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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 |
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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.
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Received: 09 October 2022
Revised: 17 November 2022
Accepted manuscript online: 02 December 2022
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PACS:
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05.10.-a
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(Computational methods in statistical physics and nonlinear dynamics)
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05.10.Gg
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(Stochastic analysis methods)
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05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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| Fund: 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). |
Corresponding Authors:
Xianbin Liu
E-mail: xbliu@nuaa.edu.cn
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Cite this article:
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 2023 Chin. Phys. B 32 050501
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