VPNets: Volume-preserving neural networks for learning source-free dynamics

doi:10.1016/j.cam.2022.114523

CSpace

	VPNets: Volume-preserving neural networks for learning source-free dynamics
	Zhu, Aiqing 1,2; Zhu, Beibei 3; Zhang, Jiawei 1,2; Tang, Yifa 1,2; Liu, Jian 4,5
	2022-12-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	416 页码:12
摘要	We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. We propose three modules and combine them to obtain two network architectures, coined R-VPNet and LA-VPNet. The distinct feature of the proposed models is that they are intrinsic volume-preserving. In addition, the corresponding approximation theorems are proved, which theoretically guarantee the expressivity of the proposed VPNets to learn source-free dynamics. The effectiveness, generalization ability and structure-preserving property of the VP-Nets are demonstrated by numerical experiments. (C) 2022 Elsevier B.V. All rights reserved.
关键词	Deep learning Neural networks Discovery of dynamics Source-free dynamics Volume-preserving
DOI	10.1016/j.cam.2022.114523
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[11775222] ; National Natural Science Foundation of China[11901564] ; National Natural Science Foundation of China[12171466] ; Geo-Algorithmic Plasma Simulator (GAPS) Project
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000888195600001
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60563
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Jian
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China 4.Univ Sci & Technol China, Sch Nucl Sci & Technol, Hefei 230026, Anhui, Peoples R China 5.Qilu Univ Technol, Shandong Comp Sci Ctr, Adv Algorithm Joint Lab, Jinan 250014, Shandong, Peoples R China
推荐引用方式 GB/T 7714	Zhu, Aiqing,Zhu, Beibei,Zhang, Jiawei,et al. VPNets: Volume-preserving neural networks for learning source-free dynamics[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2022,416:12.
APA	Zhu, Aiqing,Zhu, Beibei,Zhang, Jiawei,Tang, Yifa,&Liu, Jian.(2022).VPNets: Volume-preserving neural networks for learning source-free dynamics.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,416,12.
MLA	Zhu, Aiqing,et al."VPNets: Volume-preserving neural networks for learning source-free dynamics".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 416(2022):12.