A deep learning method for computing mean exit time excited by weak Gaussian noise

Exit events induced by noise from the attracting domain containing a stable fixed point are ubiquitous phenomena in physical systems, wherein mean exit time is an important quantity which has been widely used in engineering, physical, chemical and biological fields. In this work, we devise a deep learning method to compute the mean exit time for dynamical systems excited by weak Gaussian noise. More specifically, we first derive a complete group of ordinary differential equations governing the most probable path, the quasipotential, and the prefactor along the path via WKB approximation. Then a neural network architechture is proposed to solve it in terms of automatic differentiation. The results of numerical experiments show the effectiveness and accuracy of the algorithm and imply its potential applications to discover the mechanisms of rare events triggered by random fluctuations in practical models.