proposed hepatitis B virus (HBV) infection dynamics model to predict infection transmission within the liver. This model consists of four compartments: uninfected and infected hepatocytes, rcDNA-containing capsids, and free viruses. Leveraging the power of DINNs, we study the impacts of (i) variations in parameter range, (ii) experimental noise in data, (iii) sample sizes, (iv) network architecture and (v) learning rate. We employ this methodology in experimental data collected from nine HBV-infected chimpanzees and observe that it reliably estimates the model parameters. DINNs can capture infection dynamics and predict their future progression even when data of some compartments of the system are missing. Additionally, it identifies the influential model parameters that determine whether the HBV infection is cleared or persists within the host.

Paperid: 1309, https://arxiv.org/pdf/2503.07619.pdf

Abstract:
Accurate free energy representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy model by training a neural network on DFT-informed Monte Carlo data. To optimize sampling in the high-dimensional Monte Carlo space, we present an Active Learning framework that integrates space-filling sampling, uncertainty-based sampling, and physics-informed sampling. Additionally, our approach includes methods such as hyperparameter tuning, dynamic sampling, and novelty enforcement. These strategies can be combined to reduce MSE,either globally or in targeted regions of interest,while minimizing the number of required data points. The framework introduced here is broadly applicable to Monte Carlo sampling of a range of materials systems.

Paperid: 1310, https://arxiv.org/pdf/2503.06995.pdf

Abstract:
This study introduces a unified control framework that addresses the challenge of precise quadruped locomotion with unknown payloads, named as online payload identification-based physics-informed neural network predictive control (OPI-PINNPC). By integrating online payload identification with physics-informed neural networks (PINNs), our approach embeds identified mass parameters directly into the neural network's loss function, ensuring physical consistency while adapting to changing load conditions. The physics-constrained neural representation serves as an efficient surrogate model within our nonlinear model predictive controller, enabling real-time optimization despite the complex dynamics of legged locomotion. Experimental validation on our quadruped robot platform demonstrates 35% improvement in position and orientation tracking accuracy across diverse payload conditions (25-100 kg), with substantially faster convergence compared to previous adaptive control methods. Our framework provides a adaptive solution for maintaining locomotion performance under variable payload conditions without sacrificing computational efficiency.

Paperid: 1311, https://arxiv.org/pdf/2503.00420.pdf

Abstract:
Advanced slot and winding designs are imperative to create future high performance electrical machines (EM). As a result, the development of methods to design and improve slot filling factor (SFF) has attracted considerable research. Recent developments in manufacturing processes, such as additive manufacturing and alternative materials, has also highlighted a need for novel high-fidelity design techniques to develop high performance complex geometries and topologies. This study therefore introduces a novel physics-informed machine learning (PIML) design optimization process for improving SFF in traction electrical machines used in electric vehicles. A maximum entropy sampling algorithm (MESA) is used to seed a physics-informed Bayesian optimization (PIBO) algorithm, where the target function and its approximations are produced by Gaussian processes (GP)s. The proposed PIBO-MESA is coupled with a 2D finite element model (FEM) to perform a GP-based surrogate and provide the first demonstration of the optimal combination of complex design variables for an electrical machine. Significant computational gains were achieved using the new PIBO-MESA approach, which is 45% faster than existing stochastic methods, such as the non-dominated sorting genetic algorithm II (NSGA-II). The FEM results confirm that the new design optimization process and keystone shaped wires lead to a higher SFF (i.e. by 20%) and electromagnetic improvements (e.g. maximum torque by 12%) with similar resistivity. The newly developed PIBO-MESA design optimization process therefore presents significant benefits in the design of high-performance electric machines, with reduced development time and costs.

Paperid: 1312, https://arxiv.org/pdf/2503.00317.pdf

Abstract:
Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising performance in learning operators that govern partial differential equations (PDEs), including diffusion-reaction systems and Burgers' equations. However, the accuracy of DeepONets is often constrained by computational limitations and optimization challenges inherent in training deep neural networks. Furthermore, the computational cost associated with training these networks is typically very high. To address these challenges, we leverage randomized neural networks (RaNNs), in which the parameters of the hidden layers remain fixed following random initialization. RaNNs compute the output layer parameters using the least-squares method, significantly reducing training time and mitigating optimization errors. In this work, we integrate DeepONets with RaNNs to propose RaNN-DeepONets, a hybrid architecture designed to balance accuracy and efficiency. Furthermore, to mitigate the need for extensive data preparation, we introduce the concept of physics-informed RaNN-DeepONets. Instead of relying on data generated through other time-consuming numerical methods, we incorporate PDE information directly into the training process. We evaluate the proposed model on three benchmark PDE problems: diffusion-reaction dynamics, Burgers' equation, and the Darcy flow problem. Through these tests, we assess its ability to learn nonlinear operators with varying input types. When compared to the standard DeepONet framework, RaNN-DeepONets achieves comparable accuracy while reducing computational costs by orders of magnitude. These results highlight the potential of RaNN-DeepONets as an efficient alternative for operator learning in PDE-based systems.

Paperid: 1313, https://arxiv.org/pdf/2502.17597.pdf

Abstract:
We parametrically solve the Boltzmann equations governing freeze-in dark matter (DM) in alternative cosmologies with Physics-Informed Neural Networks (PINNs), a mesh-free method. Through inverse PINNs, using a single DM experimental point -- observed relic density -- we determine the physical attributes of the theory, namely power-law cosmologies, inspired by braneworld scenarios, and particle interaction cross sections. The expansion of the Universe in such alternative cosmologies has been parameterized through a switch-like function reproducing the Hubble law at later times. Without loss of generality, we model more realistically this transition with a smooth function. We predict a distinct pair-wise relationship between power-law exponent and particle interactions: for a given cosmology with negative (positive) exponent, smaller (larger) cross sections are required to reproduce the data. Lastly, via Bayesian methods, we quantify the epistemic uncertainty of theoretical parameters found in inverse problems.

Paperid: 1314, https://arxiv.org/pdf/2502.17452.pdf

Abstract:
Earthquake forecasting remains a significant scientific challenge, with current methods falling short of achieving the performance necessary for meaningful societal benefits. Traditional models, primarily based on past seismicity and geomechanical data, struggle to capture the complexity of seismic patterns and often overlook valuable non-seismic precursors such as geophysical, geochemical, and atmospheric anomalies. The integration of such diverse data sources into forecasting models, combined with advancements in AI technologies, offers a promising path forward. AI methods, particularly deep learning, excel at processing complex, large-scale datasets, identifying subtle patterns, and handling multidimensional relationships, making them well-suited for overcoming the limitations of conventional approaches. This review highlights the importance of combining AI with geophysical knowledge to create robust, physics-informed forecasting models. It explores current AI methods, input data types, loss functions, and practical considerations for model development, offering guidance to both geophysicists and AI researchers. While many AI-based studies oversimplify earthquake prediction, neglecting critical features such as data imbalance and spatio-temporal clustering, the integration of specialized geophysical insights into AI models can address these shortcomings. We emphasize the importance of interdisciplinary collaboration, urging geophysicists to experiment with AI architectures thoughtfully and encouraging AI experts to deepen their understanding of seismology. By bridging these disciplines, we can develop more accurate, reliable, and societally impactful earthquake forecasting tools.

Paperid: 1316, https://arxiv.org/pdf/2502.10949.pdf

Abstract:
We present a method leveraging extreme learning machine (ELM) type randomized neural networks (NNs) for learning the exact time integration algorithm for initial value problems (IVPs). The exact time integration algorithm for non-autonomous systems can be represented by an algorithmic function in higher dimensions, which satisfies an associated system of partial differential equations with corresponding boundary conditions. Our method learns the algorithmic function by solving this associated system using ELM with a physics informed approach. The trained ELM network serves as the learned algorithm and can be used to solve the IVP with arbitrary initial data or step sizes from some domain. When the right hand side of the non-autonomous system exhibits a periodicity with respect to any of its arguments, while the solution itself to the problem is not periodic, we show that the algorithmic function is either periodic, or when it is not, satisfies a well-defined relation for different periods. This property can greatly simplify the algorithm learning in many problems. We consider explicit and implicit NN formulations, leading to explicit or implicit time integration algorithms, and discuss how to train the ELM network by the nonlinear least squares method. Extensive numerical experiments with benchmark problems, including non-stiff, stiff and chaotic systems, show that the learned NN algorithm produces highly accurate solutions in long-time simulations, with its time-marching errors decreasing nearly exponentially with increasing degrees of freedom in the neural network. We compare extensively the computational performance (accuracy vs.~cost) between the current NN algorithm and the leading traditional time integration algorithms. The learned NN algorithm is computationally competitive, markedly outperforming the traditional algorithms in many problems.

Paperid: 1317, https://arxiv.org/pdf/2502.05044.pdf

Abstract:
This study introduces a hybrid machine learning-based scale-bridging framework for predicting the permeability of fibrous textile structures. By addressing the computational challenges inherent to multiscale modeling, the proposed approach evaluates the efficiency and accuracy of different scale-bridging methodologies combining traditional surrogate models and even integrating physics-informed neural networks (PINNs) with numerical solvers, enabling accurate permeability predictions across micro- and mesoscales. Four methodologies were evaluated: Single Scale Method (SSM), Simple Upscaling Method (SUM), Scale-Bridging Method (SBM), and Fully Resolved Model (FRM). SSM, the simplest method, neglects microscale permeability and exhibited permeability values deviating by up to 150\% of the FRM model, which was taken as ground truth at an equivalent lower fiber volume content. SUM improved predictions by considering uniform microscale permeability, yielding closer values under similar conditions, but still lacked structural variability. The SBM method, incorporating segment-based microscale permeability assignments, showed significant enhancements, achieving almost equivalent values while maintaining computational efficiency and modeling runtimes of ~45 minutes per simulation. In contrast, FRM, which provides the highest fidelity by fully resolving microscale and mesoscale geometries, required up to 270 times more computational time than SSM, with model files exceeding 300 GB. Additionally, a hybrid dual-scale solver incorporating PINNs has been developed and shows the potential to overcome generalization errors and the problem of data scarcity of the data-driven surrogate approaches. The hybrid framework advances permeability modelling by balancing computational cost and prediction reliability, laying the foundation for further applications in fibrous composite manufacturing.

Paperid: 1318, https://arxiv.org/pdf/2502.01820.pdf

Abstract:
Modeling plays a critical role in additive manufacturing (AM), enabling a deeper understanding of underlying processes. Parametric solutions for such models are of great importance, enabling the optimization of production processes and considerable cost reductions. However, the complexity of the problem and diversity of spatio-temporal scales involved in the process pose significant challenges for traditional numerical methods. Surrogate models offer a powerful alternative by accelerating simulations and facilitating real-time monitoring and control. The present study presents an operator learning approach that relies on the deep operator network (DeepONet) and physics-informed neural networks (PINN) to predict the three-dimensional temperature distribution during melting and consolidation in laser powder bed fusion (LPBF). Parametric solutions for both single-track and multi-track scenarios with respect to tool path are obtained. To address the challenges in obtaining parametric solutions for multi-track scenarios using DeepONet architecture, a sequential PINN approach is proposed to efficiently manage the increased training complexity inherent in those scenarios. The accuracy and consistency of the model are verified against finite-difference computations. The developed surrogate allows us to efficiently analyze the effect of scanning paths and laser parameters on the thermal history.

Paperid: 1319, https://arxiv.org/pdf/2502.00280.pdf

Abstract:
Spectral bias, the tendency of neural networks to prioritize learning low-frequency components of functions during the initial training stages, poses a significant challenge when approximating solutions with high-frequency details. This issue is particularly pronounced in physics-informed neural networks (PINNs), widely used to solve differential equations that describe physical phenomena. In the literature, contributions such as Wavelet Kolmogorov Arnold Networks (Wav-KANs) have demonstrated promising results in capturing both low- and high-frequency components. Similarly, Fourier features (FF) are often employed to address this challenge. However, the theoretical foundations of Wav-KANs, particularly the relationship between the frequency of the mother wavelet and spectral bias, remain underexplored. A more in-depth understanding of how Wav-KANs manage high-frequency terms could offer valuable insights for addressing oscillatory phenomena encountered in parabolic, elliptic, and hyperbolic differential equations. In this work, we analyze the eigenvalues of the neural tangent kernel (NTK) of Wav-KANs to enhance their ability to converge on high-frequency components, effectively mitigating spectral bias. Our theoretical findings are validated through numerical experiments, where we also discuss the limitations of traditional approaches, such as standard PINNs and Fourier features, in addressing multi-frequency problems.

Paperid: 1320, https://arxiv.org/pdf/2502.00194.pdf

Abstract:
Railroad bridges are a crucial component of the U.S. freight rail system, which moves over 40 percent of the nation's freight and plays a critical role in the economy. However, aging bridge infrastructure and increasing train traffic pose significant safety hazards and risk service disruptions. The U.S. rail network includes over 100,000 railroad bridges, averaging one every 1.4 miles of track, with steel bridges comprising over 50% of the network's total bridge length. Early identification and assessment of damage in these bridges remain challenging tasks. This study proposes a physics-informed neural network (PINN) based approach for damage identification in steel truss railroad bridges. The proposed approach employs an unsupervised learning approach, eliminating the need for large datasets typically required by supervised methods. The approach utilizes train wheel load data and bridge response during train crossing events as inputs for damage identification. The PINN model explicitly incorporates the governing differential equations of the linear time-varying (LTV) bridge-train system. Herein, this model employs a recurrent neural network (RNN) based architecture incorporating a custom Runge-Kutta (RK) integrator cell, designed for gradient-based learning. The proposed approach updates the bridge finite element model while also quantifying damage severity and localizing the affected structural members. A case study on the Calumet Bridge in Chicago, Illinois, with simulated damage scenarios, is used to demonstrate the model's effectiveness in identifying damage while maintaining low false-positive rates. Furthermore, the damage identification pipeline is designed to seamlessly integrate prior knowledge from inspections and drone surveys, also enabling context-aware updating and assessment of bridge's condition.

Paperid: 1321, https://arxiv.org/pdf/2501.18078.pdf

Abstract:
Thermal protection systems (TPS) of space vehicles are designed computationally rather than experimentally. They are validated using ground experiments, but all aspects of the flight cannot be replicated on ground. This ground-to-flight mapping introduces uncertainties which need to be accounted for while designing any thermal protection system. Thus, precise computational models along with uncertainty quantification in the models are required to design the TPS. The focus of this study is to estimate the thermal material parameters of TPS based on the target reliability requirements using statistical methods. To perform uncertainty quantification (UQ) of a system, a simulated model of the system needs to be solved many times on statistical samples, increasing the computational time and cost of the overall process. A physics-informed neural network (PINN) model is used in the analysis instead of traditional physics based numerical solutions. The accuracy of PINN is comparable to that of the numerical solution. To find the parameter distribution, sampling of the parameter space is performed using Sequential Monte- Carlo (SMC) method. The sampling method is efficient as it generates samples based on the target distribution in parallel and it also generates diverse samples for proper UQ. Combining the use of both PINN predictive model and SMC sampling, the framework can approximate the parameter distributions that satisfy the TPS design reliability constraints. The framework achieved remarkable increases in the speed of performing the reliability analysis of the TPS. This reliability analysis can be used for design optimization of the TPS based on risk analysis along with other systems of the vehicle.

Paperid: 1322, https://arxiv.org/pdf/2501.16867.pdf

Abstract:
Micro-structured surfaces influence nucleation characteristics and bubble dynamics besides increasing the heat transfer surface area, thus enabling efficient nucleate boiling heat transfer. Modeling the pool boiling heat transfer characteristics of these surfaces under varied conditions is essential in diverse applications. A new empirical correlation for nucleate boiling on microchannel structured surfaces has been proposed with the data collected from various experiments in previous studies since the existing correlations are limited by their accuracy and narrow operating ranges. This study also examines various Machine Learning (ML) algorithms and Deep Neural Networks (DNN) on the microchannel structured surfaces dataset to predict the nucleate pool boiling Heat Transfer Coefficient (HTC). With the aim to integrate both the ML and domain knowledge, a Physics-Informed Machine Learning Aided Framework (PIMLAF) is proposed. The proposed correlation in this study is employed as the prior physics-based model for PIMLAF, and a DNN is employed to model the residuals of the prior model. This hybrid framework achieved the best performance in comparison to the other ML models and DNNs. This framework is able to generalize well for different datasets because the proposed correlation provides the baseline knowledge of the boiling behavior. Also, SHAP interpretation analysis identifies the critical parameters impacting the model predictions and their effect on HTC prediction. This analysis further makes the model more robust and reliable. Keywords: Pool boiling, Microchannels, Heat transfer coefficient, Correlation analysis, Machine learning, Deep neural network, Physics-informed machine learning aided framework, SHAP analysis

Paperid: 1323, https://arxiv.org/pdf/2501.16362.pdf

Abstract:
A novel Trunk-Branch (TB)-net physics-informed neural network (PINN) architecture is developed, which is a PINN-based method incorporating trunk and branch nets to capture both global and local features. The aim is to solve four main classes of problems: forward flow problem, forward heat transfer problem, inverse heat transfer problem, and transfer learning problem within the porous medium, which are notoriously complex that could not be handled by origin PINN. In the proposed TB-net PINN architecture, a Fully-connected Neural Network (FNN) is used as the trunk net, followed by separated FNNs as the branch nets with respect to outputs, and automatic differentiation is performed for partial derivatives of outputs with respect to inputs by considering various physical loss. The effectiveness and flexibility of the novel TB-net PINN architecture is demonstrated through a collection of forward problems, and transfer learning validates the feasibility of resource reuse. Combining with the superiority over traditional numerical methods in solving inverse problems, the proposed TB-net PINN shows its great potential for practical engineering applications.

Paperid: 1324, https://arxiv.org/pdf/2501.14709.pdf

Abstract:
We present a physics-informed deep learning framework to address common limitations in Confocal Laser Scanning Microscopy (CLSM), such as diffraction limited resolution, noise, and undersampling due to low laser power conditions. The optical system's point spread function (PSF) and common CLSM image degradation mechanisms namely photon shot noise, dark current noise, motion blur, speckle noise, and undersampling were modeled and were directly included into model architecture. The model reconstructs high fidelity images from heavily noisy inputs by using convolutional and transposed convolutional layers. Following the advances in compressed sensing, our approach significantly reduces data acquisition requirements without compromising image resolution. The proposed method was extensively evaluated on simulated CLSM images of diverse structures, including lipid droplets, neuronal networks, and fibrillar systems. Comparisons with traditional deconvolution algorithms such as Richardson-Lucy (RL), non-negative least squares (NNLS), and other methods like Total Variation (TV) regularization, Wiener filtering, and Wavelet denoising demonstrate the superiority of the network in restoring fine structural details with high fidelity. Assessment metrics like Structural Similarity Index (SSIM) and Peak Signal to Noise Ratio (PSNR), underlines that the AdaptivePhysicsAutoencoder achieved robust image enhancement across diverse CLSM conditions, helping faster acquisition, reduced photodamage, and reliable performance in low light and sparse sampling scenarios holding promise for applications in live cell imaging, dynamic biological studies, and high throughput material characterization.

Paperid: 1325, https://arxiv.org/pdf/2501.14107.pdf

Abstract:
Parameter estimation and trajectory reconstruction for data-driven dynamical systems governed by ordinary differential equations (ODEs) are essential tasks in fields such as biology, engineering, and physics. These inverse problems -- estimating ODE parameters from observational data -- are particularly challenging when the data are noisy, sparse, and the dynamics are nonlinear. We propose the Eigen-Fourier Physics-Informed Gaussian Process (EFiGP), an algorithm that integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework. This approach eliminates the need for numerical integration, significantly enhancing computational efficiency and accuracy. Built on a principled Bayesian framework, EFiGP incorporates the ODE system through probabilistic conditioning, enforcing governing equations in the Fourier domain while truncating high-frequency terms to achieve denoising and computational savings. The use of eigen-decomposition further simplifies Gaussian Process covariance operations, enabling efficient recovery of trajectories and parameters even in dense-grid settings. We validate the practical effectiveness of EFiGP on three benchmark examples, demonstrating its potential for reliable and interpretable modeling of complex dynamical systems while addressing key challenges in trajectory recovery and computational cost.

Paperid: 1326, https://arxiv.org/pdf/2501.12145.pdf

Abstract:
We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dimensional PDEs, demonstrating both high accuracy and low computational cost. Specifically, we prove that RaNNs can approximate certain classes of functions, including Sobolev functions, in the $H^2$-norm at dimension-independent convergence rates, thereby alleviating the curse of dimensionality. Numerical experiments are provided for the high-dimensional heat equation, the Black-Scholes model, and the Heston model, demonstrating the accuracy and efficiency of randomized neural networks.

Paperid: 1327, https://arxiv.org/pdf/2501.10684.pdf

Abstract:
We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven learning with physical constraints, our method achieves robust and accurate solutions across diverse scenarios. Bayesian training is implemented through variational inference, allowing for comprehensive uncertainty quantification for both aleatoric and epistemic uncertainties. This ensures reliable predictions and parameter estimates even in noisy conditions or when some of the physical equations governing the problem are missing. The framework demonstrates its efficacy in solving forward and inverse problems, including the 1D unsteady heat equation and 2D reaction-diffusion equations, as well as regression tasks with sparse, noisy observations. This approach provides a computationally efficient and generalizable method for addressing uncertainty quantification in PDE surrogate modeling.

