Exchanging replicas with unequal cost, infinitely and permanently

TL;DR

This paper introduces a parallelizable replica exchange method that handles replicas with unequal computational costs, using a new detailed-balance proof and an algorithm for infinite exchange rates, demonstrated with path sampling applications.

Contribution

It presents a novel replica exchange algorithm accommodating unequal costs and infinite exchange rates, with a new proof of detailed-balance and practical implementation in path sampling.

Findings

Effective parallelization of replica exchange with unequal costs

Infinite exchange rate achieved without factorial scaling

Successful application to path sampling systems

Abstract

We developed a replica exchange method that is effectively parallelizable even if the computational cost of the Monte Carlo moves in the parallel replicas are considerably different, for instance, because the replicas run on different type of processor units or because of the algorithmic complexity. To prove detailed-balance, we make a paradigm shift from the common conceptual viewpoint in which the set of parallel replicas represents a high-dimensional superstate, to an ensemble based criterion in which the other ensembles represent an environment that might or might not participate in the Monte Carlo move. In addition, based on a recent algorithm for computing permanents, we effectively increase the exchange rate to infinite without the steep factorial scaling as function of the number of replicas. We illustrate the effectiveness of the replica exchange methodology by combining it with a quantitative path sampling method, replica exchange transition interface sampling (RETIS), in which the costs for a Monte Carlo move can vary enormously as paths in a RETIS algorithm do not have the same length and the average path lengths tend to vary considerably for the different path ensembles that run in parallel. This combination, coined $\infty$RETIS, was tested on three model systems.