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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Publication details
- Journal
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- Open access
- Green open access
Cite this article
APA 7
Chiang, L., Yao, J., Lin, T. Y. L., & Anandkumar, A. (2026). Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics. https://omanscience.com/en/articles/physics-is-the-best-teacher-consistency-learning-for-time-invariant-operators-of-chaotic-dynamics
MLA 9
Chiang, Lufang, et al. "Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics." https://omanscience.com/en/articles/physics-is-the-best-teacher-consistency-learning-for-time-invariant-operators-of-chaotic-dynamics.
Chicago (author–date)
Chiang, Lufang, Jiachen Yao, Thomas Y. L. Lin, and Anima Anandkumar. 2026. "Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics." https://omanscience.com/en/articles/physics-is-the-best-teacher-consistency-learning-for-time-invariant-operators-of-chaotic-dynamics.
Harvard
Chiang, L., Yao, J., Lin, T. Y. L. and Anandkumar, A. (2026) 'Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics', Available at: https://omanscience.com/en/articles/physics-is-the-best-teacher-consistency-learning-for-time-invariant-operators-of-chaotic-dynamics.
Vancouver
Chiang L, Yao J, Lin TYL, Anandkumar A. Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics. https://omanscience.com/en/articles/physics-is-the-best-teacher-consistency-learning-for-time-invariant-operators-of-chaotic-dynamics
IEEE
L. Chiang, J. Yao, T. Y. L. Lin, and A. Anandkumar, "Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics," https://omanscience.com/en/articles/physics-is-the-best-teacher-consistency-learning-for-time-invariant-operators-of-chaotic-dynamics.