Capturing non-Markovian dynamics in non-equilibrium stochastic systems using flow matching

Abstract:Hydrodynamic models of stochastic particle systems represented by coarse-grained stochastic partial differential equations (SPDE), such as the regularized Dean-Kawasaki (DK) equation, do not accurately capture the short-time system dynamics that is dominated by non-Markovian effects, and low particle density regimes where the distributions are highly non-Gaussian. We develop a generative flow matching method that directly models the probability distribution of fluxes from particle simulations that explicitly incorporates non-Markovian and non-Gaussian effects. As a demonstration, we use this method to simulate the Kramers first passage time problem for a system of non-interacting Brownian particles. We show the model accurately captures the short-time behavior and provides better predictions of the statistical moments of the number density when compared against the solution of the Markovian baseline, regularized DK equation.

Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Computational Physics (physics.comp-ph)

arXiv:2606.06658 [cs.LG]

(or arXiv:2606.06658v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.06658 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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