Computing large deviation prefactors of stochastic dynamical systems based on machine learning
This work addresses the challenge of more precise rare event analysis in stochastic systems, which is incremental as it builds on existing large deviation theory with machine learning enhancements.
The paper tackles the problem of accurately calculating mean exit times for rare events in stochastic dynamical systems under weak noise by computing large deviation prefactors, using a neural network framework that demonstrates higher effectiveness and accuracy in numerical experiments.
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.