Efficiency and Parameter Selection of a micro-macro Markov chain Monte Carlo method for molecular dynamics

TL;DR

This paper analyzes the efficiency and parameter choices of a micro-macro MCMC method designed to accelerate molecular dynamics sampling by leveraging time-scale separation, with experiments on small molecules.

Contribution

It investigates how different parameters affect the efficiency of the mM-MCMC method in molecular dynamics simulations.

Findings

Parameter choices significantly impact sampling efficiency

Macroscopic proposal distributions influence convergence speed

Reconstruction distribution quality affects microscopic sampling accuracy

Abstract

We recently introduced a mM-MCMC scheme that is able to accelerate the sampling of Gibbs distributions when there is a time-scale separation between the complete molecular dynamics and the slow dynamics of a low dimensional reaction coordinate. The mM-MCMC Markov chain works in three steps: 1) compute the reaction coordinate value associated to the current molecular state; 2) generate a new macroscopic proposal using some approximate macroscopic distribution; 3) reconstruct a molecular configuration that is consistent with the newly sampled macroscopic value. There are a number of method parameters that impact the efficiency of the mM-MCMC method. On the macroscopic level, the proposal- and approximate macroscopic distributions are important, while on the microscopic level the reconstruction distribution is of significant importance. In this manuscript, we will investigate the impact of these parameters on the efficiency of the mM-MCMC method on two molecules: a simple three-atom molecule and butane.