analiza aiqbench
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)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 258 cuvinte
Subiecte conexe
Latent Laplace Diffusion for Irregular Multivariate Time Series
arXiv · 3 iun. 2026
Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds
arXiv · 17 sept. 2026
Reducing Spatial and Temporal Dimensionality in the Multidimensional Caldeira-Leggett Model
Quantum Journal · 2 sept. 2026
Weak monitoring boosts quantum correlations, strong monitoring changes state
Quantum Zeitgeist · 17 sept. 2026