Data-driven computation for periodic stochastic differential equations

TL;DR

This paper extends data-driven computational methods to time-periodic stochastic differential equations, enabling efficient calculation of invariant measures and convergence analysis using grid and neural network approaches.

Contribution

It introduces novel adaptations of autonomous Fokker-Planck tools for periodic SDEs, facilitating accurate and efficient computation of time-periodic invariant measures.

Findings

Successfully computed time-periodic invariant measures.

Demonstrated convergence of algorithms through numerical tests.

Compared performance of grid-based and neural network methods.

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.