Action Functional Gradient Descent algorithm for estimating escape paths in Stochastic Chemical Reaction Networks

TL;DR

This paper introduces an action functional gradient descent algorithm based on Hamilton-Jacobi theory to efficiently estimate escape paths in stochastic chemical reaction networks, independent of system dimensionality.

Contribution

The authors develop a novel variational algorithm for escape path estimation that leverages Hamilton-Jacobi theory, enabling scalable and accurate analysis of complex stochastic systems.

Findings

Algorithm performs well against traditional methods like shooting and stochastic simulation.

The method is independent of system dimensionality and converges towards the continuum limit.

Applicable across disciplines including chemistry, biology, and control theory.

Abstract

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic stochastic chemical reaction network that exhibits multiple fixed points. The design of our algorithm is such that it is independent of the underlying dimensionality of the system, the discretization control parameters are updated towards the continuum limit, and there is an easy-to-calculate measure for the correctness of its solution. We consider several applications of the algorithm and verify them against computationally expensive means such as the shooting method and stochastic simulation. While we employ theoretical techniques from mathematical physics, numerical optimization and chemical reaction network theory, we hope that our work finds practical applications with an inter-disciplinary audience including chemists, biologists, optimal control theorists and game theorists.