Simulating Stochastic Dynamics Using Large Time Steps

TL;DR

This paper introduces a field theoretic method to efficiently simulate long-time stochastic dynamics of complex systems using larger time steps, significantly reducing computational effort for rare transition events.

Contribution

A novel analytical approach that averages short-time fluctuations to create an effective theory enabling larger simulation time steps for long-time dynamics.

Findings

Effective theory reproduces original long-time dynamics

Time steps can be increased by a factor of ~100

Method improves efficiency for rare conformational transitions

Abstract

We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and long time scales and both Molecular Dynamics (MD) or Monte Carlo (MC) simulations are generally inefficient. Using a field theoretic approach, we perform analytically the average over the short-time stochastic fluctuations. This way, we obtain an effective theory, which generates the same long-time dynamics of the original theory, but has a lower time resolution power. Such an approach is used to develop an improved version of the MC algorithm, which is particularly suitable to investigate the dynamics of rare conformational transitions. In the specific case of molecular systems at room temperature, we show that elementary integration time steps used to simulate the effective theory can be chosen a factor ~100 larger than those used in the original theory. Our results are illustrated and tested on a simple system, characterized by a rugged energy landscape.