Differentiable free energy surface: a variational approach to directly observing rare events using generative deep-learning models

TL;DR

The paper introduces VaFES, a variational, dataset-free deep learning framework that models free energy surfaces directly, enabling efficient identification and generation of rare events in complex systems.

Contribution

It presents a novel variational approach using generative models to directly learn and sample free energy surfaces without pre-existing simulation data.

Findings

Successfully reproduces analytical solutions for bistable dimer potential.

Identifies chignolin native folded state consistent with NMR data.

Enables one-shot generation of rare-event configurations.

Abstract

Rare events are central to the evolution of complex many-body systems, characterized as key transitional configurations on the free energy surface (FES). Conventional methods require adequate sampling of rare event transitions to obtain the FES, which is computationally very demanding. Here we introduce the variational free energy surface (VaFES), a dataset-free framework that directly models FESs using tractable-density generative models. Rare events can then be immediately identified from the FES with their configurations generated directly via one-shot sampling of generative models. By extending a coarse-grained collective variable (CV) into its reversible equivalent, VaFES constructs a latent space of intermediate representation in which the CVs explicitly occupy a subset of dimensions. This latent-space construction preserves the physical interpretability and transparent controllability of the CVs by design, while accommodating arbitrary CV formulations. The reversibility makes the system energy exactly accessible, enabling variational optimization of the FES without pre-generated simulation data. A single optimization yields a continuous, differentiable FES together with one-shot generation of rare-event configurations. Our method can reproduce the exact analytical solution for the bistable dimer potential and identify a chignolin native folded state in close alignment with the experimental NMR structure. Our approach thus establishes a scalable, systematic framework for advancing the study of complex statistical systems.