Generative model predicts long-term random dynamics from short observations
Generative Modeling of Stochastic Dynamics for Long-Time Evolution
Machine Learning
Summary
Predicting how complex random systems change over long times usually needs detailed equations, which are often unknown. The authors show that by looking at pairs of system states separated by short times, a special AI model can learn to generate future system behavior far into the future. Their method works well on a simulated physical model and on real experiments tracking tiny particles in an optical trap. This means short snapshots contain enough information to foresee long-term random changes without knowing the underlying rules.
What this means in practice
- •For industrial process engineers: Forecast long-term behavior of noisy physical processes using brief short-time data without explicit dynamic equations.
- •For robotics system designers: Predict future uncertain system states from short observational windows to improve control in stochastic environments.
Authors
Yang-yang Tan, Jinyang Li, Lingxiao Wang
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.