Free Energy Surface Sampling via Reduced Flow Matching

TL;DR

The paper introduces FES-FM, a reduced flow matching method that efficiently samples free energy surfaces by training a dynamical transport map in CV space, significantly lowering computational costs and improving accuracy.

Contribution

It presents a novel reduced flow matching approach for free energy surface sampling that directly models the distribution in CV space, with a physically meaningful prior for many-particle systems.

Findings

Drastically reduces computational costs compared to traditional methods.

Achieves superior accuracy per unit sampling time.

Effective across various potential functions and collective variables.

Abstract

Sampling the free energy surface, namely, the distribution of collective variables (CVs), is a crucial problem in statistical physics, as it underpins a better understanding of chemical reactions and conformational transitions. Traditional methods for free energy surface sampling involve simulation in high-dimensional configuration space and projecting the resulting configurations onto the CV space. To reduce the computational costs of such sampling, we propose FES-FM, a reduced flow matching (FM) method for free energy sampling (FES). We train a dynamical transport map in the CV space, thereby enabling direct sampling of the free energy surface. For many-particle systems, we construct a prior distribution based on the Hessian at a local minimum of the potential, which ensures both rotation-translation invariance and physically meaningful configurations. We evaluate the proposed method across a variety of potential functions and collective variables. Comparative experiments demonstrate that our approach drastically reduces computational costs while delivering superior accuracy per unit sampling time.