Paperid: 1328, https://arxiv.org/pdf/2501.07809.pdf

Abstract:
We focus on designing and solving the neutral inclusion problem via neural networks. The neutral inclusion problem has a long history in the theory of composite materials, and it is exceedingly challenging to identify the precise condition that precipitates a general-shaped inclusion into a neutral inclusion. Physics-informed neural networks (PINNs) have recently become a highly successful approach to addressing both forward and inverse problems associated with partial differential equations. We found that traditional PINNs perform inadequately when applied to the inverse problem of designing neutral inclusions with arbitrary shapes. In this study, we introduce a novel approach, Conformal mapping Coordinates Physics-Informed Neural Networks (CoCo-PINNs), which integrates complex analysis techniques into PINNs. This method exhibits strong performance in solving forward-inverse problems to construct neutral inclusions of arbitrary shapes in two dimensions, where the imperfect interface condition on the inclusion's boundary is modeled by training neural networks. Notably, we mathematically prove that training with a single linear field is sufficient to achieve neutrality for untrained linear fields in arbitrary directions, given a minor assumption. We demonstrate that CoCo-PINNs offer enhanced performances in terms of credibility, consistency, and stability.

Paperid: 1329, https://arxiv.org/pdf/2501.06335.pdf

Abstract:
This study aims to benchmark candidate strategies for embedding neural network (NN) surrogates in nonlinear model predictive control (NMPC) formulations that are subject to systems described with partial differential equations and that are solved via direct transcription (i.e., simultaneous methods). This study focuses on the use of physics-informed NNs and physics-informed convolutional NNs as the internal (surrogate) models within the NMPC formulation. One strategy embeds NN models as explicit algebraic constraints, leveraging the automatic differentiation (AD) of an algebraic modelling language (AML) to evaluate the derivatives. Alternatively, the solver can be provided with derivatives computed external to the AML via the AD routines of the machine learning environment the NN is trained in. The three numerical experiments considered in this work reveal that replacing mechanistic models with NN surrogates may not always offer computational advantages when smooth activation functions are used in conjunction with a local nonlinear solver (e.g., Ipopt), even with highly nonlinear systems. Moreover, in this context, the external function evaluation of the NN surrogates often outperforms the embedding strategies that rely on explicit algebraic constraints, likely due to the difficulty in initializing the auxiliary variables and constraints introduced by explicit algebraic reformulations.

Paperid: 1330, https://arxiv.org/pdf/2501.04013.pdf

Abstract:
The present work is focused on exploring convergence of Physics-informed Neural Networks (PINNs) when applied to a specific class of second-order fully nonlinear Partial Differential Equations (PDEs). It is well-known that as the number of data grows, PINNs generate a sequence of minimizers which correspond to a sequence of neural networks. We show that such sequence converges to a unique viscosity solution of a certain class of second-order fully nonlinear PDE's, provided the latter satisfies the comparison principle in the viscosity sense.

Paperid: 1331, https://arxiv.org/pdf/2412.21132.pdf

Abstract:
Structural optimization is essential for designing safe, efficient, and durable components with minimal material usage. Traditional methods for vibration control often rely on active systems to mitigate unpredictable vibrations, which may lead to resonance and potential structural failure. However, these methods face significant challenges when addressing the nonlinear inverse eigenvalue problems required for optimizing structures subjected to a wide range of frequencies. As a result, no existing approach has effectively addressed the need for real-time vibration suppression within this context, particularly in high-performance environments such as automotive noise, vibration and harshness, where computational efficiency is crucial. This study introduces DeepF-fNet, a novel neural network framework designed to replace traditional active systems in vibration-based structural optimization. Leveraging DeepONets within the context of physics-informed neural networks, DeepF-fNet integrates both data and the governing physical laws. This enables rapid identification of optimal parameters to suppress critical vibrations at specific frequencies, offering a more efficient and real-time alternative to conventional methods. The proposed framework is validated through a case study involving a locally resonant metamaterial used to isolate structures from user-defined frequency ranges. The results demonstrate that DeepF-fNet outperforms traditional genetic algorithms in terms of computational speed while achieving comparable results, making it a promising tool for vibration-sensitive applications. By replacing active systems with machine learning techniques, DeepF-fNet paves the way for more efficient and cost-effective structural optimization in real-world scenarios.

Paperid: 1332, https://arxiv.org/pdf/2412.20575.pdf

Abstract:
In this paper we consider time-dependent PDEs discretized by a special class of Physics Informed Neural Networks whose design is based on the framework of Runge--Kutta and related time-Galerkin discretizations. The primary motivation for using such methods is that alternative time-discrete schemes not only enable higher-order approximations but also have a crucial impact on the qualitative behavior of the discrete solutions. The design of the methods follows a novel training approach based on two key principles: (a) the discrete loss is designed using a time-discrete framework, and (b) the final loss formulation incorporates Runge--Kutta or time-Galerkin discretization in a carefully structured manner. We then demonstrate that the resulting methods inherit the stability properties of the Runge--Kutta or time-Galerkin schemes, and furthermore, their computational behavior aligns with that of the original time discrete method used in their formulation. In our analysis, we focus on linear parabolic equations, demonstrating both the stability of the methods and the convergence of the discrete minimizers to solutions of the underlying evolution PDE. An important novel aspect of our work is the derivation of maximal regularity (MR) estimates for B-stable Runge--Kutta schemes and both continuous and discontinuous Galerkin time discretizations. This allows us to provide new energy-based proofs for maximal regularity estimates previously established by KovÃ¡cs, Li, and Lubich, now in the Hilbert space setting and with the flexibility of variable time steps.

Paperid: 1333, https://arxiv.org/pdf/2412.18344.pdf

Abstract:
Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling's functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden-Fletcher-Goldfarb-Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. Future research work includes minimization of error induced by parameters, bifurcation analysis, and sensitivity analysis of the parameters.

Paperid: 1334, https://arxiv.org/pdf/2412.17827.pdf

Abstract:
This paper introduces a hybrid learning framework that combines convolutional neural networks (CNNs) and physics-informed neural networks (PINNs) to address the challenging problem of full-inverse electrical impedance tomography (EIT). EIT is a noninvasive imaging technique that reconstructs the spatial distribution of internal conductivity based on boundary voltage measurements from injected currents. This method has applications across medical imaging, multiphase flow detection, and tactile sensing. However, solving EIT involves a nonlinear partial differential equation (PDE) derived from Maxwell's equations, posing significant computational challenges as an ill-posed inverse problem. Existing PINN approaches primarily address semi-inverse EIT, assuming full access to internal potential data, which limits practical applications in realistic, full-inverse scenarios. Our framework employs a forward CNN-based supervised network to map differential boundary voltage measurements to a discrete potential distribution under fixed Neumann boundary conditions, while an inverse PINN-based unsupervised network enforces PDE constraints for conductivity reconstruction. Instead of traditional automatic differentiation, we introduce discrete numerical differentiation to bridge the forward and inverse networks, effectively decoupling them, enhancing modularity, and reducing computational demands. We validate our framework under realistic conditions, using a 16-electrode setup and rigorous testing on complex conductivity distributions with sharp boundaries, without Gaussian smoothing. This approach demonstrates robust flexibility and improved applicability in full-inverse EIT, establishing a practical solution for real-world imaging challenges.

Paperid: 1335, https://arxiv.org/pdf/2412.14683.pdf

Abstract:
We investigate the numerical solution of multiscale transport equations using Physics Informed Neural Networks (PINNs) with ReLU activation functions. Therefore, we study the analogy between PINNs and Least-Squares Finite Elements (LSFE) which lies in the shared approach to reformulate the PDE solution as a minimization of a quadratic functional. We prove that in the diffusive regime, the correct limit is not reached, in agreement with known results for first-order LSFE. A diffusive scaling is introduced that can be applied to overcome this, again in full agreement with theoretical results for LSFE. We provide numerical results in the case of slab geometry that support our theoretical findings.

Paperid: 1336, https://arxiv.org/pdf/2412.14132.pdf

Abstract:
jinns is an open-source Python library for physics-informed neural networks, built to tackle both forward and inverse problems, as well as meta-model learning. Rooted in the JAX ecosystem, it provides a versatile framework for efficiently prototyping real-problems, while easily allowing extensions to specific needs. Furthermore, the implementation leverages existing popular JAX libraries such as equinox and optax for model definition and optimisation, bringing a sense of familiarity to the user. Many models are available as baselines, and the documentation provides reference implementations of different use-cases along with step-by-step tutorials for extensions to specific needs. The code is available on Gitlab https://gitlab.com/mia_jinns/jinns.

Paperid: 1337, https://arxiv.org/pdf/2412.06842.pdf

Abstract:
Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing physics. It uses the partition of unity networks (POUs) to divide the space into subdomains, assigning unique nonlinear model parameters to each, which are integrated into the physics model. A vital feature of this method is a physics residual-based loss function that detects variations in physical properties without requiring labeled data. This approach enables the discovery of spatial decompositions and nonlinear parameters in partial differential equations (PDEs), optimizing the solution space by dividing it into subdomains and improving accuracy. Its effectiveness is demonstrated through applications in porous media thermal ablation and ice-sheet modeling, showcasing its potential for tackling real-world physics challenges.

Paperid: 1338, https://arxiv.org/pdf/2412.05525.pdf

Abstract:
Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs variational methods, specifically by leveraging the principle of minimum pressure gradient, which turns the fluid mechanics problem into a minimization problem whose solution can be used to predict the flow field in unsteady incompressible viscous flows. This method exhibits two particulary intriguing properties. First, it circumvents the chronic issues of pressure-velocity coupling in incompressible flows, which often dominates the computational cost in computational fluid dynamics (CFD). Second, this method eliminates the reliance on unphysical assumptions at the outflow boundary, addressing another longstanding challenge in CFD. We apply this framework to three benchmark examples across a range of Reynolds numbers: (i) unsteady flow field in a lid-driven cavity, (ii) Poiseuille flow, and (iii) flow past a circular cylinder. The minimization framework is carried out using a physics-informed neural network (PINN), which integrates the underlying physical principles directly into the training of the model. The results from the proposed method are validated against high-fidelity CFD simulations, showing an excellent agreement. Comparison of the proposed variational method to the conventional method, wherein PINNs is directly applied to solve Navier-Stokes Equations, reveals that the proposed method outperforms conventional PINNs in terms of both convergence rate and time, demonstrating its potential for solving complex fluid mechanics problems.

Paperid: 1339, https://arxiv.org/pdf/2412.03609.pdf

Abstract:
Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty adhering to physical laws, which negatively affect its performance. Addressing these issues, we present Online Physics-informed DMD (OPIDMD), a novel adaptation of DMD into a convex optimization framework. This approach not only ensures convergence to a unique global optimum, but also enhances the efficiency and accuracy of modeling dynamical systems in an online setting. Leveraging the Bayesian DMD framework, we propose a probabilistic interpretation of Physics-informed DMD (piDMD), examining the impact of physical constraints on the DMD linear operator. Further, we implement online proximal gradient descent and formulate specific algorithms to tackle problems with different physical constraints, enabling real-time solutions across various scenarios. Compared with existing algorithms such as Exact DMD, Online DMD, and piDMD, OPIDMD achieves the best prediction performance in short-term forecasting, e.g. an $R^2$ value of 0.991 for noisy Lorenz system. The proposed method employs a time-varying linear operator, offering a promising solution for the real-time simulation and control of complex dynamical systems.

Paperid: 1340, https://arxiv.org/pdf/2412.00225.pdf

Abstract:
This paper proposes a new way to learn Physics-Informed Neural Network loss functions using Generalized Additive Models. We apply our method by meta-learning parametric partial differential equations, PDEs, on Burger's and 2D Heat Equations. The goal is to learn a new loss function for each parametric PDE using meta-learning. The derived loss function replaces the traditional data loss, allowing us to learn each parametric PDE more efficiently, improving the meta-learner's performance and convergence.

Paperid: 1341, https://arxiv.org/pdf/2411.13848.pdf

Abstract:
The use of neural networks to solve differential equations, as an alternative to traditional numerical solvers, has increased recently. However, error bounds for the obtained solutions have only been developed for certain equations. In this work, we report important progress in calculating error bounds of physics-informed neural networks (PINNs) solutions of nonlinear first-order ODEs. We give a general expression that describes the error of the solution that the PINN-based method provides for a nonlinear first-order ODE. In addition, we propose a technique to calculate an approximate bound for the general case and an exact bound for a particular case. The error bounds are computed using only the residual information and the equation structure. We apply the proposed methods to particular cases and show that they can successfully provide error bounds without relying on the numerical solution.

Paperid: 1342, https://arxiv.org/pdf/2411.11497.pdf

Abstract:
Physics Informed Machine Learning has emerged as a popular approach for modeling and simulation in digital twins, enabling the generation of accurate models of processes and behaviors in real-world systems. However, existing methods either rely on simple loss regularizations that offer limited physics integration or employ highly specialized architectures that are difficult to generalize across diverse physical systems. This paper presents a generic approach based on a novel physics-encoded residual neural network (PERNN) architecture that seamlessly combines data-driven and physics-based analytical models to overcome these limitations. Our method integrates differentiable physics blocks-implementing mathematical operators from physics-based models with feed-forward learning blocks, while intermediate residual blocks ensure stable gradient flow during training. Consequently, the model naturally adheres to the underlying physical principles even when prior physics knowledge is incomplete, thereby improving generalizability with low data requirements and reduced model complexity. We investigate our approach in two application domains. The first is a steering model for autonomous vehicles in a simulation environment, and the second is a digital twin for climate modeling using an ordinary differential equation (ODE)-based model of Net Ecosystem Exchange (NEE) to enable gap-filling in flux tower data. In both cases, our method outperforms conventional neural network approaches as well as state-of-the-art Physics Informed Machine Learning methods.

Paperid: 1343, https://arxiv.org/pdf/2411.11276.pdf

Abstract:
The Physics-Informed Neural Network (PINN) is an innovative approach to solve a diverse array of partial differential equations (PDEs) leveraging the power of neural networks. This is achieved by minimizing the residual loss associated with the explicit physical information, usually coupled with data derived from initial and boundary conditions. However, a challenge arises in the context of nonlinear conservation laws where derivatives are undefined at shocks, leading to solutions that deviate from the true physical phenomena. To solve this issue, the physical solution must be extracted from the weak formulation of the PDE and is typically further bounded by entropy conditions. Within the numerical framework, finite volume methods (FVM) are employed to address conservation laws. These methods resolve the integral form of conservation laws and delineate the shock characteristics. Inspired by the principles underlying FVM, this paper introduces a novel Coupled Integrated PINN methodology that involves fitting the integral solutions of equations using additional neural networks. This technique not only augments the conventional PINN's capability in modeling shock waves, but also eliminates the need for spatial and temporal discretization. As such, it bypasses the complexities of numerical integration and reconstruction associated with non-convex fluxes. Finally, we show that the proposed new Integrated PINN performs well in conservative law and outperforms the vanilla PINN when tackle the challenging shock problems using examples of Burger's equation, Buckley-Leverett Equation and Euler System.

Paperid: 1344, https://arxiv.org/pdf/2411.10064.pdf

Abstract:
This paper introduces an adaptive physics-guided neural network (APGNN) framework for predicting quality attributes from image data by integrating physical laws into deep learning models. The APGNN adaptively balances data-driven and physics-informed predictions, enhancing model accuracy and robustness across different environments. Our approach is evaluated on both synthetic and real-world datasets, with comparisons to conventional data-driven models such as ResNet. For the synthetic data, 2D domains were generated using three distinct governing equations: the diffusion equation, the advection-diffusion equation, and the Poisson equation. Non-linear transformations were applied to these domains to emulate complex physical processes in image form. In real-world experiments, the APGNN consistently demonstrated superior performance in the diverse thermal image dataset. On the cucumber dataset, characterized by low material diversity and controlled conditions, APGNN and PGNN showed similar performance, both outperforming the data-driven ResNet. However, in the more complex thermal dataset, particularly for outdoor materials with higher environmental variability, APGNN outperformed both PGNN and ResNet by dynamically adjusting its reliance on physics-based versus data-driven insights. This adaptability allowed APGNN to maintain robust performance across structured, low-variability settings and more heterogeneous scenarios. These findings underscore the potential of adaptive physics-guided learning to integrate physical constraints effectively, even in challenging real-world contexts with diverse environmental conditions.

Paperid: 1345, https://arxiv.org/pdf/2411.09728.pdf

Abstract:
Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of interest (e.g. at finite element nodes). The lack of explicit model error approximators has been addressed recently with the emergence of machine learning (ML), which closes the loop between numerical model features/solutions and explicit model error approximations. In this paper, we propose physics-informed neural networks (PINNs) for simultaneous numerical model error approximation and superresolution. To test our approach, numerical data was generated using finite element simulations on a two-dimensional elastic plate with a central opening. Four- and eight-node quadrilateral elements were used in the discretization to represent the reduced-order and higher-order models, respectively. It was found that the developed PINNs effectively predict model errors in both x and y displacement fields with small differences between predictions and ground truth. Our findings demonstrate that the integration of physics-informed loss functions enables neural networks (NNs) to surpass a purely data-driven approach for approximating model errors.

Paperid: 1346, https://arxiv.org/pdf/2411.09704.pdf

Abstract:
Non-linear convection-reaction-diffusion (CRD) partial differential equations (PDEs) are crucial for modeling complex phenomena in fields such as biology, ecology, population dynamics, physics, and engineering. Numerical approximation of these non-linear systems is essential due to the challenges of obtaining exact solutions. Traditionally, the Galerkin finite element method (GFEM) has been the standard computational tool for solving these PDEs. With the advancements in machine learning, Physics-Informed Neural Network (PINN) has emerged as a promising alternative for approximating non-linear PDEs. In this study, we compare the performance of PINN and GFEM by solving four distinct one-dimensional CRD problems with varying initial and boundary conditions and evaluate the performance of PINN over GFEM. This evaluation metrics includes error estimates, and visual representations of the solutions, supported by statistical methods such as the root mean squared error (RMSE), the standard deviation of error, the the Wilcoxon Signed-Rank Test and the coefficient of variation (CV) test. Our findings reveal that while both methods achieve solutions close to the analytical results, PINN demonstrate superior accuracy and efficiency. PINN achieved significantly lower RMSE values and smaller standard deviations for Burgers' equation, Fisher's equation, and Newell-Whitehead-Segel equation, indicating higher accuracy and greater consistency. While GFEM shows slightly better accuracy for the Burgers-Huxley equation, its performance was less consistent over time. In contrast, PINN exhibit more reliable and robust performance, highlighting their potential as a cutting-edge approach for solving non-linear PDEs.

Paperid: 1347, https://arxiv.org/pdf/2411.08760.pdf

Abstract:
This paper investigates a numerical solution of Allen-Cahn equation with constant and degenerate mobility, with polynomial and logarithmic energy functionals, with deterministic and random initial functions, and with advective term in one, two, and three spatial dimensions, based on the physics-informed neural network (PINN). To improve the learning capacity of the PINN, we incorporate the energy dissipation property of the Allen-Cahn equation as a penalty term into the loss function of the network. To facilitate the learning process of random initials, we employ a continuous analogue of the initial random condition by utilizing the Fourier series expansion. Adaptive methods from traditional numerical analysis are also integrated to enhance the effectiveness of the proposed PINN. Numerical results indicate a consistent decrease in the discrete energy, while also revealing phenomena such as phase separation and metastability.

Paperid: 1348, https://arxiv.org/pdf/2411.07918.pdf

Abstract:
Mueller matrix polarimetry captures essential information about polarized light interactions with a sample, presenting unique challenges for data augmentation in deep learning due to its distinct structure. While augmentations are an effective and affordable way to enhance dataset diversity and reduce overfitting, standard transformations like rotations and flips do not preserve the polarization properties in Mueller matrix images. To this end, we introduce a versatile simulation framework that applies physically consistent rotations and flips to Mueller matrices, tailored to maintain polarization fidelity. Our experimental results across multiple datasets reveal that conventional augmentations can lead to falsified results when applied to polarimetric data, underscoring the necessity of our physics-based approach. In our experiments, we first compare our polarization-specific augmentations against real-world captures to validate their physical consistency. We then apply these augmentations in a semantic segmentation task, achieving substantial improvements in model generalization and performance. This study underscores the necessity of physics-informed data augmentation for polarimetric imaging in deep learning (DL), paving the way for broader adoption and more robust applications across diverse research in the field. In particular, our framework unlocks the potential of DL models for polarimetric datasets with limited sample sizes. Our code implementation is available at github.com/hahnec/polar_augment.

