KMS Of Academy of mathematics and systems sciences, CAS
| SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems | |
| Jin, Pengzhan1,2; Zhang, Zhen3; Zhu, Aiqing1,2; Tang, Yifa1,2; Karniadakis, George Em3 | |
| 2020-12-01 | |
| Source Publication | NEURAL NETWORKS
 |
| ISSN | 0893-6080 |
| Volume | 132Pages:166-179 |
| Abstract | 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. |
| Keyword | Deep learning Physics-informed Dynamical systems Hamiltonian systems Symplectic maps Symplectic integrators |
| DOI | 10.1016/j.neunet.2020.08.017 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science ; Neurosciences & Neurology |
| WOS Subject | Computer Science, Artificial Intelligence ; Neurosciences |
| WOS ID | WOS:000590619800015 |
| Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/57811 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Tang, Yifa; Karniadakis, George Em |
| Affiliation | 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 |
| Recommended Citation 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. |
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