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Capturing non-Markovian dynamics in non-equilibrium stoch...
[Submitted on 4 Jun 2026] · 2026-06-08 · via cs.LG updates on arXiv.org

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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.

Submission history

From: Bhargav Sriram Siddani [view email]
[v1] Thu, 4 Jun 2026 19:06:10 UTC (1,296 KB)