Paperid: 1349, https://arxiv.org/pdf/2410.22796.pdf

Abstract:
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable solutions, their accuracy is often tied to the use of computationally intensive fine meshes. Moreover, they do not naturally account for measurements or prior solutions, and any change in the problem parameters requires results to be fully recomputed. Neural network-based approaches, such as physics-informed neural networks and neural operators, offer a mesh-free alternative by directly fitting those models to the PDE solution. They can also integrate prior knowledge and tackle entire families of PDEs by simply aggregating additional training losses. Nevertheless, they are highly sensitive to hyperparameters such as collocation points and the weights associated with each loss. This paper addresses these challenges by developing a science-constrained learning (SCL) framework. It demonstrates that finding a (weak) solution of a PDE is equivalent to solving a constrained learning problem with worst-case losses. This explains the limitations of previous methods that minimize the expected value of aggregated losses. SCL also organically integrates structural constraints (e.g., invariances) and (partial) measurements or known solutions. The resulting constrained learning problems can be tackled using a practical algorithm that yields accurate solutions across a variety of PDEs, neural network architectures, and prior knowledge levels without extensive hyperparameter tuning and sometimes even at a lower computational cost.

Paperid: 1350, https://arxiv.org/pdf/2410.20186.pdf

Abstract:
Accurately predicting the dynamic responses of building structures under seismic loads is essential for ensuring structural safety and minimizing potential damage. This critical aspect of structural analysis allows engineers to evaluate how structures perform under various loading conditions, facilitating informed design and safety decisions. Traditional methods, which rely on complex finite element models often struggle with balancing computational efficiency and accuracy. To address this challenge, we introduce SeisGPT, a data-driven, large physics-informed model that leverages deep neural networks based on the Generative Pre-trained Transformer (GPT) architecture. SeisGPT is designed to predict, in real-time the dynamic behavior of building structures under seismic forces. Trained on a diverse corpus of seismic data and structural engineering principles, it instantly generates predictive responses, including displacement, acceleration, and inter-story drift, with high accuracy and computational efficiency. Its adaptability across various building typologies and seismic intensities makes this framework a valuable tool for designing robust structures and assessing seismic risk. Through comprehensive validation, this approach exhibits superior performance, offering engineers and researchers a powerful tool for assessing seismic response and informing resilient design strategies. This innovative framework represents a significant advancement in seismic engineering practice, with potential applications in mitigating seismic hazards and enhancing structural resilience.

Paperid: 1351, https://arxiv.org/pdf/2410.14270.pdf

Abstract:
Our proposal is on a new stochastic optimizer for non-convex and possibly non-smooth objective functions typically defined over large dimensional design spaces. Towards this, we have tried to bridge noise-assisted global search and faster local convergence, the latter being the characteristic feature of a Newton-like search. Our specific scheme -- acronymed FINDER (Filtering Informed Newton-like and Derivative-free Evolutionary Recursion), exploits the nonlinear stochastic filtering equations to arrive at a derivative-free update that has resemblance with the Newton search employing the inverse Hessian of the objective function. Following certain simplifications of the update to enable a linear scaling with dimension and a few other enhancements, we apply FINDER to a range of problems, starting with some IEEE benchmark objective functions to a couple of archetypal data-driven problems in deep networks to certain cases of physics-informed deep networks. The performance of the new method vis-Ã¡-vis the well-known Adam and a few others bears evidence to its promise and potentialities for large dimensional optimization problems of practical interest.

Paperid: 1352, https://arxiv.org/pdf/2410.13295.pdf

Abstract:
For the 3D localization problem using point spread function (PSF) engineering, we propose a novel enhancement of our previously introduced localization neural network, LocNet. The improved network is a physics-informed neural network (PINN) that we call PiLocNet. Previous works on the localization problem may be categorized separately into model-based optimization and neural network approaches. Our PiLocNet combines the unique strengths of both approaches by incorporating forward-model-based information into the network via a data-fitting loss term that constrains the neural network to yield results that are physically sensible. We additionally incorporate certain regularization terms from the variational method, which further improves the robustness of the network in the presence of image noise, as we show for the Poisson and Gaussian noise models. This framework accords interpretability to the neural network, and the results we obtain show its superiority. Although the paper focuses on the use of single-lobe rotating PSF to encode the full 3D source location, we expect the method to be widely applicable to other PSFs and imaging problems that are constrained by known forward processes.

Paperid: 1353, https://arxiv.org/pdf/2410.06523.pdf

Abstract:
We address an inverse problem in modeling holographic superconductors. We focus our research on the critical temperature behavior depicted by experiments. We use a physics-informed neural network method to find a mass function $M(F^2)$, which is necessary to understand phase transition behavior. This mass function describes a nonlinear interaction between superconducting order and charge carrier density. We introduce positional embedding layers to improve the learning process in our algorithm, and the Adam optimization is used to predict the critical temperature data via holographic calculation with appropriate accuracy. Consideration of the positional embedding layers is motivated by the transformer model of natural-language processing in the artificial intelligence (AI) field. We obtain holographic models that reproduce borderlines of the normal and superconducting phases provided by actual data. Our work is the first holographic attempt to match phase transition data quantitatively obtained from experiments. Also, the present work offers a new methodology for data-based holographic models.

Paperid: 1354, https://arxiv.org/pdf/2410.04299.pdf

Abstract:
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to solve two challenging problems in dynamical systems theory: dynamics discovery and parameter estimation. Results demonstrate the effectiveness of the proposed approaches on a suite of test problems exhibiting oscillatory and chaotic dynamics. When comparing the performance of various numerical schemes, such as the Runge-Kutta and linear multistep families of methods, we observe promising results in predicting the system dynamics and estimating physical parameters, given appropriate choices of spatial and temporal discretization schemes and numerical method orders.

Paperid: 1355, https://arxiv.org/pdf/2410.04167.pdf

Abstract:
Transformer Neural Networks are driving an explosion of activity and discovery in the field of Large Language Models (LLMs). In contrast, there have been only a few attempts to apply Transformers in engineering physics. Aiming to offer an easy entry point to physics-centric Transformers, we introduce a physics-informed Transformer model for solving the heat conduction problem in a 2D plate with Dirichlet boundary conditions. The model is implemented in the machine learning framework MLX and leverages the unified memory of Apple M-series processors. The use of MLX means that the models can be trained and perform predictions efficiently on personal machines with only modest memory requirements. To train, validate and test the Transformer model we solve the 2D heat conduction problem using central finite differences. Each finite difference solution in these sets is initialized with four random Dirichlet boundary conditions, a uniform but random internal temperature distribution and a randomly selected thermal diffusivity. Validation is performed in-line during training to monitor against over-fitting. The excellent performance of the trained model is demonstrated by predicting the evolution of the temperature field to steady state for the unseen test set of conditions.

Paperid: 1356, https://arxiv.org/pdf/2410.01599.pdf

Abstract:
We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) Physics-Informed Neural Networks (PINNs) and Finite Basis Physics-Informed Neural Networks (FBPINNs), in learning the dynamics of test models with a quasi-stationary longtime behavior. We test the approaches for data sets in different dynamical regions and with varying noise level. As results, we find a better performance for the FBPINN approach compared to the vanilla PINN approach, even in cases with data from only a quasi-stationary time domain with few dynamics.

Paperid: 1357, https://arxiv.org/pdf/2410.00422.pdf

Abstract:
Physics-informed neural networks (PINNs) have emerged as a versatile and widely applicable concept across various science and engineering domains over the past decade. This article offers a comprehensive overview of the fundamentals of PINNs, tracing their evolution, modifications, and various variants. It explores the impact of different parameters on PINNs and the optimization algorithms involved. The review also delves into the theoretical advancements related to the convergence, consistency, and stability of numerical solutions using PINNs, while highlighting the current state of the art. Given their ability to address equations involving complex physics, the article discusses various applications of PINNs, with a particular focus on their utility in computational fluid dynamics problems. Additionally, it identifies current gaps in the research and outlines future directions for the continued development of PINNs.

Paperid: 1358, https://arxiv.org/pdf/2409.19647.pdf

Abstract:
Accurate dynamic modeling is critical for autonomous racing vehicles, especially during high-speed and agile maneuvers where precise motion prediction is essential for safety. Traditional parameter estimation methods face limitations such as reliance on initial guesses, labor-intensive fitting procedures, and complex testing setups. On the other hand, purely data-driven machine learning methods struggle to capture inherent physical constraints and typically require large datasets for optimal performance. To address these challenges, this paper introduces the Fine-Tuning Hybrid Dynamics (FTHD) method, which integrates supervised and unsupervised Physics-Informed Neural Networks (PINNs), combining physics-based modeling with data-driven techniques. FTHD fine-tunes a pre-trained Deep Dynamics Model (DDM) using a smaller training dataset, delivering superior performance compared to state-of-the-art methods such as the Deep Pacejka Model (DPM) and outperforming the original DDM. Furthermore, an Extended Kalman Filter (EKF) is embedded within FTHD (EKF-FTHD) to effectively manage noisy real-world data, ensuring accurate denoising while preserving the vehicle's essential physical characteristics. The proposed FTHD framework is validated through scaled simulations using the BayesRace Physics-based Simulator and full-scale real-world experiments from the Indy Autonomous Challenge. Results demonstrate that the hybrid approach significantly improves parameter estimation accuracy, even with reduced data, and outperforms existing models. EKF-FTHD enhances robustness by denoising real-world data while maintaining physical insights, representing a notable advancement in vehicle dynamics modeling for high-speed autonomous racing.

Paperid: 1359, https://arxiv.org/pdf/2409.16008.pdf

Abstract:
In this paper, we restructure the Neural Interconnection and Damping Assignment - Passivity Based Control (Neural IDA-PBC) design methodology, and we formally analyze its closed-loop properties. Neural IDA-PBC redefines the IDA-PBC design approach as an optimization problem by building on the framework of Physics Informed Neural Networks (PINNs). However, the closed-loop stability and robustness properties under Neural IDA-PBC remain unexplored. To address the issue, we study the behavior of classical IDA-PBC under approximations. Our theoretical analysis allows deriving conditions for practical and asymptotic stability of the desired equilibrium point. Moreover, it extends the Neural IDA-PBC applicability to port-Hamiltonian systems where the matching conditions cannot be solved exactly. Our renewed optimization-based design introduces three significant aspects: i) it involves a novel optimization objective including stability and robustness constraints issued from our theoretical analysis; ii) it employs separate Neural Networks (NNs), which can be structured to reduce the search space to relevant functions; iii) it does not require knowledge about the port-Hamiltonian formulation of the system's model. Our methodology is validated with simulations on three standard benchmarks: a double pendulum, a nonlinear mass-spring-damper and a cartpole. Notably, classical IDA-PBC designs cannot be analytically derived for the latter.

Paperid: 1360, https://arxiv.org/pdf/2409.15872.pdf

Abstract:
The main focus of this paper is to analyze the behavior of a numerical solution of the Timoshenko system coupled with Thermoelasticity and incorporating second sound effects. In order to address this target, we employ the Physics-Informed Neural Networks (PINNs) framework to derive an approximate solution for the system. Our investigation delves into the extent to which this approximate solution can accurately capture the asymptotic behavior of the discrete energy, contingent upon the stability number $Ï$. Interestingly, the PINNs overcome the major difficulties encountered while using the standard numerical methods.

Paperid: 1361, https://arxiv.org/pdf/2409.14035.pdf

Abstract:
Accurate estimation of the speed-of-sound (SoS) is important for ultrasound (US) image reconstruction techniques and tissue characterization. Various approaches have been proposed to calculate SoS, ranging from tomography-inspired algorithms like CUTE to convolutional networks, and more recently, physics-informed optimization frameworks based on differentiable beamforming. In this work, we utilize implicit neural representations (INRs) for SoS estimation in US. INRs are a type of neural network architecture that encodes continuous functions, such as images or physical quantities, through the weights of a network. Implicit networks may overcome the current limitations of SoS estimation techniques, which mainly arise from the use of non-adaptable and oversimplified physical models of tissue. Moreover, convolutional networks for SoS estimation, usually trained using simulated data, often fail when applied to real tissues due to out-of-distribution and data-shift issues. In contrast, implicit networks do not require extensive training datasets since each implicit network is optimized for an individual data case. This adaptability makes them suitable for processing US data collected from varied tissues and across different imaging protocols. We evaluated the proposed SoS estimation method based on INRs using data collected from a tissue-mimicking phantom containing four cylindrical inclusions, with SoS values ranging from 1480 m/s to 1600 m/s. The inclusions were immersed in a material with an SoS value of 1540 m/s. In experiments, the proposed method achieved strong performance, clearly demonstrating the usefulness of implicit networks for quantitative US applications.

Paperid: 1362, https://arxiv.org/pdf/2409.13241.pdf

Abstract:
We explore the possibilities of using energy minimization for the numerical modeling of strain localization in solids as a sharp discontinuity in the displacement field. For this purpose, we consider (regularized) strong discontinuity kinematics in elastoplastic solids. The corresponding mathematical model is discretized using Artificial Neural Networks (ANNs), aiming to predict both the magnitude and location of the displacement jump from energy minimization, $\textit{i.e.}$, within a variational setting. The architecture takes care of the kinematics, while the loss function takes care of the variational statement of the boundary value problem. The main idea behind this approach is to solve both the equilibrium problem and the location of the localization band by means of trainable parameters in the ANN. As a proof of concept, we show through both 1D and 2D numerical examples that the computational modeling of strain localization for elastoplastic solids using energy minimization is feasible.

Paperid: 1363, https://arxiv.org/pdf/2409.12998.pdf

Abstract:
In the field of pharmacokinetics and pharmacodynamics (PKPD) modeling, which plays a pivotal role in the drug development process, traditional models frequently encounter difficulties in fully encapsulating the complexities of drug absorption, distribution, and their impact on targets. Although multi-compartment models are frequently utilized to elucidate intricate drug dynamics, they can also be overly complex. To generalize modeling while maintaining simplicity, we propose an innovative approach that enhances PK and integrated PK-PD modeling by incorporating fractional calculus or time-varying parameter(s), combined with constant or piecewise constant parameters. These approaches effectively model anomalous diffusion, thereby capturing drug trapping and escape rates in heterogeneous tissues, which is a prevalent phenomenon in drug dynamics. Furthermore, this method provides insight into the dynamics of drug in cancer in multi-dose administrations. Our methodology employs a Physics-Informed Neural Network (PINN) and fractional Physics-Informed Neural Networks (fPINNs), integrating ordinary differential equations (ODEs) with integer/fractional derivative order from compartmental modeling with neural networks. This integration optimizes parameter estimation for variables that are time-variant, constant, piecewise constant, or related to the fractional derivative order. The results demonstrate that this methodology offers a robust framework that not only markedly enhances the model's depiction of drug absorption rates and distributed delayed responses but also unlocks different drug-effect dynamics, providing new insights into absorption rates, anomalous diffusion, drug resistance, peristance and pharmacokinetic tolerance, all within a system of just two (fractional) ODEs with explainable results.

Paperid: 1364, https://arxiv.org/pdf/2409.10910.pdf

Abstract:
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the components of deep learning. A large class of physical problems in materials science and mechanics involve moving boundaries, where interface flux balance conditions are to be satisfied while solving DEs. Examples of such systems include free surface flows, shock propagation, solidification of pure and alloy systems etc. While recent research works have explored applicability of PINNs for an uncoupled system (such as solidification of pure system), the present work reports a PINN-based approach to solve coupled systems involving multiple governing parameters (energy and species, along with multiple interface balance equations). This methodology employs an architecture consisting of a separate network for each variable with a separate treatment of each phase, a training strategy which alternates between temporal learning and adaptive loss weighting, and a scheme which progressively reduces the optimisation space. While solving the benchmark problem of binary alloy solidification, it is distinctly successful at capturing the complex composition profile, which has a characteristic discontinuity at the interface and the resulting predictions align well with the analytical solutions. The procedure can be generalised for solving other transient multiphysics problems especially in the low-data regime and in cases where measurements can reveal new physics.

Paperid: 1365, https://arxiv.org/pdf/2409.10777.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine learning methods to train the model. However, recent research has noted that PINNs may fail to learn relatively complex Partial Differential Equations (PDEs). This paper addresses the failure modes of PINNs by introducing a novel, hard-constrained deep learning method -- trust-region Sequential Quadratic Programming (trSQP-PINN). In contrast to directly training the penalized soft-constrained loss as in PINNs, our method performs a linear-quadratic approximation of the hard-constrained loss, while leveraging the soft-constrained loss to adaptively adjust the trust-region radius. We only trust our model approximations and make updates within the trust region, and such an updating manner can overcome the ill-conditioning issue of PINNs. We also address the computational bottleneck of second-order SQP methods by employing quasi-Newton updates for second-order information, and importantly, we introduce a simple pretraining step to further enhance training efficiency of our method. We demonstrate the effectiveness of trSQP-PINN through extensive experiments. Compared to existing hard-constrained methods for PINNs, such as penalty methods and augmented Lagrangian methods, trSQP-PINN significantly improves the accuracy of the learned PDE solutions, achieving up to 1-3 orders of magnitude lower errors. Additionally, our pretraining step is generally effective for other hard-constrained methods, and experiments have shown the robustness of our method against both problem-specific parameters and algorithm tuning parameters.

Paperid: 1366, https://arxiv.org/pdf/2409.10388.pdf

Abstract:
Solving unsteady partial differential equations (PDEs) using recurrent neural networks (RNNs) typically requires numerical derivatives between each block of the RNN to form the physics informed loss function. However, this introduces the complexities of numerical derivatives into the training process of these models. In this study, we propose modifying the structure of the traditional RNN to enable the prediction of each block over a time interval, making it possible to calculate the derivative of the output with respect to time using the backpropagation algorithm. To achieve this, the time intervals of these blocks are overlapped, defining a mutual loss function between them. Additionally, the employment of conditional hidden states enables us to achieve a unique solution for each block. The forget factor is utilized to control the influence of the conditional hidden state on the prediction of the subsequent block. This new model, termed the Mutual Interval RNN (MI-RNN), is applied to solve three different benchmarks: the Burgers equation, unsteady heat conduction in an irregular domain, and the Green vortex problem. Our results demonstrate that MI-RNN can find the exact solution more accurately compared to existing RNN models. For instance, in the second problem, MI-RNN achieved one order of magnitude less relative error compared to the RNN model with numerical derivatives.

Paperid: 1367, https://arxiv.org/pdf/2409.08832.pdf

Abstract:
The domain of laser fusion presents a unique and challenging predictive modeling application landscape for machine learning methods due to high problem complexity and limited training data. Data-driven approaches utilizing prescribed functional forms, inductive biases and physics-informed learning (PIL) schemes have been successful in the past for achieving desired generalization ability and model interpretation that aligns with physics expectations. In complex multi-physics application domains, however, it is not always obvious how architectural biases or discriminative penalties can be formulated. In this work, focusing on nuclear fusion energy using high powered lasers, we present the use of Kolmogorov-Arnold Networks (KANs) as an alternative to PIL for developing a new type of data-driven predictive model which is able to achieve high prediction accuracy and physics interpretability. A KAN based model, a MLP with PIL, and a baseline MLP model are compared in generalization ability and interpretation with a domain expert-derived symbolic regression model. Through empirical studies in this high physics complexity domain, we show that KANs can potentially provide benefits when developing predictive models for data-starved physics applications.

Paperid: 1368, https://arxiv.org/pdf/2409.07671.pdf

Abstract:
Singularly perturbed problems are known to have solutions with steep boundary layers that are hard to resolve numerically. Traditional numerical methods, such as Finite Difference Methods (FDMs), require a refined mesh to obtain stable and accurate solutions. As Physics-Informed Neural Networks (PINNs) have been shown to successfully approximate solutions to differential equations from various fields, it is natural to examine their performance on singularly perturbed problems. The convection-diffusion equation is a representative example of such a class of problems, and we consider the use of PINNs to produce numerical solutions of this equation. We study two ways to use PINNS: as a method for correcting oscillatory discrete solutions obtained using FDMs, and as a method for modifying reduced solutions of unperturbed problems. For both methods, we also examine the use of input transformation to enhance accuracy, and we explain the behavior of input transformations analytically, with the help of neural tangent kernels.

Paperid: 1369, https://arxiv.org/pdf/2409.07028.pdf

Abstract:
This paper introduces a dynamic, error-bounded hierarchical matrix (H-matrix) compression method tailored for Physics-Informed Neural Networks (PINNs). The proposed approach reduces the computational complexity and memory demands of large-scale physics-based models while preserving the essential properties of the Neural Tangent Kernel (NTK). By adaptively refining hierarchical matrix approximations based on local error estimates, our method ensures efficient training and robust model performance. Empirical results demonstrate that this technique outperforms traditional compression methods, such as Singular Value Decomposition (SVD), pruning, and quantization, by maintaining high accuracy and improving generalization capabilities. Additionally, the dynamic H-matrix method enhances inference speed, making it suitable for real-time applications. This approach offers a scalable and efficient solution for deploying PINNs in complex scientific and engineering domains, bridging the gap between computational feasibility and real-world applicability.

