Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning
This work addresses the control of exit times in stochastic systems, which is important in various scientific fields, but it appears to be an incremental improvement by integrating existing methods.
The authors tackled the problem of controlling the mean exit time for stochastic dynamical systems by proposing a strategy that combines the quasipotential concept with machine learning, achieving effective and sufficiently accurate control as demonstrated in numerical experiments.
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.