Coarse-Grained Dynamics with Spatial Disorder and Non-Markovian Memory

Abstract

We introduce the spatial disorder-generalized Langevin equation (SD-GLE), a data-driven method for constructing coarse-grained (CG) dynamics in heterogeneous systems. Unlike conventional CG approaches that rely on a mean-field potential, SD-GLE utilizes a variational Bayesian framework with a random field prior to explicitly disentangle static spatial disorder from viscoelastic friction. Numerical results demonstrate the limits of standard GLEs, whereas SD-GLE accurately extrapolates long-time dynamics to capture the anomalous diffusion crossover from short trajectories and recover the ensemble statistical properties inherent to the disordered nature of these systems.