Paperid: 1370, https://arxiv.org/pdf/2409.01914.pdf

Abstract:
We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing equations are completely unknown or cannot be defined, a condition that is often met in complex engineering problems. GradINNs leverage prior beliefs about a system's gradient to constrain the predicted function's gradient across all input dimensions. This is achieved using two neural networks: one modeling the target function and an auxiliary network expressing prior beliefs, e.g., smoothness. A customized loss function enables training the first network while enforcing gradient constraints derived from the auxiliary network. We demonstrate the advantages of GradINNs, particularly in low-data regimes, on diverse problems spanning non time-dependent systems (Friedman function, Stokes Flow) and time-dependent systems (Lotka-Volterra, Burger's equation). Experimental results showcase strong performance compared to standard neural networks and PINN-like approaches across all tested scenarios.

Paperid: 1371, https://arxiv.org/pdf/2409.01744.pdf

Abstract:
Studying the magnetic field properties on the solar surface is crucial for understanding the solar and heliospheric activities, which in turn shape space weather in the solar system. Surface Flux Transport (SFT) modeling helps us to simulate and analyse the transport and evolution of magnetic flux on the solar surface, providing valuable insights into the mechanisms responsible for solar activity. In this work, we demonstrate the use of machine learning techniques in solving magnetic flux transport, making it accurate. We have developed a novel Physics-Informed Neural Networks (PINN)-based model to study the evolution of Bipolar Magnetic Regions (BMRs) using SFT in one-dimensional azimuthally averaged and also in two-dimensions. We demonstrate the efficiency and computational feasibility of our PINN-based model by comparing its performance and accuracy with that of a numerical model implemented using the Runge-Kutta Implicit-Explicit (RK-IMEX) scheme. The mesh-independent PINN method can be used to reproduce the observed polar magnetic field with better flux conservation. This advancement is important for accurately reproducing observed polar magnetic fields, thereby providing insights into the strength of future solar cycles. This work paves the way for more efficient and accurate simulations of solar magnetic flux transport and showcases the applicability of PINN in solving advection-diffusion equations with a particular focus on heliophysics.

Paperid: 1372, https://arxiv.org/pdf/2409.00956.pdf

Abstract:
Digital Image Correlation (DIC) is a key technique in experimental mechanics for full-field deformation measurement, traditionally relying on subset matching to determine displacement fields. However, selecting optimal parameters like shape functions and subset size can be challenging in non-uniform deformation scenarios. Recent deep learning-based DIC approaches, both supervised and unsupervised, use neural networks to map speckle images to deformation fields, offering precise measurements without manual tuning. However, these methods require complex network architectures to extract speckle image features, which does not guarantee solution accuracy This paper introduces PINN-DIC, a novel DIC method based on Physics-Informed Neural Networks (PINNs). Unlike traditional approaches, PINN-DIC uses a simple fully connected neural network that takes the coordinate domain as input and outputs the displacement field. By integrating the DIC governing equation into the loss function, PINN-DIC directly extracts the displacement field from reference and deformed speckle images through iterative optimization. Evaluations on simulated and real experiments demonstrate that PINN-DIC maintains the accuracy of deep learning-based DIC in non-uniform fields while offering three distinct advantages: 1) enhanced precision with a simpler network by directly fitting the displacement field from coordinates, 2) effective handling of irregular boundary displacement fields with minimal parameter adjustments, and 3) easy integration with other neural network-based mechanical analysis methods for comprehensive DIC result analysis.

Paperid: 1373, https://arxiv.org/pdf/2601.21724.pdf

Abstract:
This paper summarizes and consolidates fusion power-plant costing work performed in support of ARPA-E from 2017 through 2024, and documents the evolution of the associated analysis framework from early capital-cost-focused studies to a standards-aligned, auditable costing capability. Early efforts applied ARIES-style cost-scaling relations to generate Nth-of-a-kind (NOAK) estimates and were calibrated through a pilot study with Bechtel and Decysive Systems to benchmark balance-of-plant (BOP) costs and validate plant-level reasonableness from an engineering, procurement, and construction (EPC) perspective. Subsequent work, informed by Lucid Catalyst studies of nuclear cost drivers, expanded the methodology to treat indirect costs explicitly and to evaluate cost-reduction pathways for non-fusion-island systems through design-for-cost practices, modularization, centralized manufacturing, and learning. As ARPA-E's fusion portfolio expanded, these methods were applied across BETHE and GAMOW concepts (and select ALPHA revisits), including enhanced treatment of tritium handling and plant integration supported by Princeton/PPPL expertise. In 2023 the capability was refactored to align with the IAEA-GEN-IV EMWG-EPRI code-of-accounts lineage, while key ARIES-derived scaling relations were replaced by bottom-up subsystem models for dominant fusion cost drivers (e.g., magnets, lasers, power supplies, and power-core components) coupled to physics-informed power balances and engineering-constrained radial builds. These developments were implemented in the spreadsheet-based Fusion Economics code (FECONs) and released as an open-source Python framework (pyFECONs), providing a transparent mapping from subsystem estimates to standardized accounts and a consistent computation of LCOE.

Paperid: 1374, https://arxiv.org/pdf/2601.19244.pdf

Abstract:
Traditional e-commerce recommender systems primarily optimize for user engagement and purchase likelihood, often neglecting the rigid physiological constraints required for human health. Standard collaborative filtering algorithms are structurally blind to these hard limits, frequently suggesting bundles that fail to meet specific total daily energy expenditure and macronutrient balance requirements. To address this disconnect, this paper introduces a Physics-Informed Neuro-Symbolic Recommender System that integrates nutritional science directly into the recommendation pipeline via a dual-layer architecture. The framework begins by constructing a semantic knowledge graph using sentence-level encoders to strictly align commercial products with authoritative nutritional data. During the training phase, an implicit physics regularizer applies a differentiable thermodynamic loss function, ensuring that learned latent embeddings reflect nutritional plausibility rather than simple popularity. Subsequently, during the inference phase, an explicit physics optimizer employs simulated annealing and elastic quantity optimization to generate discrete grocery bundles that strictly adhere to the user's protein and caloric targets.

Paperid: 1375, https://arxiv.org/pdf/2601.12551.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit within the training domain, leading to poor generalization when extrapolating beyond trained spatiotemporal regions. This work presents SPIKE (Sparse Physics-Informed Koopman-Enhanced), a framework that regularizes PINNs with continuous-time Koopman operators to learn parsimonious dynamics representations. By enforcing linear dynamics $dz/dt = Az$ in a learned observable space, both PIKE (without explicit sparsity) and SPIKE (with L1 regularization on $A$) learn sparse generator matrices, embodying the parsimony principle that complex dynamics admit low-dimensional structure. Experiments across parabolic, hyperbolic, dispersive, and stiff PDEs, including fluid dynamics (Navier-Stokes) and chaotic ODEs (Lorenz), demonstrate consistent improvements in temporal extrapolation, spatial generalization, and long-term prediction accuracy. The continuous-time formulation with matrix exponential integration provides unconditional stability for stiff systems while avoiding diagonal dominance issues inherent in discrete-time Koopman operators.

Paperid: 1377, https://arxiv.org/pdf/2601.09567.pdf

Abstract:
We present the Physics-Informed Optimal Homotopy Analysis Method (PI-OHAM) for solving nonlinear differential equations. PI-OHAM, based on classical HAM, employs a physics-informed residual loss to optimize convergence-control parameters systematically by combining data, boundary conditions, and governing equations in the manner similar to Physics Informed Neural Networks (PINNs). The combination of the flexibility of PINNs and the analytical transparency of HAM provides the approach with high numerical stability, rapid convergence, and high consistency with traditional numerical solutions. PI-OHAM has superior accuracy-time trade-offs and faster and more accurate convergence than standard HAM and PINNs when applied to the Blasius boundary-layer problem. It is also very close to numerical standards available in the literature. PI-OHAM ensures analytical transparency and interpretability by series-based solutions, unlike purely data-driven or data-free PINNs. Significant contributions are a conceptual bridge between decades of homotopy-based analysis and modern physics-inspired methods, and a numerically aided but analytically interpretable solver of nonlinear differential equations. PI-OHAM appears as a computationally efficient, accurate and understandable alternative to nonlinear fluid flow, heat transfer and other industrial problems in cases where robustness and interpretability are important.

Paperid: 1378, https://arxiv.org/pdf/2601.07733.pdf

Abstract:
We present a physics-informed Wasserstein GAN with gradient penalty (WGAN-GP) for solving the inverse Chafee--Infante problem on two-dimensional domains with Dirichlet boundary conditions. The objective is to reconstruct an unknown initial condition from a near-equilibrium state obtained after 100 explicit forward Euler iterations of the reaction-diffusion equation \[ u_t - γΔu + κ\left(u^3 - u\right)=0. \] Because this mapping strongly damps high-frequency content, the inverse problem is severely ill-posed and sensitive to noise. Our approach integrates a U-Net generator, a PatchGAN critic with spectral normalization, Wasserstein loss with gradient penalty, and several physics-informed auxiliary terms, including Lyapunov energy matching, distributional statistics, and a crucial forward-simulation penalty. This penalty enforces consistency between the predicted initial condition and its forward evolution under the \emph{same} forward Euler discretization used for dataset generation. Earlier experiments employing an Eyre-type semi-implicit solver were not compatible with this residual mechanism due to the cost and instability of Newton iterations within batched GPU training. On a dataset of 50k training and 10k testing pairs on $128\times128$ grids (with natural $[-1,1]$ amplitude scaling), the best trained model attains a mean absolute error (MAE) of approximately \textbf{0.23988159} on the full test set, with a sample-wise standard deviation of about \textbf{0.00266345}. The results demonstrate stable inversion, accurate recovery of interfacial structure, and robustness to high-frequency noise in the initial data.

Paperid: 1379, https://arxiv.org/pdf/2601.07017.pdf

Abstract:
Physics-informed neural networks based on automatic differentiation (AD-PINNs) and their finite-difference counterparts (FD-PINNs) are widely used for solving partial differential equations (PDEs), yet their analytical properties remain poorly understood. This work provides a unified mathematical foundation for both formulations. Under mild regularity assumptions on the activation function and for sufficiently wide neural networks of depth at least two, we prove that both the AD- and FD-PINN optimization problems are ill-posed: whenever a minimizer exists, there are in fact infinitely many, and uniqueness fails regardless of the choice of collocation points or finite-difference stencil. Nevertheless, we establish two structural properties. First, whenever the underlying PDE or its finite-difference discretization admits a solution, the corresponding AD-PINN or FD-PINN loss also admits a minimizer, realizable by a neural network of finite width. Second, FD-PINNs are tightly coupled to the underlying finite-difference scheme: every FD-PINN minimizer agrees with a finite-difference minimizer on the grid, and in regimes where the discrete PDE solution is unique, all zero-loss FD-PINN minimizers coincide with the discrete PDE solution on the stencil. Numerical experiments illustrate these theoretical insights: FD-PINNs remain stable in representative forward and inverse problems, including settings where AD-PINNs may fail to converge. We also include an inverse problem with noisy data, demonstrating that FD-PINNs retain robustness in this setting as well. Taken together, our results clarify the analytical limitations of AD-PINNs and explain the structural reasons for the more stable behavior observed in FD-PINNs.

Paperid: 1380, https://arxiv.org/pdf/2601.04557.pdf

Abstract:
The explicit constraint force method (ECFM) was recently introduced as a novel formulation of the physics-informed solution reconstruction problem, and was subsequently extended to inverse problems. In both solution reconstruction and inverse problems, model parameters are estimated with the help of measurement data. In practice, experimentalists seek to design experiments such that the acquired data leads to the most robust recovery of the missing parameters in a subsequent inverse problem. While there are well-established techniques for designing experiments with standard approaches to the inverse problem, optimal experimental design (OED) has yet to be explored with the ECFM formulation. In this work, we investigate OED with a constraint force objective. First, we review traditional approaches to OED based on the Fisher information matrix, and propose an analogous formulation based on constraint forces. Next, we reflect on the different interpretations of the objective from standard and constraint force-based inverse problems. We then test our method on several example problems. These examples suggest that an experiment which is optimal in the sense of constraint forces tends to position measurements in the stiffest regions of the system. Because the responses -- and thus the measurements -- are small in these regions, this strategy is impractical in the presence of measurement noise and/or finite measurement precision. As such, our provisional conclusion is that ECFM is not a viable approach to OED.

Paperid: 1381, https://arxiv.org/pdf/2601.00647.pdf

Abstract:
Large Protein Language Models have shown strong potential for generative protein design, yet they frequently produce structural hallucinations, generating sequences with high linguistic likelihood that fold into thermodynamically unstable conformations. Existing alignment approaches such as Direct Preference Optimization are limited in this setting, as they model preferences as binary labels and ignore the continuous structure of the physical energy landscape. We propose Physio-DPO, a physics informed alignment framework that grounds protein language models in thermodynamic stability. Physio-DPO introduces a magnitude aware objective that scales optimization updates according to the energy gap between native structures and physics perturbed hard negatives. Experiments show that Physio-DPO consistently outperforms strong baselines including SFT, PPO, and standard DPO, reducing self consistency RMSD to 1.28 Å and increasing foldability to 92.8%. Qualitative analysis further demonstrates that Physio-DPO effectively mitigates structural hallucinations by recovering biophysical interactions such as hydrophobic core packing and hydrogen bond networks.

Paperid: 1382, https://arxiv.org/pdf/2512.24365.pdf

Abstract:
Deep learning methods -- physics-informed neural networks (PINNs), deep operator networks (DeepONet), and graph network simulators (GNS) -- are increasingly proposed for geotechnical problems. This paper tests these methods against traditional solvers on canonical problems: wave propagation and beam-foundation interaction. PINNs run 90,000 times slower than finite difference with larger errors. DeepONet requires thousands of training simulations and breaks even only after millions of evaluations. Multi-layer perceptrons fail catastrophically when extrapolating beyond training data -- the common case in geotechnical prediction. GNS shows promise for geometry-agnostic simulation but faces scaling limits and cannot capture path-dependent soil behavior. For inverse problems, automatic differentiation through traditional solvers recovers material parameters with sub-percent accuracy in seconds. We recommend: use automatic differentiation for inverse problems; apply site-based cross-validation to account for spatial autocorrelation; reserve neural networks for problems where traditional solvers are genuinely expensive and predictions remain within the training envelope. When a method is four orders of magnitude slower with less accuracy, it is not a viable replacement for proven solvers.

Paperid: 1383, https://arxiv.org/pdf/2512.23396.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) are a methodology that aims to solve physical systems by directly embedding PDE constraints into the neural network training process. In electromagnetism, where well-established methodologies such as FDTD and FEM already exist, new methodologies are expected to provide clear advantages to be accepted. Despite their mesh-free nature and applicability to inverse problems, PINNs can exhibit deficiencies in terms of accuracy and energy metrics when compared to FDTD solutions. This study demonstrates hybrid training strategies can bring PINNs closer to FDTD-level accuracy and energy consistency. This study presents a hybrid methodology addressing common challenges in wave propagation scenarios. The causality collapse problem in time-dependent PINN training is addressed via time marching and causality-aware weighting. In order to mitigate the discontinuities that are introduced by time marching, a two-stage interface continuity loss is applied. In order to suppress loss accumulation, which is manifested as cumulative energy drift in electromagnetic waves, a local Poynting-based regularizer has been developed. In the developed PINN model, high field accuracy is achieved with an average 0.09\% $NRMSE$ and 1.01\% $L^2$ error over time. Energy conservation is achieved on the PINN side with only a 0.024\% relative energy mismatch in the 2D PEC cavity scenario. Training is performed without labeled field data, using only physics-based residual losses; FDTD is used solely for post-training evaluation. The results demonstrate that PINNs can achieve competitive results with FDTD in canonical electromagnetic examples and are a viable alternative.

Paperid: 1384, https://arxiv.org/pdf/2512.22190.pdf

Abstract:
Power transformers are critical assets in power networks, whose reliability directly impacts grid resilience and stability. Traditional condition monitoring approaches, often rule-based or purely physics-based, struggle with uncertainty, limited data availability, and the complexity of modern operating conditions. Recent advances in machine learning (ML) provide powerful tools to complement and extend these methods, enabling more accurate diagnostics, prognostics, and control. In this two-part series, we examine the role of Neural Networks (NNs) and their extensions in transformer condition monitoring and health management tasks. This first paper introduces the basic concepts of NNs, explores Convolutional Neural Networks (CNNs) for condition monitoring using diverse data modalities, and discusses the integration of NN concepts within the Reinforcement Learning (RL) paradigm for decision-making and control. Finally, perspectives on emerging research directions are also provided.

Paperid: 1385, https://arxiv.org/pdf/2512.22189.pdf

Abstract:
The integration of physics-based knowledge with machine learning models is increasingly shaping the monitoring, diagnostics, and prognostics of electrical transformers. In this two-part series, the first paper introduced the foundations of Neural Networks (NNs) and their variants for health assessment tasks. This second paper focuses on integrating physics and uncertainty into the learning process. We begin with the fundamentals of Physics-Informed Neural Networks (PINNs), applied to spatiotemporal thermal modeling and solid insulation ageing. Building on this, we present Bayesian PINNs as a principled framework to quantify epistemic uncertainty and deliver robust predictions under sparse data. Finally, we outline emerging research directions that highlight the potential of physics-aware and trustworthy machine learning for critical power assets.

Paperid: 1386, https://arxiv.org/pdf/2512.21349.pdf

Abstract:
This thesis presents a physics-informed machine learning framework for solving the Floquet-Bloch eigenvalue problem associated with particles in two-dimensional periodic potentials, with a focus on honeycomb lattice geometry, due to its distinctive band topology featuring Dirac points and its relevance to materials such as graphene. By leveraging neural networks to learn complex Bloch functions and their associated eigenvalues (energies) simultaneously, we develop a mesh-free solver enforcing the governing Schrödinger equation, Bloch periodicity, and normalization constraints through a composite loss function without supervision. The model is trained over the Brillouin zone to recover band structures and Bloch modes, with numerical validation against traditional plane-wave expansion methods. We further explore transfer learning techniques to adapt the solver from nearly-free electron potentials to strongly varying potentials, demonstrating its ability to capture changes in band structure topology. This work contributes to the growing field of physics-informed machine learning for quantum eigenproblems, providing insights into the interplay between symmetry, band structure, and neural architectures.

Paperid: 1387, https://arxiv.org/pdf/2512.16967.pdf

Abstract:
Short-term prediction (nowcasting) of low-visibility and precipitation events is critical for aviation safety and operational efficiency. Current operational approaches rely on computationally intensive numerical weather prediction guidance and human-issued TAF products, which often exhibit conservative biases and limited temporal resolution. This study presents a lightweight gradient boosting framework (XGBoost) trained exclusively on surface observation data (METAR) and enhanced through physics-guided feature engineering based on thermodynamic principles. The framework is evaluated across 11 international airports representing distinct climatic regimes (including SCEL, KJFK, KORD, KDEN, SBGR, and VIDP) using historical data from 2000 to 2024. Results suggest that the model successfully captures underlying local physical processes without manual configuration. In a blind comparative evaluation against operational TAF forecasts, the automated model achieved substantially higher detection rates at tactical horizons (3 hours), with a 2.5 to 4.0 times improvement in recall while reducing false alarms. Furthermore, SHAP analysis reveals that the model performs an implicit reconstruction of local physical drivers (advection, radiation, and subsidence), providing actionable explainability for operational situational awareness. Keywords: aviation meteorology; physics-guided machine learning; explainable artificial intelligence; lightweight machine learning; nowcasting; METAR; TAF verification; edge computing

Paperid: 1388, https://arxiv.org/pdf/2512.13708.pdf

Abstract:
The interaction structure of a complex dynamical system governs its collective behavior, yet existing reconstruction methods struggle with nonlinear, heterogeneous, and higher-order couplings, especially when only steady states are observable. We propose a Variational Physics-Informed Ansatz (VPIA) that infers general interaction operators directly from heterogeneous steady-state data. VPIA embeds the steady-state constraints of the dynamics into a differentiable variational representation and reconstructs the underlying couplings by minimizing a physics-derived steady-state residual, without requiring temporal trajectories, derivative estimation, or supervision. Residual sampling combined with natural-gradient optimization enables scalable learning of large and higher-order networks. Across diverse nonlinear systems, VPIA accurately recovers directed, weighted, and multi-body structures under substantial noise, providing a unified and robust framework for physics-constrained inference of complex interaction networks in settings where only snapshot observations are available.

Paperid: 1389, https://arxiv.org/pdf/2512.12708.pdf

Abstract:
We study optimal trade execution with a hard-zero terminal inventory constraint, modeled via Hamilton-Jacobi-Bellman (HJB) equations. Vanilla PINNs often under-enforce this constraint and produce unstable controls. We propose a Multi-Trajectory PINN (MT-PINN) that adds a rollout-based trajectory loss and propagates a terminal penalty on terminal inventory via backpropagation-through-time, directly enforcing zero terminal inventory. A lightweight lambda-curriculum is adopted to stabilize training as the state expands from a risk-neutral reduced HJB to a risk-averse HJB. On the Gatheral-Schied single-asset model, MT-PINN aligns closely with their derived closed-form solutions and concentrates terminal inventory tightly around zero while reducing errors along optimal paths. We apply MT-PINNs on SPY intraday data, matching TWAP when risk-neutral, and achieving lower exposure and competitive costs, especially in falling windows, for higher risk-aversion.

