Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning

The mean exit time escaping basin of attraction in the presence white noise is practical importance various scientific fields. In this work, we propose a strategy to control general stochastic dynamical systems achieve desired value based on quasipotential concept and machine learning. Specifically, develop neural network architecture compute global function. Then design systematic iterated numerical algorithm calculate controller for given time. Moreover, identify most probable path between metastable attractors with help effective Hamilton–Jacobi scheme trained network. Numercal experiments dimensions structures demonstrate that our sufficiently accurate.