Year: 2021
Type: preprint
Abstract: Identifying hidden dynamics from observed data is a significant and challenging task in a wide range of applications. Recently, the combination of linear multistep methods (LMMs) and deep learning has been successfully employed to discover dynamics, whereas a complete convergence analysis of this approach is still under development. In this work, we consider the deep network-based LMMs for the discovery of dynamics. We put forward error estimates for these methods using the approximation property of deep networks. It indicates, for certain families of LMMs, that the $\ell^2$ grid error is bounded by the sum of $O(h^p)$ and the network approximation error, where $h$ is the time step size and $p$ is the local truncation error order. Numerical results of several physically relevant examples are provided to demonstrate our theory.
Source: arXiv (Cornell University)
Authors: Du, Qiang, Gu, Yiqi, Yang, Haizhao, Zhou, Chao
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Mathematical and Numerical Analysis of Asymptotically Compatible Discretization of Nonlocal Models, G4970230818, CAREER: Deep Learning Based Scientific Computing: Mathematical Theory and Algorithms, GOALI: Collaborative Research: Model-Predictive Safety Systems for Predictive Detection of Operation Hazards, 关于几个带数据分析成本的金融数学问题以及深度学习数值方法
OpenAlex ID: W3136934051