Computational efficiency study of a micro-macro Markov chain Monte Carlo method for molecular dynamics

We study the numerical properties of a recently introduced micro-macro Markov chain Monte Carlo (mM-MCMC) scheme that accelerates sampling of Gibbs distributions when there is a time-scale separation between the complete (microscopic) molecular dynamics and the slow dynamics of a low dimensional reaction coordinate. The micro-macro 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 a proposal distribution; 3) reconstruct a molecular configuration that is consistent with the newly sampled macroscopic value. Here, we systematically study the impact of method parameters on the efficiency of the micro-macro Markov chain Monte Carlo method, namely the chosen macroscopic dynamics and the microscopic reconstruction distribution. We specifically investigate the impact of the macroscopic and reconstruction proposal distributions and their parameters on this efficiency on two prototypical molecular systems, a three-atom molecule and butane. We find, through detailed computational experiments, that the efficiency is largest when these proposal distributions are close to their time-invariant counterparts and that it is robust with respect to parameter changes.