OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

doi:10.1103/PhysRevFluids.6.114402

	OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle
	Yu, Haijun 1,6; Tian, Xinyuan 1,6; Weinan, E.4,5; Li, Qianxiao 2,3
刊名	PHYSICAL REVIEW FLUIDS
	2021-11-23
卷号	6 期号:11 页码:32
ISSN号	2469-990X
DOI	10.1103/PhysRevFluids.6.114402
英文摘要	We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parametrized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion, and external forces. For high-dimensional problems with a low-dimensional slow manifold, an autoencoder with metric-preserving regularization is introduced to find the low-dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Benard convection and learn Lorenz-like low-dimensional autonomous reduced-order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced-order models for forced-dissipative systems.
资助项目	NNSFC[91852116] ; NNSFC[11771439] ; China Science Challenge Project[TZ2018001] ; NUS PYP program
WOS研究方向	Physics
语种	英语
出版者	AMER PHYSICAL SOC
WOS记录号	WOS:000723134400003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59640]
专题	中国科学院数学与系统科学研究院
通讯作者	Yu, Haijun
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.ASTAR, Inst High Performance Comp, Singapore 138632, Singapore 3.Natl Univ Singapore, Dept Math, Singapore 119077, Singapore 4.Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA 5.Princeton Univ, Dept Math, Princeton, NJ 08544 USA 6.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS & LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Yu, Haijun,Tian, Xinyuan,Weinan, E.,et al. OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle[J]. PHYSICAL REVIEW FLUIDS,2021,6(11):32.
APA	Yu, Haijun,Tian, Xinyuan,Weinan, E.,&Li, Qianxiao.(2021).OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle.PHYSICAL REVIEW FLUIDS,6(11),32.
MLA	Yu, Haijun,et al."OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle".PHYSICAL REVIEW FLUIDS 6.11(2021):32.