从反应轨迹中自动学习反应路径与坐标，提升罕见事件采样效率。
Reactive Flux Matching: Mechanism Discovery and Adaptive Sampling of Rare Events
- 基于反应轨迹数据直接学习电流速度与标量势函数。
- 无需动力学模型即可获得反应路径与速率常数，精度高。
- 适合研究分子反应机制或需高效采样的复杂系统。
路径采样方法可生成连接亚稳态的反应轨迹集合，但从中提取机制性洞见仍具挑战。本文提出流匹配（Flux Matching）框架，直接从反应轨迹数据中学习两个互补对象：电流速度 $u(z)$，其流线追踪主导反应路径；以及通过加权Helmholtz-Hodge分解得到的标量势 $h(z)$，作为数据驱动的反应坐标。两者均在反应路径集合上最小化二次泛函，类似于生成建模中的流匹配损失，且无需了解底层动力学或平稳分布。与基于始发概率的方法不同，$u$ 和 $h$ 在投影到非马尔可夫集体变量时依然定义良好，其等值面可作为自适应界面，用于改进增强采样方法。该方法在分子系统上验证了电流速度轨迹生成与速率常数计算的有效性。
原文摘要 · Abstract (English)
Path sampling methods generate ensembles of reactive trajectories connecting metastable states, but extracting mechanistic insight from these data remains nontrivial. We introduce Flux Matching, a framework that learns two complementary objects directly from reactive trajectory data: a current velocity $u(z)$, whose streamlines trace the dominant reaction pathways, and a scalar potential $h(z)$, obtained from a weighted Helmholtz-Hodge decomposition of the reactive current, that serves as a data-driven reaction coordinate. Both minimize quadratic functionals over the reactive path ensemble, analogous to the flow matching loss in generative modeling, and require no knowledge of the underlying dynamics or stationary distribution. Unlike committor-based methods, $u$ and $h$ remain well-defined under projection onto non-Markovian collective variables, and their level sets in turn provide adaptive interfaces for improved sampling with enhanced sampling methods. Flux Matching is validated through the generation of current velocity trajectories and rate constant calculations on molecular systems.
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