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arXiv · 2606.06658

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

Bhargav Sriram Siddani·John B. Bell·Alejandro L. Garcia·Ishan Srivastava
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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.

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Bhargav Sriram Siddani, John B. Bell, Alejandro L. Garcia, Ishan Srivastava. 2026-06-04. Capturing non-Markovian dynamics in non-equilibrium stochastic systems using flow matching. https://arxiv.org/abs/2606.06658

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