Navigating Phase Transitions with Path-Finding Algorithms: A Strategic Approach to Replica Exchange Monte Carlo

TL;DR

This paper introduces a novel graph-based optimization scheme using Dijkstra's algorithm to enhance replica exchange Monte Carlo efficiency by constructing optimal exchange paths, particularly near phase transitions.

Contribution

It presents a new method that systematically improves replica exchange efficiency by optimizing exchange paths using path-finding algorithms, applicable to systems with slow relaxation.

Findings

Speeds up sampling near critical points

Improves exchange efficiency systematically

Provides insights into relaxation dynamics control

Abstract

The replica exchange method is a powerful tool for overcoming slow relaxation in molecular simulations, but its efficiency depends strongly on the choice of the number and interval of replicas and their exchange probabilities. Here, we propose a new optimization scheme based on the Dijkstra algorithm that constructs an optimal exchange path by representing replicas and their exchange probabilities as a graph. Inspired by path-finding techniques widely used in computer science, including applications in game algorithms, our approach ensures that transitions follow a minimum entropy gradient path and effectively speeds up sampling even in systems exhibiting slow relaxation near critical points or phase transition regions. The method provides a systematic way to improve replica exchange efficiency and offers new insights into the control of relaxation dynamics, as demonstrated through applications to the solid-liquid phase transition of the Lennard-Jones bulk system.