Efficient Monte Carlo sampling of metastable systems using non-local collective variable updates

TL;DR

This paper introduces a generalized Monte Carlo sampling algorithm using non-local collective variable updates, improving efficiency for complex molecular systems, especially with generative machine learning proposals.

Contribution

It extends existing non-local CV sampling methods to non-linear CVs and underdamped Langevin dynamics, demonstrating significant performance gains.

Findings

Substantial performance increase over overdamped Langevin methods

Algorithm proven to be reversible

Effective for systems with tens to hundreds of CVs

Abstract

Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several works. Here, we generalize these approaches and explicitly spell out an algorithm for non-linear CVs and underdamped Langevin dynamics. We prove reversibility of the resulting scheme and demonstrate its performance on several numerical examples, observing a substantial performance increase compared to methods based on overdamped Langevin dynamics as considered previously. Advances in generative machine-learning-based proposal samplers now enable efficient sampling in CV spaces of intermediate dimensionality (tens to hundreds of variables), and our results extend their applicability toward more realistic molecular systems.