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

• Published in: Communications in nonlinear science & numerical simulation 2023-11, Vol.126, p.107425, Article 107425
• Main Authors: Li, Yang, Yuan, Shenglan, Xu, Shengyuan
• Format: Article
• Language: English
• Subjects: Machine learning; Mean exit time; Quasipotential; Stochastic control
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2023.107425

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 the help of the effective Hamilton–Jacobi scheme and the trained neural network. Numerical experiments with various dimensions and structures demonstrate that our control strategy is effective and sufficiently accurate. •A strategy to control mean exit time of general stochastic dynamical systems is proposed.•A neural network architecture to compute the global quasipotential function is designed.•The most probable path between metastable attractors is computed based on the trained neural network.