Paperid: 1390, https://arxiv.org/pdf/2512.11184.pdf

Abstract:
Physics-informed machine learning uses governing ordinary and/or partial differential equations to train neural networks to represent the solution field. Like any machine learning problem, the choice of activation function influences the characteristics and performance of the solution obtained from physics-informed training. Several studies have compared common activation functions on benchmark differential equations, and have unanimously found that the rectified linear unit (ReLU) is outperformed by competitors such as the sigmoid, hyperbolic tangent, and swish activation functions. In this work, we diagnose the poor performance of ReLU on physics-informed machine learning problems. While it is well-known that the piecewise linear form of ReLU prevents it from being used on second-order differential equations, we show that ReLU fails even on variational problems involving only first derivatives. We identify the cause of this failure as second derivatives of the activation, which are taken not in the formulation of the loss, but in the process of training. Namely, we show that automatic differentiation in PyTorch fails to characterize derivatives of discontinuous fields, which causes the gradient of the physics-informed loss to be mis-specified, thus explaining the poor performance of ReLU.

Paperid: 1391, https://arxiv.org/pdf/2512.11138.pdf

Abstract:
Implicit Neural Representations (INRs) have emerged as a powerful paradigm for parameterizing physical fields, yet they often suffer from spectral bias and the computational expense of non-convex optimization. We introduce the Vekua Layer (VL), a differentiable spectral method grounded in the classical theory of Generalized Analytic Functions. By restricting the hypothesis space to the kernel of the governing differential operator -- specifically utilizing Harmonic and Fourier-Bessel bases -- the VL transforms the learning task from iterative gradient descent to a strictly convex least-squares problem solved via linear projection. We evaluate the VL against Sinusoidal Representation Networks (SIRENs) on homogeneous elliptic Partial Differential Equations (PDEs). Our results demonstrate that the VL achieves machine precision ($\text{MSE} \approx 10^{-33}$) on exact reconstruction tasks and exhibits superior stability in the presence of incoherent sensor noise ($\text{MSE} \approx 0.03$), effectively acting as a physics-informed spectral filter. Furthermore, we show that the VL enables "holographic" extrapolation of global fields from partial boundary data via analytic continuation, a capability absent in standard coordinate-based approximations.

Paperid: 1392, https://arxiv.org/pdf/2512.11127.pdf

Abstract:
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost becomes prohibitive for large-scale systems requiring frequent recalculations. Machine learning approaches offer promise for acceleration but often struggle with constraint satisfaction and cost optimality. We present a novel two-stage learning framework that combines physics-informed Graph Neural Networks (GNNs) with Continuous Flow Matching (CFM) for solving DC-OPF problems. Our approach embeds fundamental physical principles--including economic dispatch optimality conditions, Kirchhoff's laws, and Karush-Kuhn-Tucker (KKT) complementarity conditions--directly into the training objectives. The first stage trains a GNN to produce feasible initial solutions by learning from physics-informed losses that encode power system constraints. The second stage employs CFM, a simulation-free continuous normalizing flow technique, to refine these solutions toward optimality through learned vector field regression. Evaluated on the IEEE 30-bus system across five load scenarios ranging from 70\% to 130\% nominal load, our method achieves near-optimal solutions with cost gaps below 0.1\% for nominal loads and below 3\% for extreme conditions, while maintaining 100\% feasibility. Our framework bridges the gap between fast but approximate neural network predictions and optimal but slow numerical solvers, offering a practical solution for modern power systems with high renewable penetration requiring frequent dispatch updates.

Paperid: 1393, https://arxiv.org/pdf/2512.09319.pdf

Abstract:
Industrial cyber physical systems operate under heterogeneous sensing, stochastic dynamics, and shifting process conditions, producing data that are often incomplete, unlabeled, imbalanced, and domain shifted. High-fidelity datasets remain costly, confidential, and slow to obtain, while edge devices face strict limits on latency, bandwidth, and energy. These factors restrict the practicality of centralized deep learning, hinder the development of reliable digital twins, and increase the risk of error escape in safety-critical applications. Motivated by these challenges, this dissertation develops an efficiency grounded computational framework that enables data lean, physics-aware, and deployment ready intelligence for modern manufacturing environments. The research advances methods that collectively address core bottlenecks across multimodal and multiscale industrial scenarios. Generative strategies mitigate data scarcity and imbalance, while semi-supervised learning integrates unlabeled information to reduce annotation and simulation demands. Physics-informed representation learning strengthens interpretability and improves condition monitoring under small-data regimes. Spatially aware graph-based surrogate modeling provides efficient approximation of complex processes, and an edge cloud collaborative compression scheme supports real-time signal analytics under resource constraints. The dissertation also extends visual understanding through zero-shot vision language reasoning augmented by domain specific retrieval, enabling generalizable assessment in previously unseen scenarios. Together, these developments establish a unified paradigm of data efficient and resource aware intelligence that bridges laboratory learning with industrial deployment, supporting reliable decision-making across diverse manufacturing systems.

Paperid: 1394, https://arxiv.org/pdf/2512.08846.pdf

Abstract:
In this paper, I further continue an investigation on Beltrami Flows began in 2015 with A. Sorin and amply revised and developed in 2022 with M. Trigiante. Instead of a compact $3$-torus $T^3=\mathbb{R}^3/Λ$ where $Λ$ is a crystallographic lattice, as done in previous work, here I considered flows confined in a cylinder with identified opposite bases. In this topology I considered axial symmetric flows and found a complete basis of axial symmetric harmonic $1$-forms that, for each energy level, decomposes into six components: two Beltrami, two anti-Beltrami and two closed forms. These objects, that are written in terms of trigonometric and Bessel functions, constitute a function basis for an $L^2$ space of axial symmetric flows. I have presented a general scheme for the search of axial symmetric solutions of Navier Stokes equation by reducing the latter to an hierachy of quadratic relations on the development coefficients of the flow in the above described functional basis. It is proposed that the coefficients can be determined by means of a Physics Informed like Neural Network optimization recursive algorithm. Indeed the present paper provides the theoretical foundations for such a algorithmic construction that is planned for a future publication.

Paperid: 1395, https://arxiv.org/pdf/2512.01920.pdf

Abstract:
This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven (statistical) formalism to a constrained or ``physics-informed'' formalism, which integrates physical knowledge and methods from traditional computational engineering. In the first part, we introduce the general concepts and the statistical flavor of regression versus other forms of curve fitting. We then move to an overview of traditional methods from machine learning and their classification and ways to link these to traditional computational science. Finally, we close with a note on methods to combine machine learning and numerical methods for physics

Paperid: 1396, https://arxiv.org/pdf/2511.20283.pdf

Abstract:
Understanding household behaviour is essential for modelling macroeconomic dynamics and designing effective policy. While heterogeneous agent models offer a more realistic alternative to representative agent frameworks, their implementation poses significant computational challenges, particularly in continuous time. The Aiyagari-Bewley-Huggett (ABH) framework, recast as a system of partial differential equations, typically relies on grid-based solvers that suffer from the curse of dimensionality, high computational cost, and numerical inaccuracies. This paper introduces the ABH-PINN solver, an approach based on Physics-Informed Neural Networks (PINNs), which embeds the Hamilton-Jacobi-Bellman and Kolmogorov Forward equations directly into the neural network training objective. By replacing grid-based approximation with mesh-free, differentiable function learning, the ABH-PINN solver benefits from the advantages of PINNs of improved scalability, smoother solutions, and computational efficiency. Preliminary results show that the PINN-based approach is able to obtain economically valid results matching the established finite-difference solvers.

Paperid: 1397, https://arxiv.org/pdf/2511.12788.pdf

Abstract:
The semiconductor industry faces a computational crisis in extreme ultraviolet (EUV) lithography optimization, where traditional methods consume billions of CPU hours while failing to achieve sub-nanometer precision. We present a physics-constrained adaptive learning framework that automatically calibrates electromagnetic approximations through learnable parameters $\boldsymbolθ = \{θ_d, θ_a, θ_b, θ_p, θ_c\}$ while simultaneously minimizing Edge Placement Error (EPE) between simulated aerial images and target photomasks. The framework integrates differentiable modules for Fresnel diffraction, material absorption, optical point spread function blur, phase-shift effects, and contrast modulation with direct geometric pattern matching objectives, enabling cross-geometry generalization with minimal training data. Through physics-constrained learning on 15 representative patterns spanning current production to future research nodes, we demonstrate consistent sub-nanometer EPE performance (0.664-2.536 nm range) using only 50 training samples per pattern. Adaptive physics learning achieves an average improvement of 69.9\% over CNN baselines without physics constraints, with a significant inference speedup over rigorous electromagnetic solvers after training completion. This approach requires 90\% fewer training samples through cross-geometry generalization compared to pattern-specific CNN training approaches. This work establishes physics-constrained adaptive learning as a foundational methodology for real-time semiconductor manufacturing optimization, addressing the critical gap between academic physics-informed neural networks and industrial deployment requirements through joint physics calibration and manufacturing precision objectives.

Paperid: 1398, https://arxiv.org/pdf/2511.11638.pdf

Abstract:
Standard physics-informed neural network implementations have produced large error rates when using these models to solve the regularized long wave (RLW) equation. Two improved PINN approaches were developed in this research: an adaptive approach with self-adaptive loss weighting and a conservative approach enforcing explicit conservation laws. Three benchmark tests were used to demonstrate how effective PINN's are as they relate to the type of problem being solved (i.e., time dependent RLW equation). The first was a single soliton traveling along a line (propagation), the second was the interaction between two solitons, and the third was the evolution of an undular bore over the course of $t=250$. The results demonstrated that the effectiveness of PINNs are problem specific. The adaptive PINN was significantly better than both the conservative PINN and the standard PINN at solving problems involving complex nonlinear interactions such as colliding two solitons. The conservative approach was significantly better at solving problems involving long term behavior of single solitons and undular bores. However, the most important finding from this research is that explicitly enforcing conservation laws may be harmful to optimizing the solution of highly nonlinear systems of equations and therefore requires special training methods. The results from our adaptive and conservative approaches were within $O(10^{-5})$ of established numerical solutions for the same problem, thus demonstrating that PINNs can provide accurate solutions to complex systems of partial differential equations without the need for a discretization of space or time (mesh free). Moreover, the finding from this research challenges the assumptions that conservation enforcement will always improve the performance of a PINN and provides researchers with guidelines for designing PINNs for use on specific types of problems.

Paperid: 1399, https://arxiv.org/pdf/2511.06585.pdf

Abstract:
The convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with physical constraints, resulting in models that are accurate, mechanistic, generalizable, and able to extrapolate beyond observed domains. This review surveys recent advances in physics-informed neural networks and operator learning, differentiable molecular simulation, and hybrid physics-ML potentials, with emphasis on long-timescale kinetics, rare events, and free-energy estimation. We frame these approaches as solutions to the "biomolecular closure problem", recovering unresolved interactions beyond classical force fields while preserving thermodynamic consistency and mechanistic interpretability. We examine theoretical foundations, tools and frameworks, computational trade-offs, and unresolved issues, including model expressiveness and stability. We outline prospective research avenues at the intersection of machine learning, statistical physics, and computational chemistry, contending that future advancements will depend on mechanistic inductive biases, and integrated differentiable physical learning frameworks for biomolecular simulation and discovery.

Paperid: 1400, https://arxiv.org/pdf/2511.00126.pdf

Abstract:
Recent deep trajectory predictors (e.g., Jiang et al., 2023; Zhou et al., 2022) have achieved strong average accuracy but remain unreliable in complex long-tail driving scenarios. These limitations reveal the weakness of the prevailing "one-model-fits-all" paradigm, particularly in safety-critical urban contexts where simpler physics-based models can occasionally outperform advanced networks (Kalman, 1960). To bridge this gap, we propose a dynamic multi-expert gating framework that adaptively selects the most reliable trajectory predictor among a physics-informed LSTM, a Transformer, and a fine-tuned GameFormer on a per-sample basis. Our method leverages internal model signals (meta-features) such as stability and uncertainty (Gal and Ghahramani, 2016), which we demonstrate to be substantially more informative than geometric scene descriptors. To the best of our knowledge, this is the first work to formulate trajectory expert selection as a pairwise-ranking problem over internal model signals (Burges et al., 2005), directly optimizing decision quality without requiring post-hoc calibration. Evaluated on the nuPlan-mini dataset (Caesar et al., 2021) with 1,287 samples, our LLM-enhanced tri-expert gate achieves a Final Displacement Error (FDE) of 2.567 m, representing a 9.5 percent reduction over GameFormer (2.835 m), and realizes 57.8 percent of the oracle performance bound. In open-loop simulations, after trajectory horizon alignment, the same configuration reduces FDE on left-turn scenarios by approximately 10 percent, demonstrating consistent improvements across both offline validation and open-loop evaluation. These results indicate that adaptive hybrid systems enhance trajectory reliability in safety-critical autonomous driving, providing a practical pathway beyond static single-model paradigms.

Paperid: 1401, https://arxiv.org/pdf/2510.25368.pdf

Abstract:
Physics-Informed Machine Learning (PIML) has successfully integrated mechanistic understanding into machine learning, particularly in domains governed by well-known physical laws. This success has motivated efforts to apply PIML to biology, a field rich in dynamical systems but shaped by different constraints. Biological modeling, however, presents unique challenges: multi-faceted and uncertain prior knowledge, heterogeneous and noisy data, partial observability, and complex, high-dimensional networks. In this position paper, we argue that these challenges should not be seen as obstacles to PIML, but as catalysts for its evolution. We propose Biology-Informed Machine Learning (BIML): a principled extension of PIML that retains its structural grounding while adapting to the practical realities of biology. Rather than replacing PIML, BIML retools its methods to operate under softer, probabilistic forms of prior knowledge. We outline four foundational pillars as a roadmap for this transition: uncertainty quantification, contextualization, constrained latent structure inference, and scalability. Foundation Models and Large Language Models will be key enablers, bridging human expertise with computational modeling. We conclude with concrete recommendations to build the BIML ecosystem and channel PIML-inspired innovation toward challenges of high scientific and societal relevance.

Paperid: 1402, https://arxiv.org/pdf/2510.24728.pdf

Abstract:
A Minkowskian physics-informed neural network approach (M--PINN) is formulated to solve the Dyson--Schwinger integral equations (DSE) of quantum electrodynamics (QED) directly in Minkowski spacetime. Our novel strategy merges two complementary approaches: (i) a dispersive solver based on Lehmann representations and subtracted dispersion relations, and (ii) a M--PINN that learns the fermion mass function $B(p^2)$, under the same truncation and renormalization configuration (quenched, rainbow, Landau gauge) with the loss integrating the DSE residual with multi--scale regularization, and monotonicity/smoothing penalties in the spacelike branch in the same way as in our previous work in Euclidean space. The benchmarks show quantitative agreement from the infrared (IR) to the ultraviolet (UV) scales in both on-shell and momentum-subtraction schemes. In this controlled setting, our M--PINN reproduces the dispersive solution whilst remaining computationally compact and differentiable, paving the way for extensions with realistic vertices, unquenching effects, and uncertainty-aware variants.

Paperid: 1403, https://arxiv.org/pdf/2510.23149.pdf

Abstract:
Physics-informed statistical learning (PISL) integrates empirical data with physical knowledge to enhance the statistical performance of estimators. While PISL methods are widely used in practice, a comprehensive theoretical understanding of how informed regularization affects statistical properties is still missing. Specifically, two fundamental questions have yet to be fully addressed: (1) what is the trade-off between considering soft penalties versus hard constraints, and (2) what is the statistical gain of incorporating physical knowledge compared to purely data-driven empirical error minimisation. In this paper, we address these questions for PISL in convex classes of functions under physical knowledge expressed as linear equations by developing appropriate complexity dependent error rates based on the small-ball method. We show that, under suitable assumptions, (1) the error rates of physics-informed estimators are comparable to those of hard constrained empirical error minimisers, differing only by constant terms, and that (2) informed penalization can effectively reduce model complexity, akin to dimensionality reduction, thereby improving learning performance. This work establishes a theoretical framework for evaluating the statistical properties of physics-informed estimators in convex classes of functions, contributing to closing the gap between statistical theory and practical PISL, with potential applications to cases not yet explored in the literature.

Paperid: 1404, https://arxiv.org/pdf/2510.22020.pdf

Abstract:
Conventional AC Power Flow (ACPF) solvers like Newton-Raphson (NR) face significant computational and convergence challenges in modern, large-scale power systems. This paper proposes a novel, two-stage hybrid method that integrates a Physics-Informed Graph Neural Network (GNN) with a robust, iterative Linear State Estimation (LSE) refinement step to produce fast and physically-consistent solutions. The GNN, trained with a physics-informed loss function featuring an efficient dynamic weighting scheme, rapidly predicts a high-quality initial system state. This prediction is then refined using an iterative, direct linear solver inspired by state estimation techniques. This LSE refinement step solves a series of linear equations to enforce physical laws, effectively bypassing the non-linearities and convergence issues of traditional solvers. The proposed GNN-LSE framework is comprehensively validated on systems ranging from small radial distribution networks (IEEE 33-bus, 69-bus) to a large, meshed transmission system (IEEE 118-bus). Results show that our GNN variants are up to $8.4 \times 10^3$ times faster than NR. The LSE refinement provides a fast route to a physically-consistent solution, while heavy-loading stress tests (120%-150% of nominal) and N-1 contingencies demonstrate the method's reliability and generalization. This work presents a powerful and flexible framework for bridging fast, data-driven models with the rigorous constraints of power system physics, offering a practical tool for real-time operations and analysis.

Paperid: 1405, https://arxiv.org/pdf/2510.21874.pdf

Abstract:
Unmanned aerial vehicles (UAVs) operating in dynamic wind fields must generate safe and energy-efficient trajectories under physical and environmental constraints. Traditional planners, such as A* and kinodynamic RRT*, often yield suboptimal or non-smooth paths due to discretization and sampling limitations. This paper presents a physics-informed neural network (PINN) framework that embeds UAV dynamics, wind disturbances, and obstacle avoidance directly into the learning process. Without requiring supervised data, the PINN learns dynamically feasible and collision-free trajectories by minimizing physical residuals and risk-aware objectives. Comparative simulations show that the proposed method outperforms A* and Kino-RRT* in control energy, smoothness, and safety margin, while maintaining similar flight efficiency. The results highlight the potential of physics-informed learning to unify model-based and data-driven planning, providing a scalable and physically consistent framework for UAV trajectory optimization.

Paperid: 1406, https://arxiv.org/pdf/2510.21819.pdf

Abstract:
Short-term forecasting of airport fog (visibility < 1.0 km) presents challenges in geographic generalization because many machine learning models rely on location-specific features and fail to transfer across sites. This study investigates whether fundamental thermodynamic and radiative processes can be encoded in a coordinate-free (location-independent) feature set to enable geographic transferability. A gradient boosting classifier (XGBoost) trained on Santiago, Chile (SCEL, 33S) data from 2002-2009 was evaluated on a 2010-2012 holdout set and under strict zero-shot tests at Puerto Montt (SCTE), San Francisco (KSFO), and London (EGLL). The model achieved AUC values of 0.923-0.947 across distances up to 11,650 km and different fog regimes (radiative, advective, marine). Consistent SHAP feature rankings show that visibility persistence, solar angle, and thermal gradients dominate predictions, suggesting the model learned transferable physical relationships rather than site-specific patterns. Results suggest that physics-informed, coordinate-free feature engineering can yield geographically transferable atmospheric forecasting tools.

Paperid: 1407, https://arxiv.org/pdf/2510.09805.pdf

Abstract:
We present a latent-space formulation of adaptive temporal reparametrization for continuous-time dynamical systems. The method, called *temporal lifting*, introduces a smooth monotone mapping $t \mapsto τ(t)$ that regularizes near-singular behavior of the underlying flow while preserving its conservation laws. In the lifted coordinate, trajectories such as those of the incompressible Navier-Stokes equations on the torus $\mathbb{T}^3$ become globally smooth. From the standpoint of machine-learning dynamics, temporal lifting acts as a continuous-time normalization or time-warping operator that can stabilize physics-informed neural networks and other latent-flow architectures used in AI systems. The framework links analytic regularity theory with representation-learning methods for stiff or turbulent processes.

Paperid: 1408, https://arxiv.org/pdf/2510.09693.pdf

Abstract:
Partial differential equations (PDEs) underpin models across science and engineering, yet analytical solutions are atypical and classical mesh-based solvers can be costly in high dimensions. This dissertation presents a unified comparison of three mesh-free neural PDE solvers, physics-informed neural networks (PINNs), the deep Ritz method (DRM), and weak adversarial networks (WANs), on Poisson problems (up to 5D) and the time-independent Schrödinger equation in 1D/2D (infinite well and harmonic oscillator), and extends the study to a laser-driven case of Schrödinger's equation via the Kramers-Henneberger (KH) transformation. Under a common protocol, all methods achieve low $L_2$ errors ($10^{-6}$-$10^{-9}$) when paired with forced boundary conditions (FBCs), forced nodes (FNs), and orthogonality regularization (OG). Across tasks, PINNs are the most reliable for accuracy and recovery of excited spectra; DRM offers the best accuracy-runtime trade-off on stationary problems; WAN is more sensitive but competitive when weak-form constraints and FN/OG are used effectively. Sensitivity analyses show that FBC removes boundary-loss tuning, network width matters more than depth for single-network solvers, and most gains occur within 5000-10,000 epochs. The same toolkit solves the KH case, indicating transfer beyond canonical benchmarks. We provide practical guidelines for method selection and outline the following extensions: time-dependent formulations for DRM and WAN, adaptive residual-driven sampling, parallel multi-state training, and neural domain decomposition. These results support physics-guided neural solvers as credible, scalable tools for solving complex PDEs.

