标题： 潜在热力学流：从有限数据中统一表示学习和生成建模温度依赖行为 显示英文标题

标题： Latent Thermodynamic Flows: Unified Representation Learning and Generative Modeling of Temperature-Dependent Behaviors from Limited Data

摘要： 准确表征复杂分子系统的平衡分布及其对环境因素（如温度）的依赖关系，对于理解热力学性质和转变机制至关重要。将这些分布投影到有意义的低维表示上，可以实现可解释性和后续分析。生成式AI的最新进展，特别是流模型（如归一化流NFs），在建模此类分布方面显示出前景，但如果没有定制的表示学习，其应用范围是有限的。在本工作中，我们引入了潜在热力学流（LaTF），这是一个端到端框架，将表示学习和生成建模紧密结合。LaTF将状态预测信息瓶颈（SPIB）与NFs结合，同时学习称为集体变量（CVs）的低维潜在表示，分类亚稳态，并在训练数据之外的温度下生成平衡分布。表示学习和生成建模的两个组件被联合优化，确保学习到的潜在特征捕捉系统的慢速、重要自由度，同时生成模型能准确再现系统的平衡行为。我们在多种系统中展示了LaTF的有效性，包括一个模型势能、Chignolin蛋白和Lennard Jones粒子簇，通过多种指标和大量模拟进行彻底评估和基准测试。最后，我们将LaTF应用于RNA四环系统，在仅使用两种温度的模拟数据的情况下，LaTF重建了温度依赖的结构集合和熔化行为，与实验和先前广泛计算结果一致。 显示英文摘要

摘要： Accurate characterization of the equilibrium distributions of complex molecular systems and their dependence on environmental factors such as temperature is essential for understanding thermodynamic properties and transition mechanisms. Projecting these distributions onto meaningful low-dimensional representations enables interpretability and downstream analysis. Recent advances in generative AI, particularly flow models such as Normalizing Flows (NFs), have shown promise in modeling such distributions, but their scope is limited without tailored representation learning. In this work, we introduce Latent Thermodynamic Flows (LaTF), an end-to-end framework that tightly integrates representation learning and generative modeling. LaTF unifies the State Predictive Information Bottleneck (SPIB) with NFs to simultaneously learn low-dimensional latent representations, referred to as Collective Variables (CVs), classify metastable states, and generate equilibrium distributions across temperatures beyond the training data. The two components of representation learning and generative modeling are optimized jointly, ensuring that the learned latent features capture the system's slow, important degrees of freedom while the generative model accurately reproduces the system's equilibrium behavior. We demonstrate LaTF's effectiveness across diverse systems, including a model potential, the Chignolin protein, and cluster of Lennard Jones particles, with thorough evaluations and benchmarking using multiple metrics and extensive simulations. Finally, we apply LaTF to a RNA tetraloop system, where despite using simulation data from only two temperatures, LaTF reconstructs the temperature-dependent structural ensemble and melting behavior, consistent with experimental and prior extensive computational results.