Discovering mean residence time and escape probability from data of stochastic dynamical systems

TL;DR

This paper introduces a data-driven method combining machine learning and stochastic dynamics to estimate mean residence time and escape probability in systems modeled by stochastic differential equations, aiding understanding of complex stochastic behaviors.

Contribution

It develops a novel approach that learns stochastic differential equations from data and quantifies key dynamical properties, bridging data-driven modeling with stochastic analysis.

Findings

Successfully estimates mean residence time from sample path data.

Accurately computes escape probabilities in complex stochastic systems.

Applicable to diverse systems modeled by stochastic differential equations.

Abstract

We present a method to learn mean residence time and escape probability from data modeled by stochastic differential equations. This method is a combination of machine learning from data (to extract stochastic differential equations as models) and stochastic dynamics (to quantify dynamical behaviors with deterministic tools). The goal is to learn and understand stochastic dynamics based on data. This method is applicable to sample path data collected from complex systems, as long as these systems can be modeled as stochastic differential equations.