Paperid: 1409, https://arxiv.org/pdf/2510.08295.pdf

Abstract:
Conventional time-series generation often ignores domain-specific physical constraints, limiting statistical and physical consistency. We propose a hierarchical framework that embeds the inherent hierarchy of physical laws-conservation, dynamics, boundary, and empirical relations-directly into deep generative models, introducing a new paradigm of physics-informed inductive bias. Our method combines Fourier Neural Operators (FNOs) for learning physical operators with Conditional Flow Matching (CFM) for probabilistic generation, integrated via time-dependent hierarchical constraints and FNO-guided corrections. Experiments on harmonic oscillators, human activity recognition, and lithium-ion battery degradation show 16.3% higher generation quality, 46% fewer physics violations, and 18.5% improved predictive accuracy over baselines.

Paperid: 1410, https://arxiv.org/pdf/2510.05183.pdf

Abstract:
Arterial aneurysm (Fig.1) is a bulb-shape local expansion of human arteries, the rupture of which is a leading cause of morbidity and mortality in US. Therefore, the prediction of arterial aneurysm rupture is of great significance for aneurysm management and treatment selection. The prediction of aneurysm rupture depends on the analysis of the time series of aneurysm growth history. However, due to the long time scale of aneurysm growth, the time series of aneurysm growth is not always accessible. We here proposed a method to reconstruct the aneurysm growth time series directly from patient parameters. The prediction is based on data pairs of [patient parameters, patient aneurysm growth time history]. To obtain the mapping from patient parameters to patient aneurysm growth time history, we first apply autoencoder to obtain a compact representation of the time series for each patient. Then a mapping is learned from patient parameters to the corresponding compact representation of time series via a five-layer neural network. Moving average and convolutional output layer are implemented to explicitly taking account the time dependency of the time series. Apart from that, we also propose to use prior knowledge about the mechanism of aneurysm growth to improve the time series reconstruction results. The prior physics-based knowledge is incorporated as constraints for the optimization problem associated with autoencoder. The model can handle both algebraic and differential constraints. Our results show that including physical model information about the data will not significantly improve the time series reconstruction results if the training data is error-free. However, in the case of training data with noise and bias error, incorporating physical model constraints can significantly improve the predicted time series.

Paperid: 1411, https://arxiv.org/pdf/2510.04264.pdf

Abstract:
The Alternating Current Power Flow (ACPF) problem forces a trade-off between the speed of data-driven models and the reliability of analytical solvers. This paper introduces a hybrid framework that synergizes a Graph Neural Network (GNN) with the Implicit Z-Bus Recursive (IZR) method, a robust, non-iterative solver for radial distribution networks. The framework employs a physics-informed GNN for rapid initial predictions and invokes the IZR solver as a failsafe for stressed cases identified by a two-stage trigger. A failure is defined as any solution with a maximum power mismatch exceeding 0.1 p.u., a significant operational deviation. On a challenging test set of 7,500 stressed scenarios for the IEEE 33-bus system, the GNN-only model failed on 13.11 % of cases. In contrast, the hybrid framework identified all potential failures, delegating them to the IZR solver to achieve a 0.00 % failure rate, empirically matching the 100 % success rate of the analytical solver on this specific test set. An expanded ablation study confirms that both physics-informed training and Z-bus sensitivity features are critical, collaboratively reducing the GNN's failure rate from 98.72 % (data-only) to 13.11 %. The hybrid approach demonstrates a pragmatic path to achieving the empirical reliability of an analytical solver while leveraging GNN speed, enabling a significant increase in the number of scenarios analyzable in near real-time.

Paperid: 1412, https://arxiv.org/pdf/2510.03278.pdf

Abstract:
Bayesian physics-informed neural networks (B-PINNs) merge data with governing equations to solve differential equations under uncertainty. However, interpreting uncertainty and overconfidence in B-PINNs requires care due to the poorly understood effects the physical constraints have on the network; overconfidence could reflect warranted precision, enforced by the constraints, rather than miscalibration. Motivated by the need to further clarify how individual physical constraints shape these networks, we introduce a scalable, matrix-free Laplace framework that decomposes the posterior Hessian into contributions from each constraint and provides metrics to quantify their relative influence on the loss landscape. Applied to the Van der Pol equation, our method tracks how constraints sculpt the network's geometry and shows, directly through the Hessian, how changing a single loss weight non-trivially redistributes curvature and effective dominance across the others.

Paperid: 1413, https://arxiv.org/pdf/2510.02551.pdf

Abstract:
This paper presents a novel approach to finding analytical approximations for bright-soliton solutions in strongly magnetized plasmas. We leverage Physics-Informed Symbolic Regression (PISR) to discover closed-form expressions for the vector potential and number density profiles, governed by a reduced-order model derived from Maxwell-fluid equations. The PISR framework combines symbolic regression with physics-based constraints, boundary conditions, and available simulation data to guide the search for solutions. We demonstrate the effectiveness of the approach by rediscovering approximate solutions consistent with previously published numerical results, showcasing the potential of PISR for reducing simulation costs of reduced-order models in plasma physics.

Paperid: 1414, https://arxiv.org/pdf/2509.24327.pdf

Abstract:
We examine the use of a novel variant of Physics-Informed Neural Networks to predict cosmological parameters from recent supernovae and baryon acoustic oscillations (BAO) datasets. Our machine learning framework generates uncertainty estimates for target variables and the inferred unknown parameters of the underlying PDE descriptions. Built upon a hybrid of the principles of Evidential Deep Learning, Physics-Informed Neural Networks, Bayesian Neural Networks and Gaussian Processes, our model enables learning of the posterior distribution of the unknown PDE parameters through standard gradient-descent based training. We apply our model to an up-to-date BAO dataset (Bousis et al. 2024) calibrated with the CMB-inferred sound horizon, and the Pantheon$+$ Sne Ia distances (Scolnic et al. 2018), examining the relative effectiveness and mutual consistency among the standard $Î$CDM, $w$CDM and $Î_s$CDM models. Unlike previous results arising from the standard approach of minimizing an appropriate $Ï^2$ function, the posterior distributions for parameters in various models trained purely on Pantheon$+$ data were found to be largely contained within the $2Ï$ contours of their counterparts trained on BAO data. Their posterior medians for $h_0$ were within about $2Ï$ of one another, indicating that our machine learning-guided approach provides a different measure of the Hubble tension.

Paperid: 1415, https://arxiv.org/pdf/2509.22760.pdf

Abstract:
We develop a physics-informed neural network (PINN) framework for parameter estimation in fractional-order SEIRD epidemic models. By embedding the Caputo fractional derivative into the network residuals via the L1 discretization scheme, our method simultaneously reconstructs epidemic trajectories and infers both epidemiological parameters and the fractional memory order $Î±$. The fractional formulation extends classical integer-order models by capturing long-range memory effects in disease progression, incubation, and recovery. Our framework learns the fractional memory order $Î±$ as a trainable parameter while simultaneously estimating the epidemiological rates $(Î², Ï, Î³, Î¼)$. A composite loss combining data misfit, physics residuals, and initial conditions, with constraints on positivity and population conservation, ensures both accuracy and biological consistency. Tests on synthetic Mpox data confirm reliable recovery of $Î±$ and parameters under noise, while applications to COVID-19 show that optimal $Î±\in (0, 1]$ captures memory effects and improves predictive performance over the classical SEIRD model. This work establishes PINNs as a robust tool for learning memory effects in epidemic dynamics, with implications for forecasting, control strategies, and the analysis of non-Markovian epidemic processes.

Paperid: 1416, https://arxiv.org/pdf/2509.21751.pdf

Abstract:
Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, but its cost function is difficult to optimize and computationally intensive. We propose a neural field-based reformulation in which the full spatiotemporal state is represented as a continuous function parameterized by a neural network. This reparameterization removes the time-sequential dependency of classical 4DVAR, enabling parallel-in-time optimization in parameter space. Physical constraints are incorporated directly through a physics-informed loss, simplifying implementation and reducing computational cost. We evaluate the method on the two-dimensional incompressible Navier--Stokes equations with Kolmogorov forcing. Compared to a baseline 4DVAR implementation, the neural reparameterized variants produce more stable initial condition estimates without spurious oscillations. Notably, unlike most machine learning-based approaches, our framework does not require access to ground-truth states or reanalysis data, broadening its applicability to settings with limited reference information.

Paperid: 1417, https://arxiv.org/pdf/2509.18744.pdf

Abstract:
We introduce a novel convolutional neural network architecture, termed the \emph{periodic CNN}, which incorporates periodic boundary conditions into the convolutional layers. Our main theoretical contribution is a rigorous approximation theorem: periodic CNNs can approximate ridge functions depending on $d-1$ linear variables in a $d$-dimensional input space, while such approximation is impossible in lower-dimensional ridge settings ($d-2$ or fewer variables). This result establishes a sharp characterization of the expressive power of periodic CNNs. Beyond the theory, our findings suggest that periodic CNNs are particularly well-suited for problems where data naturally admits a ridge-like structure of high intrinsic dimension, such as image analysis on wrapped domains, physics-informed learning, and materials science. The work thus both expands the mathematical foundation of CNN approximation theory and highlights a class of architectures with surprising and practically relevant approximation capabilities.

Paperid: 1418, https://arxiv.org/pdf/2509.12253.pdf

Abstract:
Non-invasive glucose monitors often fail outside the lab because existing datasets ignore hardware noise, environmental drift, and person-to-person physiology. We introduce the first ultra-realistic near-infrared (NIR) simulator that injects 12-bit ADC quantisation, +/-0.1% LED ageing, photodiode dark noise, 15-45 C temperature, 30-90% relative humidity, contact-pressure variation, Fitzpatrick I-VI melanin, and diurnal glucose excursions (dawn phenomenon). Using this platform (rho glucose-NIR = 0.21), we benchmark six methods: Enhanced Beer-Lambert (physics-engineered ridge regression), three physics-informed neural networks (PINNs), a selective radiative-transfer PINN, and a shallow DNN. Beer-Lambert achieves 13.6 mg/dL RMSE, 95.8% Clarke-A and 93.8% +/-15% accuracy with only 56 parameters and 0.01 ms inference, outperforming the best PINN (14.6 mg/dL) and the SDNN baseline (35.1 mg/dL). Results overturn the assumption that deeper PINNs dominate and supply an open, end-to-end reference stack for rapid prototyping of embedded optical glucose sensors.

Paperid: 1419, https://arxiv.org/pdf/2509.11911.pdf

Abstract:
Characterizing the environmental interactions of quantum systems is a critical bottleneck in the development of robust quantum technologies. Traditional tomographic methods are often data-intensive and struggle with scalability. In this work, we introduce a novel framework for performing Lindblad tomography using Physics-Informed Neural Networks (PINNs). By embedding the Lindblad master equation directly into the neural network's loss function, our approach simultaneously learns the quantum state's evolution and infers the underlying dissipation parameters from sparse, time-series measurement data. Our results show that PINNs can reconstruct both the system dynamics and the functional form of unknown noise parameters, presenting a sample-efficient and scalable solution for quantum device characterization. Ultimately, our method produces a fully-differentiable digital twin of a noisy quantum system by learning its governing master equation.

Paperid: 1420, https://arxiv.org/pdf/2509.10565.pdf

Abstract:
Accurate and fast thermophysical models are needed to embed vapor-liquid equilibrium (VLE) calculations in design, optimization, and control loops for cryogenic mixtures. This study asks whether a structure-aware graph neural network (GNN; DimeNet++) trained on GERG-2008/CoolProp data can act as a practical surrogate for an equation of state (EoS). We generate a ternary dataset over 90-200 K and pressures to 100 bar, curate it with a 15% density filter (reducing 5,200 states to 1,516), and pair each state with a lightweight molecular-dynamics snapshot to supply structural features. The model is trained in two stages; pretraining on residual Helmholtz energy followed by pressure fine-tuning with a stability penalty; and evaluated via single-phase interpolation tests, solver-free derivative-quality diagnostics, an audited VLE driver, and a latency benchmark. Within its regime, the GNN interpolates single-phase properties reasonably well; however, the VLE driver accepts no GNN equilibria on tested binaries (all plotted VLE points are CoolProp fallback or the solver fails), and diagnostic probes reveal jagged P(V|T) paths and thermal-stability flags concentrated in dense/cold regions, indicating insufficient derivative smoothness/consistency for robust equilibrium solving. An end-to-end timing comparison shows no single-phase speed advantage relative to CoolProp (tens of milliseconds vs sub-millisecond). We conclude that, as configured, the surrogate in this study is not solver-ready for VLE and offers no runtime benefit; its value is methodological, delineating failure modes and pointing to remedies such as physics-informed training signals and targeted coverage near phase boundaries.

Paperid: 1421, https://arxiv.org/pdf/2509.05886.pdf

Abstract:
A surrogate model is developed to predict the convective heat transfer coefficient of liquid sodium (Na) flow within rectangular miniature heat sinks. Initially, kernel-based machine learning techniques and shallow neural network are applied to a dataset with 87 Nusselt numbers for liquid sodium in rectangular miniature heat sinks. Subsequently, a self-supervised physics-informed neural network and transfer learning approach are used to increase the estimation performance. In the self-supervised physics-informed neural network, an additional layer determines the weight the of physics in the loss function to balance data and physics based on their uncertainty for a better estimation. For transfer learning, a shallow neural network trained on water is adapted for use with Na. Validation results show that the self-supervised physics-informed neural network successfully estimate the heat transfer rates of Na with an error margin of approximately +8%. Using only physics for regression, the error remains between 5% to 10%. Other machine learning methods specify the prediction mostly within +8%. High-fidelity modeling of turbulent forced convection of liquid metals using computational fluid dynamics (CFD) is both time-consuming and computationally expensive. Therefore, machine learning based models offer a powerful alternative tool for the design and optimization of liquid-metal-cooled miniature heat sinks.

Paperid: 1422, https://arxiv.org/pdf/2509.01963.pdf

Abstract:
In response to recent FIA regulations reducing Formula 1 team wind tunnel hours (from 320 hours for last-place teams to 200 hours for championship leaders) and strict budget caps of 135 million USD per year, more efficient aerodynamic development tools are needed by teams. Conventional computational fluid dynamics (CFD) simulations, though offering high fidelity results, require large computational resources with typical simulation durations of 8-24 hours per configuration analysis. This article proposes a Physics-Informed Neural Network (PINN) for the fast prediction of Formula 1 front wing aerodynamic coefficients. The suggested methodology combines CFD simulation data from SimScale with first principles of fluid dynamics through a hybrid loss function that constrains both data fidelity and physical adherence based on Navier-Stokes equations. Training on force and moment data from 12 aerodynamic features, the PINN model records coefficient of determination (R-squared) values of 0.968 for drag coefficient and 0.981 for lift coefficient prediction while lowering computational time. The physics-informed framework guarantees that predictions remain adherent to fundamental aerodynamic principles, offering F1 teams an efficient tool for the fast exploration of design space within regulatory constraints.

Paperid: 1423, https://arxiv.org/pdf/2508.12996.pdf

Abstract:
Transformer neural networks are increasingly used for physics-based problems. In data-driven PDE surrogates, training samples from varying boundary and initial conditions can cause erratic losses and spiky gradients; in physics-informed neural networks (PINNs), stiff composite losses amplify this effect. We introduce Kourkoutas-Beta, an Adam-style optimizer where the fixed second-moment discount beta2 is replaced by a layer-wise dynamic value driven by a bounded ``sunspike'' ratio: the current pooled gradient norm divided by an exponential moving average (EMA) of past norms, squashed to the interval [0,1). Spikes lower beta2 toward beta2_min; calm phases keep it near beta2_max. Options include leaky-AMSGrad (decay), trust-region clipping (max_ratio), adaptive tiny terms, and several bias-correction modes ``none'', ``beta2max'', ``exact'). With all features off and bias_correction=``none'', the method is exactly Adam. We test on four settings: (i) a Transformer PDE surrogate (Heat2D), (ii) a 3D PINN for heat conduction (Heat3D), (iii) a lightweight MLX synthetic task with jitter and rare-trigger bursts, and (iv) a character-level Transformer on 30 MB of enwik8 (small-enwik8). Kourkoutas-Beta improves stability and final loss versus fixed-beta2 Adam. On small-enwik8 it lowers bits-per-character by about 38% vs Adam-0.95 and about 58% vs Adam-0.999 over 10 seeds, with smaller variance. The method remains drop-in, with runtime overhead comparable to Adam in testbeds A-C and within single-digit percent in testbed D. It preserves Adam-style convergence guarantees while improving robustness under spiky gradients.

Paperid: 1424, https://arxiv.org/pdf/2508.12314.pdf

Abstract:
We present a novel interdisciplinary framework that bridges synchronization theory and multi-agent AI systems by adapting the Kuramoto model to describe the collective dynamics of heterogeneous AI agents engaged in complex task execution. By representing AI agents as coupled oscillators with both phase and amplitude dynamics, our model captures essential aspects of agent specialization, influence, and communication within networked systems. We introduce an order parameter to quantify the degree of coordination and synchronization, providing insights into how coupling strength, agent diversity, and network topology impact emergent collective behavior. Furthermore, we formalize a detailed correspondence between Chain-of-Thought prompting in AI reasoning and synchronization phenomena, unifying human-like iterative problem solving with emergent group intelligence. Through extensive simulations on all-to-all and deterministic scale-free networks, we demonstrate that increased coupling promotes robust synchronization despite heterogeneous agent capabilities, reflecting realistic collaborative AI scenarios. Our physics-informed approach establishes a rigorous mathematical foundation for designing, analyzing, and optimizing scalable, adaptive, and interpretable multi-agent AI systems. This work opens pathways for principled orchestration of agentic AI and lays the groundwork for future incorporation of learning dynamics and adaptive network architectures to further enhance system resilience and efficiency.

Paperid: 1425, https://arxiv.org/pdf/2508.05921.pdf

Abstract:
Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme Learning Machines (PIELMs), a convex variant of neural PDE solvers, and show that asymptotic components in governing equations can produce highly ill-conditioned activation matrices, severely limiting convergence. We introduce Shifted Gaussian Encoding, a simple yet effective activation filtering step that increases matrix rank and expressivity while preserving convexity. Our method extends the solvable range of Peclet numbers in steady advection-diffusion equations by over two orders of magnitude, achieves up to six orders lower error on multi-frequency function learning, and fits high-fidelity image vectors more accurately and faster than deep networks with over a million parameters. This work highlights that conditioning, not depth, is often the bottleneck in scientific neural solvers and that simple architectural changes can unlock substantial gains.

Paperid: 1426, https://arxiv.org/pdf/2508.04590.pdf

Abstract:
Physics-Informed Neural Network (PINN) is a deep learning framework that integrates the governing equations underlying data into a loss function. In this study, we consider the problem of estimating state variables and parameters in epidemiological models governed by ordinary differential equations using PINNs. In practice, not all trajectory data corresponding to the population described by models can be measured. Learning PINNs to estimate the unmeasured state variables and epidemiological parameters using partial measurements is challenging. Accordingly, we introduce the concept of algebraic observability of the state variables. Specifically, we propose augmenting the unmeasured data based on algebraic observability analysis. The validity of the proposed method is demonstrated through numerical experiments under three scenarios in the context of epidemiological modelling. Specifically, given noisy and partial measurements, the accuracy of unmeasured states and parameter estimation of the proposed method is shown to be higher than that of the conventional methods. The proposed method is also shown to be effective in practical scenarios, such as when the data corresponding to certain variables cannot be reconstructed from the measurements.

Paperid: 1427, https://arxiv.org/pdf/2507.12468.pdf

Abstract:
Digital Twins (DTs) are virtual representations of physical systems synchronized in real time through Internet of Things (IoT) sensors and computational models. In industrial applications, DTs enable predictive maintenance, fault diagnosis, and process optimization. This paper explores the mathematical foundations of DTs, hybrid modeling techniques, including Physics Informed Neural Networks (PINNs), and their implementation in industrial scenarios. We present key applications, computational tools, and future research directions.

Paperid: 1428, https://arxiv.org/pdf/2507.12218.pdf

Abstract:
Many physical systems are described by partial differential equations (PDEs), and solving these equations and estimating their coefficients or boundary conditions (BCs) from observational data play a crucial role in understanding the associated phenomena. Recently, a machine learning approach known as physics-informed neural network, which solves PDEs using neural networks by minimizing the sum of residuals from the PDEs, BCs, and data, has gained significant attention in the scientific community. In this study, we investigate a physics-informed linear model (PILM) that uses linear combinations of basis functions to represent solutions, thereby enabling an analytical representation of optimal solutions. The PILM was formulated and verified for illustrative forward and inverse problems including cases with uncertain BCs. Furthermore, the PILM was applied to estimate crustal strain rates using geodetic data. Specifically, physical regularization that enforces elastic equilibrium on the velocity fields was compared with mathematical regularization that imposes smoothness constraints. From a Bayesian perspective, mathematical regularization exhibited superior performance. The PILM provides an analytically solvable framework applicable to linear forward and inverse problems, underdetermined systems, and physical regularization.

