String Method for Generalized Gradient Flows: Computation of Rare Events in Reversible Stochastic Processes

TL;DR

This paper introduces a numerical algorithm based on the string method to efficiently compute rare transition paths in reversible stochastic processes by leveraging their interpretation as generalized gradient flows.

Contribution

It extends the string method to reversible stochastic processes viewed as generalized gradient flows, enabling computation of rare event trajectories.

Findings

Metastable transitions correspond to heteroclinic orbits in the generalized gradient flow.

The proposed algorithm efficiently computes transition trajectories in configuration space.

The approach generalizes the string method beyond gradient diffusions.

Abstract

Rare transitions in stochastic processes can often be rigorously described via an underlying large deviation principle. Recent breakthroughs in the classification of reversible stochastic processes as gradient flows have led to a connection of large deviation principles to a generalized gradient structure. Here, we show that, as a consequence, metastable transitions in these reversible processes can be interpreted as heteroclinic orbits of the generalized gradient flow. This in turn suggests a numerical algorithm to compute the transition trajectories in configuration space efficiently, based on the string method traditionally restricted only to gradient diffusions.