Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise

doi:10.1088/1674-1056/aca7ee

中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50501-050501.doi: 10.1088/1674-1056/aca7ee

Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise

Linghongzhi Lu(陆凌弘志)¹, Yang Li(李扬)², and Xianbin Liu(刘先斌)^1,†

1 State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2 School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

收稿日期:2022-10-09 修回日期:2022-11-17 接受日期:2022-12-02 出版日期:2023-04-21 发布日期:2023-05-05
通讯作者: Xianbin Liu E-mail:xbliu@nuaa.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12172167), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise

Linghongzhi Lu(陆凌弘志)¹, Yang Li(李扬)², and Xianbin Liu(刘先斌)^1,†

1 State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2 School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2022-10-09 Revised:2022-11-17 Accepted:2022-12-02 Online:2023-04-21 Published:2023-05-05
Contact: Xianbin Liu E-mail:xbliu@nuaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12172167), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

摘要/Abstract

摘要： Massive data from observations, experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models. We present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussian α-stable Lévy noise. More explicitly, firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers-Moyal formulas. Then the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the process. Three examples are then given to demonstrate the feasibility. This approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.

关键词: data-driven modelling, noise-induced transitions, Lévy noise, Kramers-Moyal formuas

Abstract: Massive data from observations, experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models. We present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussian α-stable Lévy noise. More explicitly, firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers-Moyal formulas. Then the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the process. Three examples are then given to demonstrate the feasibility. This approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.

Key words: data-driven modelling, noise-induced transitions, Lévy noise, Kramers-Moyal formuas

中图分类号: (Computational methods in statistical physics and nonlinear dynamics)

05.10.-a

05.10.Gg (Stochastic analysis methods) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)

Linghongzhi Lu(陆凌弘志), Yang Li(李扬), and Xianbin Liu(刘先斌). Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise[J]. 中国物理B, 2023, 32(5): 50501-050501.

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Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise

Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussian α-stable Lévy noise

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