Paperid: 1429, https://arxiv.org/pdf/2507.11799.pdf

Abstract:
This paper presents a neural network (NN)-based solver for an integro-differential equation that models shrinkage-induced fragmentation. The proposed method directly maps input parameters to the corresponding probability density function without numerically solving the governing equation, thereby significantly reducing computational costs. Specifically, it enables efficient evaluation of the density function in Monte Carlo simulations while maintaining accuracy comparable to or even exceeding that of conventional finite difference schemes. Validatation on synthetic data demonstrates both the method's computational efficiency and predictive reliability. This study establishes a foundation for the data-driven inverse analysis of fragmentation and suggests the potential for extending the framework beyond pre-specified model structures.

Paperid: 1430, https://arxiv.org/pdf/2507.09733.pdf

Abstract:
We present the first foundational AI model for universal physics simulation that learns physical laws directly from boundary-condition data without requiring a priori equation encoding. Traditional physics-informed neural networks (PINNs) and finite-difference methods necessitate explicit mathematical formulation of governing equations, fundamentally limiting their generalizability and discovery potential. Our sketch-guided diffusion transformer approach reimagines computational physics by treating simulation as a conditional generation problem, where spatial boundary conditions guide the synthesis of physically accurate steady-state solutions. By leveraging enhanced diffusion transformer architectures with novel spatial relationship encoding, our model achieves direct boundary-to-equilibrium mapping and is generalizable to diverse physics domains. Unlike sequential time-stepping methods that accumulate errors over iterations, our approach bypasses temporal integration entirely, directly generating steady-state solutions with SSIM > 0.8 while maintaining sub-pixel boundary accuracy. Our data-informed approach enables physics discovery through learned representations analyzable via Layer-wise Relevance Propagation (LRP), revealing emergent physical relationships without predetermined mathematical constraints. This work represents a paradigm shift from AI-accelerated physics to AI-discovered physics, establishing the first truly universal physics simulation framework.

Paperid: 1431, https://arxiv.org/pdf/2507.08906.pdf

Abstract:
Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression function must satisfy. In the first part of this dissertation, we analyze the statistical properties of PIML methods. In particular, we study the properties of physics-informed neural networks (PINNs) in terms of approximation, consistency, overfitting, and convergence. We then show how PIML problems can be framed as kernel methods, making it possible to apply the tools of kernel ridge regression to better understand their behavior. In addition, we use this kernel formulation to develop novel physics-informed algorithms and implement them efficiently on GPUs. The second part explores industrial applications in forecasting energy signals during atypical periods. We present results from the Smarter Mobility challenge on electric vehicle charging occupancy and examine the impact of mobility on electricity demand. Finally, we introduce a physics-constrained framework for designing and enforcing constraints in time series, applying it to load forecasting and tourism forecasting in various countries.

Paperid: 1432, https://arxiv.org/pdf/2507.04940.pdf

Abstract:
This paper establishes an explicit $L^2$-estimate for weak solutions $u$ to linear elliptic equations in divergence form with general coefficients and external source term $f$, stating that the $L^2$-norm of $u$ over $U$ is bounded by a constant multiple of the $L^2$-norm of $f$ over $U$. In contrast to classical approaches based on compactness arguments, the proposed method, which employs a divergence-free transformation method, provides a computable and explicit constant $C>0$. The $L^2$-estimate remains robust even when there is no zero-order term, and the analysis further demonstrates that the constant $C>0$ decreases as the diffusion coefficient or the zero-order term increases. These quantitative results provide a rigorous foundation for applications such as a posteriori error estimates in Physics-Informed Neural Networks (PINNs), where explicit error bounds are essential.

Paperid: 1433, https://arxiv.org/pdf/2506.23505.pdf

Abstract:
Underwater object detection is crucial for autonomous navigation, environmental monitoring, and marine exploration, but it is severely hampered by light attenuation, turbidity, and occlusion. Current methods balance accuracy and computational efficiency, but they have trouble deploying in real-time under low visibility conditions. Through the integration of physics-informed augmentation techniques with the YOLOv12 architecture, this study advances underwater detection. With Residual ELAN blocks to preserve structural features in turbid waters and Area Attention to maintain large receptive fields for occluded objects while reducing computational complexity. Underwater optical properties are addressed by domain-specific augmentations such as turbulence adaptive blurring, biologically grounded occlusion simulation, and spectral HSV transformations for color distortion. Extensive tests on four difficult datasets show state-of-the-art performance, with Brackish data registering 98.30% mAP at 142 FPS. YOLOv12 improves occlusion robustness by 18.9%, small-object recall by 22.4%, and detection precision by up to 7.94% compared to previous models. The crucial role of augmentation strategy is validated by ablation studies. This work offers a precise and effective solution for conservation and underwater robotics applications.

Paperid: 1434, https://arxiv.org/pdf/2506.20181.pdf

Abstract:
We develop a principled framework for discovering causal structure in partial differential equations (PDEs) using physics-informed neural networks and counterfactual perturbations. Unlike classical residual minimization or sparse regression methods, our approach quantifies operator-level necessity through functional interventions on the governing dynamics. We introduce causal sensitivity indices and structural deviation metrics to assess the influence of candidate differential operators within neural surrogates. Theoretically, we prove exact recovery of the causal operator support under restricted isometry or mutual coherence conditions, with residual bounds guaranteeing identifiability. Empirically, we validate the framework on both synthetic and real-world datasets across climate dynamics, tumor diffusion, and ocean flows. Our method consistently recovers governing operators even under noise, redundancy, and data scarcity, outperforming standard PINNs and DeepONets in structural fidelity. This work positions causal PDE discovery as a tractable and interpretable inference task grounded in structural causal models and variational residual analysis.

Paperid: 1435, https://arxiv.org/pdf/2506.13554.pdf

Abstract:
We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs approximate solutions to partial differential equations (PDEs) by minimizing residual losses over sampled collocation and boundary points. We formalize both operator-level and variational notions of consistency, proving that residual minimization in Sobolev norms leads to convergence in energy and uniform norms under mild regularity. Deterministic stability bounds quantify how bounded perturbations to the network outputs propagate through the full composite loss, while probabilistic concentration results via McDiarmid's inequality yield sample complexity guarantees for residual-based generalization. A unified generalization bound links residual consistency, projection error, and perturbation sensitivity. Empirical results on elliptic, parabolic, and nonlinear PDEs confirm the predictive accuracy of our theoretical bounds across regimes. The framework identifies key structural principles, such as operator coercivity, activation smoothness, and sampling admissibility, that underlie robust and generalizable PINN training, offering principled guidance for the design and analysis of PDE-informed learning systems.

Paperid: 1436, https://arxiv.org/pdf/2506.09679.pdf

Abstract:
We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of geometric flow regularization. We augment latent spaces with geometric flows to control structure. Our techniques rely on adaptations of curvature and Ricci flow. We invent new geometric flows or discover them neurally and non-parametrically. All of our flows are solved using physics-informed learning. Traditional geometric meaning is traded for computing ability, but we maintain key geometric invariants, the primary of which are maintained, intrinsically-low structure, canonicity or a lack of irregularity, nontriviality due to sufficient lower bounds on curvature, and distortion of volume element, that develop quality in the inference stage. Our primary contributions are fourfold. We develop a loss based on Gaussian curvature using closed path circulation integration for surfaces, bypassing automatic differentiation of the Christoffel symbols through use of Stokes' theorem. We invent a new parametric flow derived from a linear version of the Gauss equation and a Riemannian decomposition for a custom tensor defined with a normal Hessian and Weyl tensor proxies. We develop two strategies based on time differentiation of functionals, one with a special case of scalar curvature for conformally-changed metrics, and another with harmonic maps, their energy, and induced metrics. Our methods, while diminished analytically, maintain overall integral latent structure. We showcase that curvature flows and the formulation of geometric structure in intermediary encoded settings enhance learning and overall zero-shot and adversarial fidelity.

Paperid: 1437, https://arxiv.org/pdf/2506.08036.pdf

Abstract:
This paper revisits Followerstopper, a phase-space-based control system that had demonstrated its ability to mitigate emergent traffic jams due to stop-and-go traffic during rush hour in the mixed-autonomy setting. Followerstopper was deployed on an autonomous vehicle. The controller attenuates the emanant traffic waves by regulating its velocity according to the relative distance and velocity of the leader car. While regulating the velocity, the controller also prevents the collision of the ego vehicle with the lead vehicle within the range specified by the controller's design parameter. The controller design is based on a configurable quadratic curve on relative distance-relative velocity phase-space that allows the transition of the regulated velocity from (i) no modification of input, (ii) decelerating to match the leader's velocity (iii) braking to avoid any imminent collision. In this paper, we explore the phase-space properties of Followerstopper and provide a detailed description of a nonlinear control law that regulates the reference input to Followerstopper within the physics-informed boundaries. We also provide a new discussion on the nominal control law that regulates the reference speed to Followerstopper to avoid unrealistic and unsafe acceleration.

Paperid: 1438, https://arxiv.org/pdf/2506.06308.pdf

Abstract:
Scientific machine learning (SciML) provides a structured approach to integrating physical knowledge into data-driven modeling, offering significant potential for advancing hydrological research. In recent years, multiple methodological families have emerged, including physics-informed machine learning, physics-guided machine learning, hybrid physics-machine learning, and data-driven physics discovery. Within each of these families, a proliferation of heterogeneous approaches has developed independently, often without conceptual coordination. This fragmentation complicates the assessment of methodological novelty and makes it difficult to identify where meaningful advances can still be made in the absence of a unified conceptual framework. This review, the first focused overview of SciML in hydrology, addresses these limitations by proposing a unified methodological framework for each SciML family, bringing together representative contributions into a coherent structure that fosters conceptual clarity and supports cumulative progress in hydrological modeling. Finally, we highlight the limitations and future opportunities of each unified family to guide systematic research in hydrology, where these methods remain underutilized.

Paperid: 1439, https://arxiv.org/pdf/2506.03161.pdf

Abstract:
Traffic congestion and collisions represent significant economic, environmental, and social challenges worldwide. Traditional traffic management approaches have shown limited success in addressing these complex, dynamic problems. To address the current research gaps, three potential tools are developed: a comprehensive 3D city-wide simulation environment that integrates both macroscopic and microscopic traffic dynamics; a collision model; and a reinforcement learning framework with custom reward functions prioritizing safety over efficiency. Unity game engine-based simulation is used for direct collision modeling. A custom reward enabled reinforcement learning method, proximal policy optimization (PPO) model, yields substantial improvements over baseline results, reducing the number of serious collisions, number of vehicle-vehicle collisions, and total distance travelled by over 3 times the baseline values. The model also improves fuel efficiency by 39% and reduces carbon emissions by 88%. Results establish feasibility for city-wide 3D traffic simulation applications incorporating the vision-zero safety principles of the Department of Transportation, including physics-informed, adaptable, realistic collision modeling, as well as appropriate reward modeling for real-world traffic signal light control towards reducing collisions, optimizing traffic flow and reducing greenhouse emissions.

Paperid: 1440, https://arxiv.org/pdf/2506.00951.pdf

Abstract:
We introduce a Physics-Informed Neural Networks(PINN) to solve a relativistic Burgers equation in the exterior domain of a Schwarzschild black hole. Our main contribution is a PINN architecture that is able to simulate shock wave formations in such curved spacetime, by training a shock-aware network block and introducing a Godunov-inspired residuals in the loss function. We validate our method with numerical experiments with different kinds of initial conditions. We show its ability to reproduce both smooth and discontinuous solutions in the context of general relativity.

Paperid: 1441, https://arxiv.org/pdf/2505.18169.pdf

Abstract:
Understanding and predicting human emotional and physiological states using wearable sensors has important applications in stress monitoring, mental health assessment, and affective computing. This study presents a novel Multi-Task Physics-Informed Neural Network (PINN) that performs Electrodermal Activity (EDA) prediction and emotion classification simultaneously, using the publicly available WESAD dataset. The model integrates psychological self-report features (PANAS and SAM) with a physics-inspired differential equation representing EDA dynamics, enforcing biophysically grounded constraints through a custom loss function. This loss combines EDA regression, emotion classification, and a physics residual term for improved interpretability. The architecture supports dual outputs for both tasks and is trained under a unified multi-task framework. Evaluated using 5-fold cross-validation, the model achieves an average EDA RMSE of 0.0362, Pearson correlation of 0.9919, and F1-score of 94.08 percent. These results outperform classical models such as SVR and XGBoost, as well as ablated variants like emotion-only and EDA-only models. In addition, the learned physical parameters including decay rate (alpha_0), emotional sensitivity (beta), and time scaling (gamma) are interpretable and stable across folds, aligning with known principles of human physiology. This work is the first to introduce a multi-task PINN framework for wearable emotion recognition, offering improved performance, generalizability, and model transparency. The proposed system provides a foundation for future interpretable and multimodal applications in healthcare and human-computer interaction.

Paperid: 1442, https://arxiv.org/pdf/2505.07222.pdf

Abstract:
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates statistical, algorithmic, and dynamical measures along three axes (regularity, randomness, and complexity) and situates them in a common conceptual space. We map statistical, algorithmic, and dynamical measures into this conceptual space, discussing their computational accessibility and approximability. This taxonomy reveals the deep challenges posed by uncomputability and highlights the emergence of modern data-driven methods (including autoencoders, latent dynamical models, symbolic regression, and physics-informed neural networks) as pragmatic approximations to classical complexity ideals. Latent spaces emerge as operational arenas where regularity extraction, noise management, and structured compression converge, bridging theoretical foundations with practical modeling in high-dimensional systems. We close by outlining implications for physics-informed AI and AI-guided discovery in complex physical systems, arguing that classical questions of complexity remain central to next-generation scientific modeling.

Paperid: 1443, https://arxiv.org/pdf/2505.01819.pdf

Abstract:
Deep learning has emerged as a powerful tool in scientific modeling, particularly for complex dynamical systems; however, accurately capturing age-structured population dynamics under policy-driven fertility changes remains a significant challenge due to the lack of effective integration between domain knowledge and long-term temporal dependencies. To address this issue, we propose two physics-informed deep learning frameworks--PINN and LSTM-PINN--that incorporate policy-aware fertility functions into a transport-reaction partial differential equation to simulate population evolution from 2024 to 2054. The standard PINN model enforces the governing equation and boundary conditions via collocation-based training, enabling accurate learning of underlying population dynamics and ensuring stable convergence. Building on this, the LSTM-PINN framework integrates sequential memory mechanisms to effectively capture long-range dependencies in the age-time domain, achieving robust training performance across multiple loss components. Simulation results under three distinct fertility policy scenarios-the Three-child policy, the Universal two-child policy, and the Separate two-child policy--demonstrate the models' ability to reflect policy-sensitive demographic shifts and highlight the effectiveness of integrating domain knowledge into data-driven forecasting. This study provides a novel and extensible framework for modeling age-structured population dynamics under policy interventions, offering valuable insights for data-informed demographic forecasting and long-term policy planning in the face of emerging population challenges.

Paperid: 1444, https://arxiv.org/pdf/2504.12949.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, their performance heavily relies on the strategy used to select training points. Conventional adaptive sampling methods, such as residual-based refinement, often require multi-round sampling and repeated retraining of PINNs, leading to computational inefficiency due to redundant points and costly gradient computations-particularly in high-dimensional or high-order derivative scenarios. To address these limitations, we propose RL-PINNs, a reinforcement learning(RL)-driven adaptive sampling framework that enables efficient training with only a single round of sampling. Our approach formulates adaptive sampling as a Markov decision process, where an RL agent dynamically selects optimal training points by maximizing a long-term utility metric. Critically, we replace gradient-dependent residual metrics with a computationally efficient function variation as the reward signal, eliminating the overhead of derivative calculations. Furthermore, we employ a delayed reward mechanism to prioritize long-term training stability over short-term gains. Extensive experiments across diverse PDE benchmarks, including low-regular, nonlinear, high-dimensional, and high-order problems, demonstrate that RL-PINNs significantly outperforms existing residual-driven adaptive methods in accuracy. Notably, RL-PINNs achieve this with negligible sampling overhead, making them scalable to high-dimensional and high-order problems.

Paperid: 1445, https://arxiv.org/pdf/2503.17368.pdf

Abstract:
Evolution-based protein structure prediction models have achieved breakthrough success in recent years. However, they struggle to generalize beyond evolutionary priors and on sequences lacking rich homologous data. Here we present a novel, out-of-domain benchmark based on sactipeptides, a rare class of ribosomally synthesized and post-translationally modified peptides (RiPPs) characterized by sulfur-to-$Î±$-carbon thioether bridges creating cross-links between cysteine residues and backbone. We evaluate recent models on predicting conformations compatible with these cross-links bridges for the 10 known sactipeptides with elucidated post-translational modifications. Crucially, the structures of 5 of them have not yet been experimentally resolved. This makes the task a challenging problem for evolution-based models, which we find exhibit limited performance (0.0% to 19.2% GDT-TS on sulfur-to-$Î±$-carbon distance). Our results point at the need for physics-informed models to sustain progress in biomolecular structure prediction.

Paperid: 1446, https://arxiv.org/pdf/2503.06436.pdf

Abstract:
Accurate tropical cyclone (TC) intensity prediction is crucial for mitigating storm hazards, yet its complex dynamics pose challenges to traditional methods. Here, we introduce a Physics-Informed Residual Neural Ordinary Differential Equation (PIR-NODE) model to precisely forecast TC intensity evolution. This model leverages the powerful non-linear fitting capabilities of deep learning, integrates residual connections to enhance model depth and training stability, and explicitly models the continuous temporal evolution of TC intensity using Neural ODEs. Experimental results in the SHIPS dataset demonstrate that the PIR-NODE model achieves a significant improvement in 24-hour intensity prediction accuracy compared to traditional statistical models and benchmark deep learning methods, with a 25. 2\% reduction in the root mean square error (RMSE) and a 19.5\% increase in R-square (R2) relative to a baseline of neural network. Crucially, the residual structure effectively preserves initial state information, and the model exhibits robust generalization capabilities. This study details the PIR-NODE model architecture, physics-informed integration strategies, and comprehensive experimental validation, revealing the substantial potential of deep learning techniques in predicting complex geophysical systems and laying the foundation for future refined TC forecasting research.

Paperid: 1447, https://arxiv.org/pdf/2502.13827.pdf

Abstract:
Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high overview of classification of the inverse problems method can be: i) Analytical, ii) Regularization, and iii) Bayesian inference methods. Even if there are straight links between them, we can say that the Bayesian inference based methods are the most powerful, as they give the possibility of accounting for prior knowledge and can account for errors and uncertainties in general. One of the main limitations stay in computational costs in particular for high dimensional imaging systems. Neural Networks (NN), and in particular Deep NNs (DNN), have been considered as a way to push farther this limit. Physics Informed Neural Networks (PINN) concept integrates physical laws with deep learning techniques to enhance the speed, accuracy and efficiency of the above mentioned problems. In this work, a new Bayesian framework for the concept of PINN (BPINN) is presented and discussed which includes the deterministic one if we use the Maximum A Posteriori (MAP) estimation framework. We consider two cases of supervised and unsupervised for training step, obtain the expressions of the posterior probability of the unknown variables, and deduce the posterior laws of the NN's parameters. We also discuss about the challenges of implementation of these methods in real applications.

Paperid: 1448, https://arxiv.org/pdf/2502.07425.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed for single PDEs, limiting their generalizability across different physical systems. In this work, we explore the potential of a foundation PINN model capable of solving multiple PDEs within a unified architecture. We investigate the efficacy of a single PINN framework trained on four distinct PDEs-the Simple Harmonic Oscillator (SHO), the 1D Heat Equation, the 1D Wave Equation, and the 2D Laplace Equation, demonstrating its ability to learn diverse physical dynamics. To enhance sample efficiency, we incorporate Active Learning (AL) using Monte Carlo (MC) Dropout-based uncertainty estimation, selecting the most informative training samples iteratively. We evaluate different active learning strategies, comparing models trained on 10%, 20%, 30%, 40%, and 50% of the full dataset, and analyze their impact on solution accuracy. Our results indicate that targeted uncertainty sampling significantly improves performance with fewer training samples, leading to efficient learning across multiple PDEs. This work highlights the feasibility of a generalizable PINN-based foundation model, capable of adapting to different physics-based problems without redesigning network architectures. Our findings suggest that multi-PDE PINNs with active learning can serve as an effective approach for reducing computational costs while maintaining high accuracy in physics-based deep learning applications.

