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

TL;DR

This paper introduces a machine learning-based method to control the mean exit time of stochastic dynamical systems by computing quasipotentials and designing controllers, with demonstrated effectiveness in numerical experiments.

Contribution

It develops a neural network approach to compute quasipotentials and an iterative algorithm to design controllers for desired mean exit times in stochastic systems.

Findings

Neural network accurately computes global quasipotential.

The control strategy effectively achieves target mean exit times.

The method identifies most probable transition paths.

Abstract

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