2026/05/01 by Zichen Liu, Tiejun Li
#cs.LG
Sampling the distribution of collective variables (CVs) and estimating the associated free energy surface are crucial problems in statistical physics, as they underpin a better understanding of chemical reactions and conformational transitions. Traditional methods usually rely on simulations in high-dimensional configuration space and project the resulting configurations onto the CV space. To improve sampling speed, we propose FES-FM, a reduced flow matching (FM) method for free energy surface (FES) sampling. We train a dynamical transport map in the CV space, thereby enabling direct sampling of CV distributions and reconstruction of the corresponding 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, including alanine dipeptide in implicit solvent as a molecular benchmark. Comparative experiments demonstrate that our approach significantly improves sampling speed while maintaining accuracy.