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

2026-04-10

AI Summary

Traditional approaches to constructing free energy surfaces require extensive sampling of transition states associated with rare events, resulting in prohibitive computational costs. This work proposes the Variational Free Energy Surface (VaFES) framework, which leverages reversible coarse-grained collective variables to build a physically interpretable latent space. By integrating differentiable density generative models with variational optimization, VaFES directly learns a continuous and differentiable free energy surface without relying on pre-generated simulation data, enabling one-shot generation of rare-event configurations. The method accommodates collective variables of arbitrary form while preserving physical interpretability and controllability. In experiments, VaFES accurately reproduces the analytical solution for a bistable dimer potential and correctly identifies the native folded state of chignolin, showing excellent agreement with NMR-derived experimental structures.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search
• Natural Language Processing: Generation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• rare events
• free energy surface
• generative deep-learning models
• collective variables
• variational approach

Innovation

• variational free energy surface
• generative deep learning
• rare event sampling
• reversible collective variables
• differentiable FES