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This research demonstrates how generative diffusion models can predict long-term non-equilibrium dynamics in stochastic systems using only short-time observational data, bypassing the need for explicit equations of motion. By successfully replicating dynamic critical scaling and experimental particle currents across larger lattices and unseen initial conditions, the study highlights a powerful application of AI for simulating complex physical processes where traditional analytical methods fail.
Generative Modeling of Stochastic Dynamics for Long-Time Evolution
arXiv:2610.00546v1 Announce Type: cross Abstract: Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.
Abstract:Exact stochastic equations for non-equilibrium dynamics are rarely accessible. We show that the long-time evolution of stochastic dynamics can be predicted from configuration pairs at a fixed short time lag, without knowledge of the equation of motion. Generative diffusion models learn the finite-time transition kernel from these pairs, and iterating it propagates the dynamics far beyond the training lag. For two-dimensional Model B, the diffusive dynamics of a conserved order parameter, the learned kernels reproduce dynamic critical scaling and self-similar $t^{1/3}$ coarsening. Agreement with direct simulations persists on lattices twice the largest training size and for initial ensembles absent from training. For driven colloids in a periodic optical potential, ten minutes of measured trajectories suffice to predict the particle current and mean passage time over the next twenty minutes within experimental uncertainty. Short-time observations thus contain the information needed to predict emergent non-equilibrium dynamics at much longer times.
21 pages, 15 figures, comments are welcome!
Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat)
arXiv:2610.00546 [cond-mat.stat-mech]
(or arXiv:2610.00546v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2610.00546 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 258 words
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