We propose the attention-inspired numerical solver (AttNS), a concise method that helps the generalization and robustness issues faced by the AI-Hybrid numerical solver in solving differential equations due to limited data. AttNS is inspired by the effectiveness of attention modules in Residual Neural Networks (ResNet) in enhancing model generalization and robustness for conventional deep learning tasks. Drawing from the dynamical system perspective of ResNet, We seamlessly incorporate attention mechanisms into the design of numerical methods tailored for the characteristics of solving differential equations. Our results on benchmarks, ranging from high-dimensional problems to chaotic systems, showcase AttNS consistently enhancing various numerical solvers without any intricate model crafting. Finally, we analyze AttNS experimentally and theoretically, demonstrating its ability to achieve strong generalization and robustness while ensuring the convergence of the solver. This includes requiring less data compared to other advanced methods to achieve comparable generalization errors and better prevention of numerical explosion issues when solving differential equations.
Paperid:812
Authors:Yue Huang, Lichao Sun, Haoran Wang, Siyuan Wu, Qihui Zhang, Yuan Li, Chujie Gao, Yixin Huang, Wenhan Lyu, Yixuan Zhang, Xiner Li, Hanchi Sun, Zhengliang Liu, Yixin Liu, Yijue Wang, Zhikun Zhang, Bertie Vidgen, Bhavya Kailkhura, Caiming Xiong, Chaowei Xiao, Chunyuan Li, Eric P. Xing, Furong Huang, Hao Liu, Heng Ji, Hongyi Wang, Huan Zhang, Huaxiu Yao, Manolis Kellis, Marinka Zitnik, Meng Jiang, Mohit Bansal, James Zou, Jian Pei, Jian Liu, Jianfeng Gao, Jiawei Han, Jieyu Zhao, Jiliang Tang, Jindong Wang, Joaquin Vanschoren, John Mitchell, Kai Shu, Kaidi Xu, Kai-Wei Chang, Lifang He, Lifu Huang, Michael Backes, Neil Zhenqiang Gong, Philip S. Yu, Pin-Yu Chen, Quanquan Gu, Ran Xu, Rex Ying, Shuiwang Ji, Suman Jana, Tianlong Chen, Tianming Liu, Tianyi Zhou, William Yang Wang, Xiang Li, Xiangliang Zhang, Xiao Wang, Xing Xie, Xun Chen, Xuyu Wang, Yan Liu, Yanfang Ye, Yinzhi Cao, Yong Chen, Yue Zhao