SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems

doi:10.1016/j.neunet.2020.08.017

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	SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
	Jin, Pengzhan 1,2; Zhang, Zhen 3; Zhu, Aiqing 1,2; Tang, Yifa 1,2; Karniadakis, George Em 3
	2020-12-01
发表期刊	NEURAL NETWORKS
ISSN	0893-6080
卷号	132 页码:166-179
摘要	We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Correspondingly, we prove two new universal approximation theorems that demonstrate that SympNets can approximate arbitrary symplectic maps based on appropriate activation functions. We then perform several experiments including the pendulum, double pendulum and three-body problems to investigate the expressivity and the generalization ability of SympNets. The simulation results show that even very small size SympNets can generalize well, and are able to handle both separable and non-separable Hamiltonian systems with data points resulting from short or long time steps. In all the test cases, SympNets outperform the baseline models, and are much faster in training and prediction. We also develop an extended version of SympNets to learn the dynamics from irregularly sampled data. This extended version of SympNets can be thought of as a universal model representing the solution to an arbitrary Hamiltonian system. (c) 2020 Elsevier Ltd. All rights reserved.
关键词	Deep learning Physics-informed Dynamical systems Hamiltonian systems Symplectic maps Symplectic integrators
DOI	10.1016/j.neunet.2020.08.017
收录类别	SCI
语种	英语
资助项目	Major Project on New Generation of Artificial Intelligence from MOST of China[2018AAA0101002] ; National Natural Science Foundation of China[11771438] ; DOE, USA PhILMs project[DE-SC0019453]
WOS研究方向	Computer Science ; Neurosciences & Neurology
WOS类目	Computer Science, Artificial Intelligence ; Neurosciences
WOS记录号	WOS:000590619800015
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57811
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, Yifa; Karniadakis, George Em
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Brown Univ, Div Appl Math, Providence, RI 02912 USA
推荐引用方式 GB/T 7714	Jin, Pengzhan,Zhang, Zhen,Zhu, Aiqing,et al. SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems[J]. NEURAL NETWORKS,2020,132:166-179.
APA	Jin, Pengzhan,Zhang, Zhen,Zhu, Aiqing,Tang, Yifa,&Karniadakis, George Em.(2020).SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems.NEURAL NETWORKS,132,166-179.
MLA	Jin, Pengzhan,et al."SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems".NEURAL NETWORKS 132(2020):166-179.