Randomized iterative trajectory reweighting for steady-state distributions without discretization error

Abstract

A significant challenge in molecular dynamics (MD) simulations is ensuring that sampled configurations converge to the equilibrium or nonequilibrium stationary distribution of interest. Lack of convergence constrains the estimation of free energies and of rates and mechanisms for molecular transitions. Here, we introduce the “Randomized ITErative trajectory reWeighting” (RiteWeight) algorithm to estimate a stationary distribution from unconverged simulation data. This method iteratively reweights trajectory segments in a self-consistent way by solving for the stationary distribution of a Markov state model (MSM), updating segment weights, and employing a new random clustering in each iteration. The repeated clustering mitigates the configuration-space discretization error inherent in existing trajectory reweighting techniques and yields quasi-continuous configuration-space distributions. RiteWeight accurately recovers the stationary distribution even without requiring the Markov property at the cluster level. We present mathematical analysis of the RiteWeight fixed point. We empirically validate the method using both synthetic MD Trp-cage trajectories, for which the stationary solution is exactly calculable, and standard atomistic MD Trp-cage trajectories, which are extracted from a long reference simulation. In both test systems, RiteWeight corrects flawed distributions and generates accurate observables for equilibrium and nonequilibrium steady states. The results highlight the value of correcting the underlying trajectory distribution rather than using a standard MSM.