Data-driven computation for periodic stochastic differential equations

Abstract

Many stochastic differential equations in various applications like coupled neuronal oscillators are driven by time-periodic forces. In this paper, we extend several data-driven computational tools from autonomous Fokker-Planck equation to the time-periodic setting. This allows us to efficiently compute the time-periodic invariant probability measure using either grid-base method or artificial neural network solver, and estimate the speed of convergence towards the time-periodic invariant probability measure. We analyze the convergence of our algorithms and test their performances with several numerical examples.