| Learning chaotic systems from noisy data via multi-step optimization and adaptive training | |
Zhang, Lei1,2; Tang, Shaoqiang3; He GW(何国威)1,2
| |
| Corresponding Author | He, Guowei([email protected]) |
| Source Publication | CHAOS
 |
| 2022-12-01 | |
| Volume | 32Issue:12Pages:16 |
| ISSN | 1054-1500 |
| Abstract | 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 |
| Indexed By | SCI |
| Language | 英语 |
| WOS ID | WOS:000895881300001 |
| WOS Keyword | IDENTIFICATION ; REGRESSION ; FRAMEWORK ; DISCOVERY ; EQUATIONS |
| WOS Research Area | Mathematics ; Physics |
| WOS Subject | Mathematics, Applied ; Physics, Mathematical |
| Funding Project | National Natural Science Foundation of China (NSFC) Basic Science Center Program[11988102] ; National Natural Science Foundation of China (NSFC)[12202451] |
| Funding Organization | National Natural Science Foundation of China (NSFC) Basic Science Center Program ; National Natural Science Foundation of China (NSFC) |
| Classification | 一类 |
| Ranking | 1 |
| Contributor | He, Guowei |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/91214 |
| Collection | 非线性力学国家重点实验室 |
| Affiliation | 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 |
| Recommended Citation 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.Rp_Au:He, Guowei |
| 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. |
| Files in This Item: | Download All | |||||
| File Name/Size | DocType | Version | Access | License | ||
| Jp2022FA043_2022_Lea（2127KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment