用黎曼流匹配生成凝聚相系统平衡态，提升采样效率与自由能精度。
Boltzmann Generators for Condensed Matter via Riemannian Flow Matching
- 基于黎曼流匹配融合周期性结构，构建适用于凝聚相的连续归一化流。
- 在单原子冰系统上实现超大规模训练，自由能估计误差显著降低。
- 适合从事分子模拟、统计力学及生成模型研究的学者使用。
平衡态采样是统计力学的基础问题。尽管流匹配已成为可扩展的先进生成建模范式，其在凝聚相系统中的平衡采样潜力仍基本未被探索。本文通过黎曼流匹配将此类系统的固有周期性融入连续归一化流中，缓解了连续归一化流固有的精确密度估计高计算成本问题，采用哈钦森迹估计器，并引入基于累积量展开的关键偏差修正步骤，使随机估计值可用于严格的热力学重加权。该方法在单原子冰系统上得到验证，展示了在前所未有的系统规模下进行训练的能力，并实现了无需传统多阶段估计器的高精度自由能估算。
原文摘要 · Abstract (English)
Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems remains largely unexplored. We address this by incorporating the periodicity inherent to these systems into continuous normalizing flows using Riemannian flow matching. The high computational cost of exact density estimation intrinsic to continuous normalizing flows is mitigated by using Hutchinson's trace estimator, utilizing a crucial bias-correction step based on cumulant expansion to render the stochastic estimates suitable for rigorous thermodynamic reweighting. Our approach is validated on monatomic ice, demonstrating the ability to train on systems of unprecedented size and obtain highly accurate free energy estimates without the need for traditional multistage estimators.
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