Regularized RiteWeight for Sparse Trajectory Data: A Smoothed Stationary Reweighting Framework

Accurate estimation of equilibrium and nonequilibrium steady-state distributions from molecular simulation data remains challenging for systems exhibiting timescales longer than can be accessed with typical computing resources. The recently introduced RiteWeight algorithm iteratively reweights trajectory segments using randomized clustering to recover stationary distributions without discretization bias. However, with smaller data sets or a large number of iterations, the original RiteWeight algorithm may exhibit instability in weight updates due to noisy cluster-level stationary estimates. Here, we introduce a simple smoothed reweighting scheme that modifies the RiteWeight update rule by interpolating between the “raw” RiteWeight weights and average cluster weights. This formulation improves iterative convergence in under-sampled datasets while introducing a small, but tunable, bias. We demonstrate the value of smoothing using downsampled Trp-cage trajectory data previously employed in the original RiteWeight study. With smaller datasets, the smoothed update procedure substantially stabilizes convergence and improves estimation of stationary densities relative to unsmoothed RiteWeight. These results establish smoothing as a practical regularization strategy for iterative trajectory reweighting in sparse-data settings, extending the applicability of RiteWeight to a wider variety of simulation workflows.