A data-driven approach for discovering stochastic dynamical systems with non-Gaussian Levy noise

PHYSICA D-NONLINEAR PHENOMENA

卷:417

Article

Li, Yang^1,2  Duan, Jinqiao² 

[1] Nanjing Univ Aeronaut & Astronaut, Coll Aerosp Engn, State Key Lab Mech & Control Mech Struct, 29 Yudao St, Nanjing 210016, Peoples R China

[2] IIT, Dept Appl Math, Coll Comp, Chicago, IL 60616 USA

关键词: Machine learning;    Data-driven approach;    Non-Gaussian Levy noise;    Stochastic dynamical systems;    Heavy-tailed fluctuations;    Rare events;   

DOI  :  10.1016/j.physd.2020.132830

来源: Elsevier

【 摘 要 】

With the rapid increase of valuable observational, experimental and simulating data for complex systems, much effort is being devoted to discovering governing laws underlying the evolution of these systems. However, the existing techniques are limited to extract governing laws from data as either deterministic differential equations or stochastic differential equations with Gaussian noise. In the present work, we develop a new data-driven approach to extract stochastic dynamical systems with non-Gaussian symmetric Levy noise, as well as Gaussian noise. First, we establish a feasible theoretical ramework, by expressing the drift coefficient, diffusion coefficient and jump measure (i.e., anomalous diffusion) for the underlying stochastic dynamical system in terms of sample paths data. We then design a numerical algorithm to compute the drift, diffusion coefficient and jump measure, and thus extract a governing stochastic differential equation with Gaussian and non-Gaussian noise. Finally, we demonstrate the efficacy and accuracy of our approach by applying to several prototypical one-, two- and three-dimensional systems. This new approach will become a tool in discovering governing dynamical laws from noisy data sets, from observing or simulating complex phenomena, such as rare events triggered by random fluctuations with heavy as well as light tail statistical features. (c) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free