用于稀有事例动力学中不确定性传播的吉尔萨诺夫重加权法
Girsanov Reweighting for Uncertainty Propagation in Rare-Event Kinetics
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中文总结 AI 辅助
研究利用机器学习原子间势进行稀有事例采样时的不确定性传播问题，结合自适应多级分裂与吉尔萨诺夫重加权法，推导估计器并验证，能构建不确定性感知概率分布，还可提供反应速率不确定性界限，为传播不确定性提供有效途径。
中文摘要 AI 辅助
机器学习原子间势（MLIPs）已成为分子动力学中稀有事例采样的有力工具，能以计算成本的一小部分提供近从头算精度。然而，与这些模型相关的不确定性仍是重大挑战。现有不确定性量化方法主要集中在逐点量或平衡热力学可观测量上。本文引入一个框架，将MLIP不确定性传播到平均转移概率，这是一个能进行反应速率计算的动力学可观测量。我们的方法结合了自适应多级分裂等稀有事例采样方法与吉尔萨诺夫重加权，以估计转移概率对MLIP参数变化的敏感性，无需为每个参数实现对反应轨迹进行昂贵的重新采样。我们推导了基于吉尔萨诺夫的精确和近似不确定性传播估计器，并在几个基准系统上进行了验证。该框架能构建稀有事例可观测量的不确定性感知概率分布，并从不确定的替代模型中成功恢复参考稀有事例概率。在关于MLIP在亚稳盆地内精度的温和假设下，该框架还能通过希尔关系提供反应速率的不确定性界限。这些结果表明路径空间重加权为将MLIP不确定性传播到稀有事例动力学提供了一条有效途径。
英文摘要
Machine-learning interatomic potentials (MLIPs) have become a powerful tool for rare event sampling in molecular dynamics, offering near ab initio accuracy at a fraction of the computational cost. However, the uncertainty associated with these models remains a major challenge. Existing uncertainty quantification approaches have largely focused on point-wise quantities, such as energies and forces, or on equilibrium thermodynamic observables. In this work, we introduce a framework for propagating MLIP uncertainty to the averaged committor probability, a kinetic observable that enables reaction-rate calculations. Our approach combines rare event sampling methods such as Adaptive Multilevel Splitting with Girsanov reweighting to estimate the sensitivity of committor probabilities to variations in MLIP parameters, without requiring the costly resampling of reactive trajectories for each parameter realization. We derive exact and approximate Girsanov-based estimators for uncertainty propagation and validate them on several benchmark systems, including a rugged Muller-Brown potential, a dimer in a solvent, and the conformational transition of butane. The proposed framework enables the construction of uncertainty-aware probability distributions for rare event observables and successfully recovers reference rare event probabilities from uncertain surrogate models. Under mild assumptions on the accuracy of the MLIP within metastable basins, the framework can also provide uncertainty bounds on reaction rates through Hill's relation. These results demonstrate that path-space reweighting provides an efficient route for propagating MLIP uncertainty to rare event kinetics.