Paperid: 1449, https://arxiv.org/pdf/2502.03963.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large number of training samples to achieve high accuracy, leading to increased computational costs. To address this issue, we propose Active Learning-Driven PINNs (AL-PINN), which integrates Uncertainty Quantification (UQ) and Active Learning (AL) strategies to optimize sample selection dynamically. AL-PINN utilizes Monte Carlo Dropout to estimate epistemic uncertainty in the model predictions, enabling the adaptive selection of high-uncertainty regions for additional training. This approach significantly enhances learning efficiency by focusing computational resources on the most informative data points. We evaluate AL-PINN on benchmark PDE problems with known analytical solutions and real-world WeatherBench climate data. Our results demonstrate that AL-PINN achieves comparable or superior accuracy compared to traditional PINNs while reducing the number of required training samples. The proposed framework is particularly beneficial for scientific and engineering applications where data collection is expensive or limited, such as climate modeling, medical simulations, and material science. Our findings highlight the potential of active learning in accelerating PINN-based PDE solvers while maintaining high accuracy and computational efficiency.

Paperid: 1450, https://arxiv.org/pdf/2501.10825.pdf

Abstract:
Estimating the material properties of thermal protection films is crucial for their effective design and application, particularly in high-temperature environments. This work presents a novel approach to determine the properties using uncertainty quantification simulations. We quantify uncertainty in the material properties for effective insulation by proposing a Bayesian distribution for them. Sampling from this distribution is performed using Monte Carlo simulations, which require repeatedly solving the predictive thermal model. To address the computational inefficiency of conventional numerical simulations, we develop a parametric Physics-Informed Neural Network (PINN) to solve the heat transfer problem. The proposed PINN significantly reduces computational time while maintaining accuracy, as verified against traditional numerical solutions. Additionally, we used the Sequential Monte Carlo (SMC) method to enable vectorized and parallel computations, further enhancing computational speedup. Our results demonstrate that integrating MCMC with PINN decreases computational time substantially compared to using standard numerical methods. Moreover, combining the SMC method with PINN yields multifold computational speedup, making this approach highly effective for the rapid and accurate estimation of material properties.

Paperid: 1451, https://arxiv.org/pdf/2501.04305.pdf

Abstract:
Adaptive physics-informed super-resolution diffusion is developed for non-invasive virtual diagnostics of the 6D phase space density of charged particle beams. An adaptive variational autoencoder (VAE) embeds initial beam condition images and scalar measurements to a low-dimensional latent space from which a 326 pixel 6D tensor representation of the beam's 6D phase space density is generated. Projecting from a 6D tensor generates physically consistent 2D projections. Physics-guided super-resolution diffusion transforms low-resolution images of the 6D density to high resolution 256x256 pixel images. Un-supervised adaptive latent space tuning enables tracking of time-varying beams without knowledge of time-varying initial conditions. The method is demonstrated with experimental data and multi-particle simulations at the HiRES UED. The general approach is applicable to a wide range of complex dynamic systems evolving in high-dimensional phase space. The method is shown to be robust to distribution shift without re-training.

Paperid: 1452, https://arxiv.org/pdf/2501.03254.pdf

Abstract:
This paper proposes an innovative method for predicting deformation in architected lattice structures that combines Physics-Informed Neural Networks (PINNs) with finite element analysis. A thorough study was carried out on FCC-based lattice beams utilizing five different materials (Structural Steel, AA6061, AA7075, Ti6Al4V, and Inconel 718) under varied edge loads (1000-10000 N). The PINN model blends data-driven learning with physics-based limitations via a proprietary loss function, resulting in much higher prediction accuracy than linear regression. PINN outperforms linear regression, achieving greater R-square (0.7923 vs 0.5686) and lower error metrics (MSE: 0.00017417 vs 0.00036187). Among the materials examined, AA6061 had the highest displacement sensitivity (0.1014 mm at maximum load), while Inconel718 had better structural stability.

Paperid: 1453, https://arxiv.org/pdf/2501.00288.pdf

Abstract:
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and kernel method. In this paper, we introduce a random feature based framework toward efficiently solving PDEs. Random feature method was originally proposed to approximate large-scale kernel machines and can be viewed as a shallow neural network as well. We provide an error analysis for our proposed method along with comprehensive numerical results on several PDE benchmarks. In contrast to the state-of-the-art solvers that face challenges with a large number of collocation points, our proposed method reduces the computational complexity. Moreover, the implementation of our method is simple and does not require additional computational resources. Due to the theoretical guarantee and advantages in computation, our approach is proven to be efficient for solving PDEs.

Paperid: 1454, https://arxiv.org/pdf/2412.18564.pdf

Abstract:
Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration process. The challenge lies in reducing the computational complexity while maintaining high accuracy for quick evaluations of multiple design alternatives. This research explores advanced methods, including surrogate models, reduced-order models (ROM), and multi-fidelity machine learning techniques, to achieve more efficient aircraft design evaluations. Specifically, the study investigates the application of Multi-fidelity Physics-Informed Neural Networks (MPINN) and autoencoders for manifold alignment, alongside the potential of Generative Adversarial Networks (GANs) for refining design geometries. Through a proof-of-concept task, the research demonstrates the ability to predict high-fidelity results from low-fidelity simulations, offering a path toward faster and more cost effective aircraft design iterations.

Paperid: 1455, https://arxiv.org/pdf/2412.15079.pdf

Abstract:
Model predictive control has emerged as an effective approach for real-time optimal control of connected and automated vehicles. However, nonlinear dynamics of vehicle and traffic systems make accurate modeling and real-time optimization challenging. Learning-based control offer a promising alternative, as they adapt to environment without requiring an explicit model. For learning control framework, an augmented state space system design is necessary since optimal control depends on both the ego vehicle's state and predicted states of other vehicles. This work develops a traffic adaptive augmented state space system that allows the control strategy to intelligently adapt to varying traffic conditions. This design ensures that while different vehicle trajectories alter initial conditions, the system dynamics remain independent of specific trajectories. Additionally, a physics-informed learning control framework is presented that combines value function from Bellman's equation with derivative of value functions from Pontryagin's Maximum Principle into a unified loss function. This method aims to reduce required training data and time while enhancing robustness and efficiency. The proposed control framework is applied to car-following scenarios in real-world data calibrated simulation environments. The results show that this learning control approach alleviates real-time computational requirements while achieving car-following behaviors comparable to model-based methods, resulting in 9% energy savings in scenarios not previously seen in training dataset.

Paperid: 1456, https://arxiv.org/pdf/2412.11526.pdf

Abstract:
Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge of the structure of output function, akin to physics-informed ML, but rooted in probabilistic principles rather than physical laws. The proposed approach integrates the probabilistic structure of the target variable (such as its cumulative distribution function) into the training process. This probabilistic information is obtained from historical data or estimated using structural reliability methods during experimental design. By embedding domain-specific probabilistic insights into the learning process, the technique enhances model accuracy and mitigates risks of overfitting and underfitting. Applications in regression, image denoising, and classification demonstrate the approach's effectiveness in addressing real-world problems.

Paperid: 1457, https://arxiv.org/pdf/2412.02222.pdf

Abstract:
This paper presents a physics-informed deep learning approach for predicting the replicator equation, allowing accurate forecasting of population dynamics. This methodological innovation allows us to derive governing differential or difference equations for systems that lack explicit mathematical models. We used the SINDy model first introduced by Fasel, Kaiser, Kutz, Brunton, and Brunt 2016a to get the replicator equation, which will significantly advance our understanding of evolutionary biology, economic systems, and social dynamics. By refining predictive models across multiple disciplines, including ecology, social structures, and moral behaviours, our work offers new insights into the complex interplay of variables shaping evolutionary outcomes in dynamic systems

Paperid: 1458, https://arxiv.org/pdf/2411.10483.pdf

Abstract:
Scientific machine learning (SciML) represents a significant advancement in integrating machine learning (ML) with scientific methodologies. At the forefront of this development are Physics-Informed Neural Networks (PINNs), which offer a promising approach by incorporating physical laws directly into the learning process, thereby reducing the need for extensive datasets. However, when data is limited or the system becomes more complex, PINNs can face challenges, such as instability and difficulty in accurately fitting the training data. In this article, we explore the capabilities and limitations of the DeepXDE framework, a tool specifically designed for implementing PINNs, in addressing both forward and inverse problems related to dielectric properties. Using RC circuit models to represent dielectric materials in HVDC systems, we demonstrate the effectiveness of PINNs in analyzing and improving system performance. Additionally, we show that applying a logarithmic transformation to the current (ln(I)) significantly enhances the stability and accuracy of PINN predictions, especially in challenging scenarios with sparse data or complex models. In inverse mode, however, we faced challenges in estimating key system parameters, such as resistance and capacitance, in more complex scenarios with longer time domains. This highlights the potential for future work in improving PINNs through transformations or other methods to enhance performance in inverse problems. This article provides pedagogical insights for those looking to use PINNs in both forward and inverse modes, particularly within the DeepXDE framework.

Paperid: 1459, https://arxiv.org/pdf/2411.02177.pdf

Abstract:
Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in the Landau gauge. By inserting the integral equation directly into the loss function, our PINN framework enables a single neural network to learn a continuous and differentiable representation of the mass function over a spectrum of momenta. Also, we benchmark our approach against a traditional numerical algorithm showing the main differences among them. Our novel strategy, which is expected to be extended to other quantum field theories, is the first step towards forefront applications of machine learning in high-level theoretical physics.

Paperid: 1460, https://arxiv.org/pdf/2410.18593.pdf

Abstract:
In an era increasingly focused on green computing and explainable AI, revisiting traditional approaches in theoretical and phenomenological particle physics is paramount. This project evaluates various machine learning (ML) algorithms-including Nearest Neighbors, Decision Trees, Random Forest, AdaBoost, Naive Bayes, Quadratic Discriminant Analysis (QDA), and XGBoost-alongside standard neural networks and a novel Physics-Informed Neural Network (PINN) for physics data analysis. We apply these techniques to a binary classification task that distinguishes the experimental viability of simulated scenarios based on Higgs observables and essential parameters. Through this comprehensive analysis, we aim to showcase the capabilities and computational efficiency of each model in binary classification tasks, thereby contributing to the ongoing discourse on integrating ML and Deep Neural Networks (DNNs) into physics research. In this study, XGBoost emerged as the preferred choice among the evaluated machine learning algorithms for its speed and effectiveness, especially in the initial stages of computation with limited datasets. However, while standard Neural Networks and Physics-Informed Neural Networks (PINNs) demonstrated superior performance in terms of accuracy and adherence to physical laws, they require more computational time. These findings underscore the trade-offs between computational efficiency and model sophistication.

Paperid: 1462, https://arxiv.org/pdf/2410.14134.pdf

Abstract:
Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem, we propose a parameter-efficient approach that fine-tunes pre-trained DeepONet models within the PINN framework (FTO-PINN), enabling more efficient meshless PDE solving. Specifically, we freeze the weights of the pre-trained DeepONet model and fine-tune the output of the branch net by incorporating a small number of new trainable parameters, which can be quickly determined using least-squares techniques. Additionally, we introduce trunk net expansions and low-rank adaptation strategies to further enhance the performance of FTO-PINN. The effectiveness of our proposed method is demonstrated through a series of numerical experiments across various types of PDEs. FTO-PINN significantly reduces the training time of vanilla PINNs while maintaining comparable accuracy, and outperforms DeepONet, which is pre-trained on general function data, in both fidelity and generalization capabilities.

Paperid: 1463, https://arxiv.org/pdf/2410.10137.pdf

Abstract:
We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework such that manifold geometries, subject to our geometric flow, embedded in Euclidean space are learned in the intermediary latent space developed by encoders and decoders. By tailoring the geometric flow in which the latent space evolves, we induce latent geometric properties of our choosing, which are reflected in empirical performance. We reformulate the traditional evidence lower bound (ELBO) loss with a considerate choice of prior. We develop a linear geometric flow with a steady-state regularizing term. This flow requires only automatic differentiation of one time derivative, and can be solved in moderately high dimensions in a physics-informed approach, allowing more expressive latent representations. We discuss how this flow can be formulated as a gradient flow, and maintains entropy away from metric singularity. This, along with an eigenvalue penalization condition, helps ensure the manifold is sufficiently large in measure, nondegenerate, and a canonical geometry, which contribute to a robust representation. Our methods focus on the modified multi-layer perceptron architecture with tanh activations for the manifold encoder-decoder. We demonstrate, on our datasets of interest, our methods perform at least as well as the traditional VAE, and oftentimes better. Our methods can outperform this and a VAE endowed with our proposed architecture, frequently reducing out-of-distribution (OOD) error between 15% to 35% on select datasets. We highlight our method on ambient PDEs whose solutions maintain minimal variation in late times. We provide empirical justification towards how we can improve robust learning for external dynamics with VAEs.

Paperid: 1464, https://arxiv.org/pdf/2410.07527.pdf

Abstract:
We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and accuracy and also implement several other recently proposed ideas from the literature. We successfully apply these to study the transient dynamics of synchronous generators. We also make progress towards applying PINNs to advanced inverter models. Such enhanced PINNs can allow us to accelerate high-fidelity simulations needed to ensure a stable and reliable renewables-rich future grid.

Paperid: 1465, https://arxiv.org/pdf/2410.04344.pdf

Abstract:
In this paper, we investigate the use of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural networks for each PDE, operator learning enables generalization across different PDEs without retraining. This study examines the performance of DeepONet in physics-informed training, focusing on two key aspects: (1) the approximation capabilities of deep branch and trunk networks, and (2) the generalization error in Sobolev norms. Our results demonstrate that deep branch networks provide substantial performance improvements, while trunk networks achieve optimal results when kept relatively simple. Furthermore, we derive a bound on the generalization error of DeepONet for solving nonlinear PDEs by analyzing the Rademacher complexity of its derivatives in terms of pseudo-dimension. This work bridges a critical theoretical gap by delivering rigorous error estimates. This paper fills a theoretical gap by providing error estimations for a wide range of physics-informed machine learning models and applications.

Paperid: 1466, https://arxiv.org/pdf/2410.04114.pdf

Abstract:
This work introduces a new neural model which follows the transport equation by design. A physical problem, the Taylor-Green vortex, defined on a bi-periodic domain, is used as a benchmark to evaluate the performance of both the standard physics-informed neural network and our model (transport-embedded neural network). Results exhibit that while the standard physics-informed neural network fails to predict the solution accurately and merely returns the initial condition for the entire time span, our model successfully captures the temporal changes in the physics, particularly for high Reynolds numbers of the flow. Additionally, the ability of our model to prevent false minima can pave the way for addressing multiphysics problems, which are more prone to false minima, and help them accurately predict complex physics.

Paperid: 1467, https://arxiv.org/pdf/2409.18397.pdf

Abstract:
Scientific machine learning (SciML) is an interdisciplinary research field that integrates machine learning, particularly deep learning, with physics theory to understand and predict complex natural phenomena. By incorporating physical knowledge, SciML reduces the dependency on observational data, which is often limited in the natural sciences. In this article, the fundamental concepts of SciML, its applications in seismology, and prospects are described. Specifically, two popular methods are mainly discussed: physics-informed neural networks (PINNs) and neural operators (NOs). PINNs can address both forward and inverse problems by incorporating governing laws into the loss functions. The use of PINNs is expanding into areas such as simultaneous solutions of differential equations, inference in underdetermined systems, and regularization based on physics. These research directions would broaden the scope of deep learning in natural sciences. NOs are models designed for operator learning, which deals with relationships between infinite-dimensional spaces. NOs show promise in modeling the time evolution of complex systems based on observational or simulation data. Since large amounts of data are often required, combining NOs with physics-informed learning holds significant potential. Finally, SciML is considered from a broader perspective beyond deep learning: statistical (or mathematical) frameworks that integrate observational data with physical principles to model natural phenomena. In seismology, mathematically rigorous Bayesian statistics has been developed over the past decades, whereas more flexible and scalable deep learning has only emerged recently. Both approaches can be considered as part of SciML in a broad sense. Theoretical and practical insights in both directions would advance SciML methodologies and thereby deepen our understanding of earthquake phenomena.

Paperid: 1468, https://arxiv.org/pdf/2409.16214.pdf

Abstract:
This paper introduces a Transformer-Enhanced Physics-Informed Neural Network (TE-PINN) designed for accurate quaternion-based orientation estimation in high-dynamic environments, particularly within the field of robotics. By integrating transformer networks with physics-informed learning, our approach innovatively captures temporal dependencies in sensor data while enforcing the fundamental physical laws governing rotational motion. TE-PINN leverages a multi-head attention mechanism to handle sequential data from inertial sensors, such as accelerometers and gyroscopes, ensuring temporal consistency. Simultaneously, the model embeds quaternion kinematics and rigid body dynamics into the learning process, aligning the network's predictions with mechanical principles like Euler's laws of motion. The physics-informed loss function incorporates the dynamics of angular velocity and external forces, enhancing the network's ability to generalize in complex scenarios. Our experimental evaluation demonstrates that TE-PINN consistently outperforms traditional methods such as Extended Kalman Filters (EKF) and LSTM-based estimators, particularly in scenarios characterized by high angular velocities and noisy sensor data. The results show a significant reduction in mean quaternion error and improved gyroscope bias estimation compared to the state-of-the-art. An ablation study further isolates the contributions of both the transformer architecture and the physics-informed constraints, highlighting the synergistic effect of both components in improving model performance. The proposed model achieves real-time performance on embedded systems typical of mobile robots, offering a scalable and efficient solution for orientation estimation in autonomous systems.

Paperid: 1469, https://arxiv.org/pdf/2409.06649.pdf

Abstract:
In this paper, we introduce the KANtrol framework, which utilizes Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving continuous time variables. We explain how Gaussian quadrature can be employed to approximate the integral parts within the problem, particularly for integro-differential state equations. We also demonstrate how automatic differentiation is utilized to compute exact derivatives for integer-order dynamics, while for fractional derivatives of non-integer order, we employ matrix-vector product discretization within the KAN framework. We tackle multi-dimensional problems, including the optimal control of a 2D heat partial differential equation. The results of our simulations, which cover both forward and parameter identification problems, show that the KANtrol framework outperforms classical MLPs in terms of accuracy and efficiency.

Paperid: 1470, https://arxiv.org/pdf/2409.05030.pdf

Abstract:
We establish a unified theoretical framework addressing the stability, consistency, and convergence of neural networks under realistic training conditions, specifically, in the presence of non-IID data, geometric constraints, and embedded physical laws. For standard supervised learning with dependent data, we derive uniform stability bounds for gradient-based methods using mixing coefficients and dynamic learning rates. In federated learning with heterogeneous data and non-Euclidean parameter spaces, we quantify model inconsistency via curvature-aware aggregation and information-theoretic divergence. For Physics-Informed Neural Networks (PINNs), we rigorously prove perturbation stability, residual consistency, Sobolev convergence, energy stability for conservation laws, and convergence under adaptive multi-domain refinements. Each result is grounded in variational analysis, compactness arguments, and universal approximation theorems in Sobolev spaces. Our theoretical guarantees are validated across parabolic, elliptic, and hyperbolic PDEs, confirming that residual minimization aligns with physical solution accuracy. This work offers a mathematically principled basis for designing robust, generalizable, and physically coherent neural architectures across diverse learning environments.

Paperid: 1471, https://arxiv.org/pdf/2409.03507.pdf

Abstract:
This paper introduces a novel methodology for solving distributed-order fractional differential equations using a physics-informed machine learning framework. The core of this approach involves extending the support vector regression (SVR) algorithm to approximate the unknown solutions of the governing equations during the training phase. By embedding the distributed-order functional equation into the SVR framework, we incorporate physical laws directly into the learning process. To further enhance computational efficiency, Gegenbauer orthogonal polynomials are employed as the kernel function, capitalizing on their fractional differentiation properties to streamline the problem formulation. Finally, the resulting optimization problem of SVR is addressed either as a quadratic programming problem or as a positive definite system in its dual form. The effectiveness of the proposed approach is validated through a series of numerical experiments on Caputo-based distributed-order fractional differential equations, encompassing both ordinary and partial derivatives.

Paperid: 1472, https://arxiv.org/pdf/2409.01293.pdf

Abstract:
This work builds off the manifold-constrained Gaussian process inference (MAGI) method for Bayesian parameter inference and trajectory reconstruction of ODE-based dynamical systems, focusing primarily on sparse and noisy data conditions. First, we introduce Pilot MAGI (pMAGI), a novel methodological upgrade on the base MAGI method that confers significantly-improved numerical stability, parameter inference, and trajectory reconstruction. Second, we demonstrate, for the first time to our knowledge, how one can combine MAGI-based methods with dynamical systems theory to provide probabilistic classifications of whether a system is stable or chaotic. Third, we demonstrate how pMAGI performs favorably in many settings against much more computationally-expensive and overparameterized methods. Fourth, we introduce Pilot MAGI Sequential Prediction (PMSP), a novel method building upon pMAGI that allows one to predict the trajectory of ODE-based dynamical systems multiple time steps into the future, given only sparse and noisy observations. We show that PMSP can output accurate future predictions even on chaotic dynamical systems and significantly outperform PINN-based methods. Overall, we contribute to the literature two novel methods, pMAGI and PMSP, that serve as Bayesian, uncertainty-quantified competitors to the Physics-Informed Neural Network.