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

doi:10.1063/5.0114542

IMECH-IR > 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 1,2; Tang, Shaoqiang 3; He GW(何国威)1,2
通讯作者	He, Guowei(hgw@lnm.imech.ac.cn)
发表期刊	CHAOS
	2022-12-01
卷号	32 期号:12 页码:16
ISSN	1054-1500
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.
DOI	10.1063/5.0114542
收录类别	SCI
语种	英语
WOS记录号	WOS:000895881300001
关键词[WOS]	IDENTIFICATION ; REGRESSION ; FRAMEWORK ; DISCOVERY ; EQUATIONS
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
资助项目	National Natural Science Foundation of China (NSFC) Basic Science Center Program[11988102] ; National Natural Science Foundation of China (NSFC)[12202451]
项目资助者	National Natural Science Foundation of China (NSFC) Basic Science Center Program ; National Natural Science Foundation of China (NSFC)
论文分区	一类
力学所作者排名	1
RpAuthor	He, Guowei
引用统计	被引频次：2[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/91214
专题	非线性力学国家重点实验室
作者单位	1.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China; 2.Univ Chinese Acad Sci, Sch Engn Sci, Beijing 100049, Peoples R China; 3.Peking Univ, Coll Engn, HEDPS & LTCS, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Lei,Tang, Shaoqiang,He GW. Learning chaotic systems from noisy data via multi-step optimization and adaptive training[J]. CHAOS,2022,32,12,:16.
APA	Zhang, Lei,Tang, Shaoqiang,&何国威.(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.

条目包含的文件		下载所有文件
文件名称/大小	文献类型	版本类型	开放类型	使用许可
Jp2022FA043_2022_Lea（2127KB）	期刊论文	出版稿	开放获取	CC BY-NC-SA	浏览下载