Learning chaotic systems from noisy data via multi-step optimization and adaptive training

doi:10.1063/5.0114542

CORC > 力学研究所 > 中国科学院力学研究所 > 非线性力学国家重点实验室

	Learning chaotic systems from noisy data via multi-step optimization and adaptive training
	Zhang, Lei 2,3; Tang, Shaoqiang 1; He, Guowei 2,3
刊名	CHAOS
	2022-12-01
卷号	32 期号:12 页码:16
ISSN号	1054-1500
DOI	10.1063/5.0114542
通讯作者	He, Guowei(hgw@lnm.imech.ac.cn)
英文摘要	A data-driven sparse identification method is developed to discover the underlying governing equations from noisy measurement data through the minimization of Multi-Step-Accumulation (MSA) in error. The method focuses on the multi-step model, while conventional sparse regression methods, such as the Sparse Identification of Nonlinear Dynamics method (SINDy), are one-step models. We adopt sparse representation and assume that the underlying equations involve only a small number of functions among possible candidates in a library. The new development in MSA is to use a multi-step model, i.e., predictions from an approximate evolution scheme based on initial points. Accordingly, the loss function comprises the total error at all time steps between the measured series and predicted series with the same initial point. This enables MSA to capture the dynamics directly from the noisy measurements, resisting the corruption of noise. By use of several numerical examples, we demonstrate the robustness and accuracy of the proposed MSA method, including a two-dimensional chaotic map, the logistic map, a two-dimensional damped oscillator, the Lorenz system, and a reduced order model of a self-sustaining process in turbulent shear flows. We also perform further studies under challenging conditions, such as noisy measurements, missing data, and large time step sizes. Furthermore, in order to resolve the difficulty of the nonlinear optimization, we suggest an adaptive training strategy, namely, by gradually increasing the length of time series for training. Higher prediction accuracy is achieved in an illustrative example of the chaotic map by the adaptive strategy. Published under an exclusive license by AIP Publishing.
资助项目	National Natural Science Foundation of China (NSFC) Basic Science Center Program[11988102] ; National Natural Science Foundation of China (NSFC)[12202451]
WOS关键词	IDENTIFICATION ; REGRESSION ; FRAMEWORK ; DISCOVERY ; EQUATIONS
WOS研究方向	Mathematics ; Physics
语种	英语
WOS记录号	WOS:000895881300001
资助机构	National Natural Science Foundation of China (NSFC) Basic Science Center Program ; National Natural Science Foundation of China (NSFC)
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/91213]
专题	力学研究所_非线性力学国家重点实验室
通讯作者	He, Guowei
作者单位	1.Peking Univ, Coll Engn, HEDPS & LTCS, Beijing 100871, Peoples R China 2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Lei,Tang, Shaoqiang,He, Guowei. Learning chaotic systems from noisy data via multi-step optimization and adaptive training[J]. CHAOS,2022,32(12):16.
APA	Zhang, Lei,Tang, Shaoqiang,&He, Guowei.(2022).Learning chaotic systems from noisy data via multi-step optimization and adaptive training.CHAOS,32(12),16.
MLA	Zhang, Lei,et al."Learning chaotic systems from noisy data via multi-step optimization and adaptive training".CHAOS 32.12(2022):16.