Solving multiscale dynamical systems by deep learning

作     者：Xu, Zhi-Qin John Yao, Junjie Yi, Yuxiao Hang, Liangkai Weinan, E. Zhang, Yaoyu Zhang, Tianhan 

作者机构：Institute of Natural Sciences School of Mathematical Sciences MOE-LSC and Qing Yuan Research Institute Shanghai Jiao Tong University China Shanghai Center for Brain Science and Brain-Inspired Technology China Center for Machine Learning Research School of Mathematical Sciences Peking University China AI for Science Institute Beijing China Department of Mechanics and Aerospace Engineering Southern University of Science and Technology China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Ordinary differential equations 

摘      要：Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often encounter severe efficiency bottlenecks. This paper introduces a novel DeePODE method, which consists of a global multiscale sampling method and a fitting by deep neural networks to handle multiscale systems. DeePODE’s primary contribution is to address the multiscale challenge of efficiently uncovering representative training sets by combining the Monte Carlo method and the ODE system’s intrinsic evolution without suffering from the curse of dimensionality. The DeePODE method is validated in multiscale systems from diverse areas, including a predator-prey model, a power system oscillation, a battery electrolyte auto-ignition, and turbulent flames. Our methods exhibit strong generalization capabilities to unseen conditions, highlighting the power of deep learning in modeling intricate multiscale dynamical processes across science and engineering domains. © 2024, CC BY.