Physics-guided estimation of mean first-passage times from censored nucleation trajectories

Mean first-passage time (MFPT) analysis is a powerful tool for extracting thermodynamic and kinetic parameters of nucleation, including the critical nucleus size, nucleation barrier, and nucleation rate, from molecular dynamics (MD) simulations. However, accurate MFPT estimation typically requires extensive sampling and long simulation durations, making it computationally expensive, especially for rare nucleation events. Here, we present an efficient method to estimate MFPT from fixed-length MD simulations by leveraging the single-exponential tail (SET) behavior of first-passage time distributions in monomer-transition-based nucleation processes. Our approach allows for the estimation of MFPT for censored samples using information from uncensored ones via the characteristic decay rate of the SET, eliminating the need to observe complete nucleation trajectories. We validate this method using both artificial nucleation datasets and unbiased MD simulations of CO₂ hydrate nucleation. The results demonstrate that, with an appropriate choice of simulation length and number of independent runs, the SET-based approach accurately recovers the full MFPT and nucleation parameters while substantially reducing computational costs. This work provides a practical and broadly applicable framework for accelerating nucleation studies in molecular simulations.