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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 |
ISSN | 0021-9991 |
EISSN | 1090-2716 |
卷号 | 428页码:#VALUE! |
DOI | 10.1016/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 |
URL | 查看原文 |
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 |
引用统计 | |
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 |
推荐引用方式 GB/T 7714 | 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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