Affiliation:
1. School of Mathematics and Statistics and Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
2. Department of Applied Mathematics, College of Computing, Illinois Institute of Technology, Chicago, Illinois 60616, USA
Abstract
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained much attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical systems to stochastic dynamical systems, especially those driven by non-Gaussian multiplicative noise. However, many log-likelihood based algorithms that work well for Gaussian cases cannot be directly extended to non-Gaussian scenarios, which could have high errors and low convergence issues. In this work, we overcome some of these challenges and identify stochastic dynamical systems driven by [Formula: see text]-stable Lévy noise from only random pairwise data. Our innovations include (1) designing a deep learning approach to learn both drift and diffusion coefficients for Lévy induced noise with [Formula: see text] across all values, (2) learning complex multiplicative noise without restrictions on small noise intensity, and (3) proposing an end-to-end complete framework for stochastic system identification under a general input data assumption, that is, an [Formula: see text]-stable random variable. Finally, numerical experiments and comparisons with the non-local Kramers–Moyal formulas with the moment generating function confirm the effectiveness of our method.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
7 articles.
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