arXiv:2604.09769physics.comp-phcond-mat.stat-mech2026-04

用生成模型直接构建自由能面,一键发现罕见构型。

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

  • 基于可微分生成模型,无需数据预采样即可建模自由能面。
  • 单次优化即得连续可导的自由能面,并一次性生成罕见事件构型。
  • 保留物理可解释性,适用于复杂系统中罕见事件的高效探测。

罕见事件是复杂多体系统演化的关键,表现为自由能面(FES)上的关键过渡构型。传统方法需充分采样稀有事件过渡才能获得FES,计算成本极高。本文提出变分自由能面(VaFES),一种无需数据集的框架,直接使用可追踪密度的生成模型建模FES。通过将粗粒度集体变量(CV)扩展为可逆形式,VaFES在潜在空间中构建中间表示,使CV显式占据部分维度,既保持物理可解释性与可控性,又兼容任意CV设定。可逆性确保系统能量精确可得,实现无预设模拟数据的变分优化。一次优化即可获得连续、可微的FES,并通过一次采样生成罕见事件构型。该方法能复现双稳态二聚体势的精确解析解,并在实验NMR结构基础上准确识别χ-环蛋白的天然折叠态。本方法为复杂统计系统的系统性研究提供了可扩展的范式。

原文摘要 · Abstract (English)

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.

自由能面生成模型罕见事件变分方法

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