基于黎曼流匹配的凝聚态物质玻尔兹曼生成器
Boltzmann Generators for Condensed Matter via Riemannian Flow Matching
AI总结：
本文提出利用黎曼流匹配将周期性特征融入连续归一化流，实现高效准确的凝聚相系统平衡分布采样，验证了在单原子冰中训练大规模系统并获得高精度自由能估计的能力。
摘要：
在统计力学中，采样平衡分布是基础性任务。尽管流匹配已成为生成建模的可扩展前沿方法，但其在凝聚相系统中的平衡采样潜力仍待探索。本文通过将这些系统的周期性特征融入连续归一化流中，采用黎曼流匹配方法。连续归一化流固有的高计算成本通过使用Hutchinson迹估计器得到缓解，利用基于累积量展开的关键偏差校正步骤，使随机估计量适合严格热力学重加权。本文方法在单原子冰上得到验证，展示了在前所未有的大规模系统上训练并获得高精度自由能估计的能力，而无需传统多阶段估计器。
英文摘要：
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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