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

作　　者：陆凌弘志 李扬 刘先斌 Linghongzhi Lu;Yang Li;Xianbin Liu(State Key Laboratory of Mechanics and Control for Mechanical Structures,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;School of Automation,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[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

出　　处：《Chinese Physics B》2023年第5期337-342,共6页中国物理B（英文版）

基　　金：the National Natural Science Foundation of China(Grant No.12172167);the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)。

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-Gaussianα-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 

分 类 号：O211.6[理学—概率论与数理统计]