Data-Efficient Multidimensional Free Energy Estimation via Physics-Informed Score Learning

TL;DR

This paper introduces an efficient method for reconstructing multidimensional free-energy landscapes from molecular dynamics simulations, overcoming computational challenges of high-dimensional sampling by leveraging physics-informed score learning and symmetry exploitation.

Contribution

The work extends Fokker--Planck Score Learning to two dimensions, enabling accurate, scalable free-energy estimation from non-equilibrium simulations with minimal computational overhead.

Findings

Successfully applied to alanine dipeptide conformational dynamics.

Achieved accurate free-energy landscapes for lipid bilayer permeation.

Demonstrated scalability over grid-based methods.

Abstract

Many biological processes involve numerous coupled degrees of freedom, yet free-energy estimation is often restricted to one-dimensional profiles to mitigate the high computational cost of multidimensional sampling. In this work, we extend Fokker--Planck Score Learning (FPSL) to efficiently reconstruct two-dimensional free-energy landscapes from non-equilibrium molecular dynamics simulations using different types of collective variables. We show that explicitly modeling orthogonal degrees of freedom reveals insights hidden in one-dimensional projections at negligible computational overhead. Additionally, exploiting symmetries in the underlying landscape enhances reconstruction accuracy, while regularization techniques ensure numerical robustness in sparsely sampled regions. We validate our approach on three distinct systems: the conformational dynamics of alanine dipeptide, as well as coarse-grained and all-atom models of solute permeation through lipid bilayers. We demonstrate that, because FPSL learns a smooth score function rather than histogram-based densities, it overcomes the exponential scaling of grid-based methods, establishing it as a data-efficient and scalable tool for multidimensional free-energy estimation.