Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics

Abstract:Accelerating the prediction of long-term behavior in chaotic systems is crucial in scientific computing. However, existing methods rely on numerical solvers or autoregressive models that advance one small step at a time, which makes long horizons expensive. We instead view this problem as learning the system's time-invariant evolution operator, which jumps the state across a large time span in a single evaluation. To this end, we derive the consistency equations a time-invariant operator must satisfy, with differential and compositional objectives in physical time. These equations also connect the learned operator to the physics-prescribed instant dynamics, enabling physics embedding in consistency learning. Across five chaotic systems, we find that physics-distilled consistency makes both short-term trajectories and long-term statistics more accurate. The learned operator survives temporal extrapolation and requires one-tenth as many evaluations as autoregressive rollout, offering an efficient route to long-term simulation of chaotic dynamics.

23 pages, 7 figures, 10 tables. Accepted for the NeurIPS 2026 Workshop on AI for Stochastic Dynamics

Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD)

arXiv:2610.04108 [cs.LG]

(or arXiv:2610.04108v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.04108 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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