Girsanov Reweighting for Uncertainty Propagation in Rare-Event Kinetics

Abstract

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.