Data-Driven Approach for Predicting Long-Time Anomalous Transport from Short Trajectories

Abstract Molecular simulations provide detailed microscopic trajectories but often do not reach the long-time transport regime. Predicting long-time transport from ensembles of short trajectories is particularly challenging in heterogeneous materials, where static spatial disorder and viscoelastic memory can produce similar transient dynamics while leading to different behaviors at longer times. We introduce the spatial-disorder generalized Langevin equation (SD-GLE), a likelihood-based generative framework that represents local effective potential landscapes as realizations of a Gaussian random field and temporal correlations through a memory kernel; variational Bayesian inference jointly learns both components from short trajectory ensembles and uses them to generate long trajectories in statistically equivalent environments. In controlled benchmarks, SD-GLE recovers the prescribed disorder covariance and memory kernel, while application to randomly cross-linked polymer networks demonstrates an accurate prediction of size-dependent long-time and non-Gaussian tracer transport, including the crossover to hopping-dominated motion. By linking short-time microscopic motion that departs from simple diffusion to long-time transport behavior, SD-GLE provides a bottom-up modeling strategy that is applicable to a broad range of molecular systems with complex transport dynamics.