"Swarm relaxation": Equilibrating a large ensemble of computer simulations

TL;DR

This paper introduces 'swarm relaxation', a method where running many independent simulations simultaneously can quickly reach equilibrium, significantly reducing wall-clock time for high-precision molecular simulations.

Contribution

The paper demonstrates that large ensembles of independent simulations can efficiently achieve equilibrium, enabling faster and more scalable molecular dynamics sampling.

Findings

Swarm relaxation confirms equilibrium within ~10 relaxation times.

It reduces wall-clock time by several hundred times compared to single long simulations.

Suitable for modern multi-processor computing systems.

Abstract

It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case of this strategy, in which we run a large ensemble of $M$ independent simulations (a "swarm"), each of which is relaxed to equilibrium. We show that if $M$ is of order $10^3$, we can monitor the swarm's relaxation to equilibrium, and confirm its attainment, within $\sim 10\bar\tau$, where $\bar\tau$ is the equilibrium relaxation time. As soon as a swarm of this size attains equilibrium, the ensemble of $M$ final microstates from each run is sufficient for the evaluation of most equilibrium properties without further sampling. This approach dramatically reduces the wall-clock time required, compared to a single long simulation, by a factor of several hundred, at the cost of an increase in the total computational effort by a small factor. It is also well-suited to modern computing systems having thousands of processors, and is a viable strategy for simulation studies that need to produce high-precision results in a minimum of wall-clock time. We present results obtained by applying this approach to several test cases.