Computing exit location distribution of stochastic dynamical systems with noncharacteristic boundary based on deep learning

Abstract

Rare events induced by random perturbations are ubiquitous phenomena in natural systems, where the exit location distribution is a significant quantity, and its computation is challenging. In this study, we compute the exit location distribution of stochastic dynamical systems with weak Gaussian noise for a noncharacteristic boundary based on deep learning and large deviation theory. First, we introduce the perturbation expressions of the prefactor and exit location distribution via Wentzel–Kramers–Brillouin approximation. We then design a deep learning method to compute the quasipotential, the prefactor, and the exit location distribution. Two examples are described to verify the effectiveness of the proposed algorithm. The findings of this study are expected to provide valuable insights into exploring the mechanisms of rare events triggered by random fluctuations.