Machine learning for prediction with missing dynamics
Harlim, John1; Jiang, Shixiao W.2; Liang, Senwei3,4; Yang, Haizhao3
2021-03-01
发表期刊JOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
EISSN1090-2716
卷号428页码:#VALUE!
DOI10.1016/j.jcp.2020.109922
摘要This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to approximate a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics. We demonstrate the effectiveness of the proposed framework with a strong convergence error bound of the resolved variables up to finite time and numerical tests on prototypical models in various scientific domains. These include the 57-mode barotropic stress models with multiscale interactions that mimic the blocked and unblocked patterns observed in the atmosphere, the nonlinear Schrodinger equation which found many applications in physics such as optics and Bose-Einstein-Condense, the Kuramoto-Sivashinsky equation which spatiotemporal chaotic pattern formation models trapped-ion modes in plasma and phase dynamics in reaction-diffusion systems. While many machine learning techniques can be used to validate the proposed framework, we found that recurrent neural networks outperform kernel regression methods in terms of recovering the trajectory of the resolved components and the equilibrium one-point and two-point statistics. This superb performance suggests that a recurrent neural network is an effective tool for recovering the missing dynamics that involves approximation of highdimensional functions. (c) 2020 Elsevier Inc. All rights reserved.
关键词Closure Modeling Missing dynamics Machine learning Long Short Term Memory
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收录类别SCI ; EI ; SCIE
语种英语
WOS研究方向Computer Science ; Physics
WOS类目Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号WOS:000612233800016
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS关键词KURAMOTO-SIVASHINSKY ; MODEL-REDUCTION ; TIME ; DRIVEN ; ERROR ; STABILITY ; EQUATIONS ; KERNEL ; BOUNDS ; FLOW
原始文献类型Article
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文献类型期刊论文
条目标识符https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/125764
专题数学科学研究所_PI研究组(P)_蒋诗晓组
通讯作者Harlim, John; Yang, Haizhao
作者单位1.Penn State Univ, Inst Computat & Data Sci, Dept Math, Dept Meteorol & Atmospher Sci, University Pk, PA 16802 USA;
2.ShanghaiTech Univ, Inst Math Sci, Shanghai 201210, Peoples R China;
3.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA;
4.Natl Univ Singapore, Dept Math, Singapore, Singapore
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Harlim, John,Jiang, Shixiao W.,Liang, Senwei,et al. Machine learning for prediction with missing dynamics[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2021,428:#VALUE!.
APA Harlim, John,Jiang, Shixiao W.,Liang, Senwei,&Yang, Haizhao.(2021).Machine learning for prediction with missing dynamics.JOURNAL OF COMPUTATIONAL PHYSICS,428,#VALUE!.
MLA Harlim, John,et al."Machine learning for prediction with missing dynamics".JOURNAL OF COMPUTATIONAL PHYSICS 428(2021):#VALUE!.
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