The parallel replica method for computing equilibrium averages of Markov chains

TL;DR

The paper introduces the parallel replica method (ParRep), an algorithm leveraging parallel processing to efficiently compute equilibrium averages of Markov chains with metastability, validated through simulations and theoretical proof.

Contribution

It presents the ParRep algorithm, a novel parallel approach for analyzing metastable Markov chains, extending previous methods to a broader class of stochastic processes.

Findings

Numerical simulations confirm the method's consistency.

Theoretical proof of convergence in an idealized setting.

Demonstrates efficiency in exploring metastable states.

Abstract

An algorithm is proposed for computing equilibrium averages of Markov chains which suffer from metastability -- the tendency to remain in one or more subsets of state space for long time intervals. The algorithm, called the parallel replica method (or ParRep), uses many parallel processors to explore these subsets more efficiently. Numerical simulations on a simple model demonstrate consistency of the method. A proof of consistency is given in an idealized setting. The parallel replica method can be considered a generalization of A.F. Voter's parallel replica dynamics, originally developed to efficiently simulate metastable Langevin stochastic dynamics.