An iterative action minimizing method for computing optimal paths in stochastic dynamical systems

TL;DR

This paper introduces an iterative numerical method to compute optimal transition paths and rates in stochastic differential systems by minimizing the effective action in a Hamiltonian framework, applicable to various stochastic models.

Contribution

The paper presents a novel iterative scheme for solving boundary value problems in Hamiltonian systems to find most probable transition paths in stochastic differential equations.

Findings

Successfully applied to nonlinear oscillators and epidemic models.

Capable of handling delay differential equations.

Validated through numerical experiments.

Abstract

We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic Hamiltonian system. The numerical method presented here involves using an iterative scheme for solving a two-point boundary value problem for the Hamiltonian system. We validate our method by applying it to both continuous stochastic systems, such as nonlinear oscillators governed by the Duffing equation, and finite discrete systems, such as epidemic problems, which are governed by a set of master equations. Furthermore, we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations.