Sampling metastable systems using collective variables and Jarzynski-Crooks paths

TL;DR

This paper introduces a novel sampling algorithm for high-dimensional multimodal distributions that leverages collective variables and Jarzynski-Crooks paths, avoiding the need to compute free energy, and demonstrates its efficiency through numerical tests.

Contribution

It extends proposal kernels in collective variable space to the full space with an accept-reject step, linking acceptance ratios to Jarzynski-Crooks work, and offers multiple algorithm variants.

Findings

The algorithm efficiently samples multimodal distributions.

Acceptance ratios relate to Jarzynski-Crooks work.

Numerical tests show competitive performance.

Abstract

We consider the problem of sampling a high dimensional multimodal target probability measure. We assume that a good proposal kernel to move only a subset of the degrees of freedoms (also known as collective variables) is known a priori. This proposal kernel can for example be built using normalizing flows. We show how to extend the move from the collective variable space to the full space and how to implement an accept-reject step in order to get a reversible chain with respect to a target probability measure. The accept-reject step does not require to know the marginal of the original measure in the collective variable (namely to know the free energy). The obtained algorithm admits several variants, some of them being very close to methods which have been proposed previously in the literature. We show how the obtained acceptance ratio can be expressed in terms of the work which appears in the Jarzynski-Crooks equality, at least for some variants. Numerical illustrations demonstrate the efficiency of the approach on various simple test cases, and allow us to compare the variants of the algorithm.