中国物理B ›› 2023, Vol. 32 ›› Issue (5): 50501-050501.doi: 10.1088/1674-1056/aca7ee
Linghongzhi Lu(陆凌弘志)1, Yang Li(李扬)2, and Xianbin Liu(刘先斌)1,†
Linghongzhi Lu(陆凌弘志)1, Yang Li(李扬)2, and Xianbin Liu(刘先斌)1,†
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.
中图分类号: (Computational methods in statistical physics and nonlinear dynamics)