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.
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BibTeX
@misc{chiang2026physics,
title = {{Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics}},
author = {Lufang Chiang and Jiachen Yao and Thomas Y. L. Lin and Anima Anandkumar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04108},
eprint = {2610.04108},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04108},
}
RIS
TY - UNPB
TI - Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics
AU - Lufang Chiang
AU - Jiachen Yao
AU - Thomas Y. L. Lin
AU - Anima Anandkumar
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.04108
UR - https://arxiv.org/abs/2610.04108
AB - 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.
ER -