Model Reduction with Memory and the Machine Learning of Dynamical Systems

Ma, Chao1; Wang, Jianchun2; E, Weinan1,3

2019-04

10.4208/cicp.OA-2018-0269

Communications in Computational Physics   影响因子和分区

1815-2406

1991-7120

The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an important but nearly impossible task in developing a good reduced model. In this work, we explore a natural analogy between recurrent neural networks and the Mori-Zwanzig formalism to establish a systematic approach for developing reduced models with memory. Two training models-a direct training model and a dynamically coupled training model-are proposed and compared. We apply these methods to the Kuramoto-Sivashinsky equation and the Navier-Stokes equation. Numerical experiments show that the proposed method can produce reduced model with good performance on both short-term prediction and long-term statistical properties.

Model reduction Mori-Zwanzig recurrent neural networks

SCI

英语

其他

NSFC[91530322]

Physics

Physics, Mathematical

WOS:000455963100001

GLOBAL SCIENCE PRESS

Web of Science

1.Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA
2.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China
3.Beijing Inst Big Data Res, Beijing 100871, Peoples R China

Ma, Chao,Wang, Jianchun,E, Weinan. Model Reduction with Memory and the Machine Learning of Dynamical Systems[J]. Communications in Computational Physics,2019,25(4):947-962.

Ma, Chao,Wang, Jianchun,&E, Weinan.(2019).Model Reduction with Memory and the Machine Learning of Dynamical Systems.Communications in Computational Physics,25(4),947-962.

Ma, Chao,et al."Model Reduction with Memory and the Machine Learning of Dynamical Systems".Communications in Computational Physics 25.4(2019):947-962.