Discovering transition phenomena from data of stochastic dynamical systems with Lévy noise

Yubin Lu, Jinqiao Duan


It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the investigation of nonlinear phenomena whose mathematical models are unavailable. The purpose of this present work is to extract information about transition phenomena (e.g., mean exit time and escape probability) from data of stochastic differential equations with non-Gaussian Lévy noise. As a tool in describing dynamical systems, the Koopman semigroup transforms a nonlinear system into a linear system, but at the cost of elevating a finite dimensional problem into an infinite dimensional one. In spite of this, using the relation between the stochastic Koopman semigroup and the infinitesimal generator of a stochastic differential equation, we learn the mean exit time and escape probability from data. Specifically, we first obtain a finite dimensional approximation of the infinitesimal generator by an extended dynamic mode decomposition algorithm. Then, we identify the drift coefficient, diffusion coefficient, and anomalous diffusion coefficient for the stochastic differential equation. Finally, we compute the mean exit time and escape probability by finit...Continue Reading


Jul 29, 2015·Proceedings of the National Academy of Sciences of the United States of America·Alexandre J Chorin, Fei Lu
Apr 2, 2016·Proceedings of the National Academy of Sciences of the United States of America·Steven L BruntonJ Nathan Kutz
Sep 28, 2017·Physical Review. E·Constantino A GarcíaDavid G Márquez
Jan 20, 2018·Physical Review. E·Naoya TakeishiTakehisa Yairi
Jul 1, 2019·The Journal of Chemical Physics·Erik H ThiedeJonathan Weare
Oct 23, 2019·Proceedings of the National Academy of Sciences of the United States of America·Kathleen ChampionSteven L Brunton

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