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In this paper, we present large deviation theory that characterizes theexponential estimate for rare events of stochastic dynamical systems in thelimit of weak noise. We aim to consider next-to-leading-order approximation formore accurate calculation of mean exit time via computing large deviationprefactors with the research efforts of machine learning. More specifically, wedesign a neural network framework to compute quasipotential, most probablepaths and prefactors based on the orthogonal decomposition of vector field. Wecorroborate the higher effectiveness and accuracy of our algorithm with apractical example. Numerical experiments demonstrate its powerful function inexploring internal mechanism of rare events triggered by weak randomfluctuations.

Computing large deviation prefactors of stochastic dynamical systems based on machine learning