Computing large deviation prefactors of stochastic dynamical systems
  based on machine learning
Yang Li Shenglan Yuan Linghongzhi Lu Xianbin Liu
In this paper, we present large deviation theory that characterizes the
exponential estimate for rare events of stochastic dynamical systems in the
limit of weak noise. We aim to consider next-to-leading-order approximation for
more accurate calculation of mean exit time via computing large deviation
prefactors with the research efforts of machine learning. More specifically, we
design a neural network framework to compute quasipotential, most probable
paths and prefactors based on the orthogonal decomposition of vector field. We
corroborate the higher effectiveness and accuracy of our algorithm with a
practical example. Numerical experiments demonstrate its powerful function in
exploring internal mechanism of rare events triggered by weak random
fluctuations.