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

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. Numercal experiments demonstrate that our control strategy is effective and sufficiently accurate.

Slow Manifolds for Stochastic Koper Models with Stable Lévy Noises

“…The orbits can escape from the region of the metastable equilibrium if we face random perturbation [35]. It is interesting to characterize the most probable transition from one metastable state to another [36,37].…”