Capturing non-Markovian dynamics in non-equilibrium stochastic systems using flow matching
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Computer Science > Machine Learning
Title: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.
| Comments: | 5 pages, 1 figure, Accepted to 2026 Conference on Physics and AI (PAI26) |
| Subjects: | Machine Learning (cs.LG); Statistical Mechanics (cond-mat.stat-mech); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2606.06658 [cs.LG] |
| (or arXiv:2606.06658v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.06658
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Bhargav Sriram Siddani [view email][v1] Thu, 4 Jun 2026 19:06:10 UTC (1,296 KB)
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