Free Energy Surface Sampling via Reduced Flow Matching

2026-04-30

AI Summary

This work proposes FES-FM, a novel method for efficiently sampling free energy surfaces (FES) to elucidate chemical reaction and conformational transition mechanisms. By introducing reduced flow matching into FES sampling for the first time, the approach constructs a dynamic transport map directly in collective variable (CV) space, enabling efficient and direct sampling of the FES while circumventing costly simulations in high-dimensional configuration space. The method incorporates a prior distribution derived from the potential energy Hessian, enhancing physical plausibility while preserving rotational and translational invariance, and leverages CV projection techniques to improve sampling accuracy. Benchmarking across diverse potential functions and collective variables demonstrates that FES-FM substantially reduces computational cost and achieves superior sampling precision per unit time compared to conventional approaches.

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.

Problem

• free energy surface
• collective variables
• sampling
• statistical physics
• computational cost

Innovation

• flow matching
• free energy surface
• collective variables
• reduced sampling
• dynamical transport map