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 | |
| Source Publication | PHYSICAL REVIEW FLUIDS
 |
| ISSN | 2469-990X |
| Volume | 6Issue:11Pages:32 |
| Abstract | 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 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NNSFC[91852116] ; NNSFC[11771439] ; China Science Challenge Project[TZ2018001] ; NUS PYP program |
| WOS Research Area | Physics |
| WOS Subject | Physics, Fluids & Plasmas |
| WOS ID | WOS:000723134400003 |
| Publisher | AMER PHYSICAL SOC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59641 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Yu, Haijun |
| Affiliation | 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 |
| Recommended Citation 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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