Marginal Girsanov Reweighting: Stable Variance Reduction for Long-Timescale Dynamics from Biased Simulation

Abstract

Recovering unbiased kinetic and thermodynamic observables from the enhanced sampling simulations is a central challenge in rare-event sampling. Classical Girsanov Reweighting (GR) offers a principled solution by yielding exact pathwise probability ratios between biased and unbiased processes. However, the variance of GR weights grows rapidly with time, rendering it impractical for long-horizon reweighting. We introduce Marginal Girsanov Reweighting (MGR), which mitigates variance explosion by marginalizing over intermediate paths, producing stable and scalable weights for long-timescale dynamics. Experiments on various molecular dynamics systems demonstrate that MGR accurately recovers unbiased kinetic properties from trajectories generated under both umbrella sampling and metadynamics biases.