KMS Of Academy of mathematics and systems sciences, CAS
OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle | |
Yu, Haijun1,2; Tian, Xinyuan1,2; Weinan, E.3,4; Li, Qianxiao5,6 | |
2021-11-23 | |
发表期刊 | PHYSICAL REVIEW FLUIDS |
ISSN | 2469-990X |
卷号 | 6期号:11页码:32 |
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. |
DOI | 10.1103/PhysRevFluids.6.114402 |
收录类别 | SCI |
语种 | 英语 |
资助项目 | NNSFC[91852116] ; NNSFC[11771439] ; China Science Challenge Project[TZ2018001] ; NUS PYP program |
WOS研究方向 | Physics |
WOS类目 | Physics, Fluids & Plasmas |
WOS记录号 | WOS:000723134400003 |
出版者 | AMER PHYSICAL SOC |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/59641 |
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.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, NCMIS & LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Princeton Univ, Dept Math, Princeton, NJ 08544 USA 4.Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA 5.Natl Univ Singapore, Dept Math, Singapore 119077, Singapore 6.ASTAR, Inst High Performance Comp, Singapore 138632, Singapore |
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. |
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