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

2026-10-02

AI Summary

This study addresses the limitations of autoregressive models in long-term chaotic system prediction, specifically their restricted step sizes and high computational costs. We propose a learning framework based on time-invariant evolution operators that embeds physical instantaneous dynamics into the training process by deriving consistency equations. By integrating differential and compositional objective functions with physical constraints, the method achieves consistent learning, enabling it to span long temporal horizons in a single evaluation rather than relying on traditional step-by-step propagation. Experimental results demonstrate that this approach improves both short-term trajectory accuracy and long-term statistical properties while supporting temporal extrapolation. Notably, it reduces the number of required evaluations by an order of magnitude, thereby achieving highly efficient simulation 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.

Problem

• chaotic dynamics
• long-term prediction
• time-invariant operator
• autoregressive models
• computational cost

Innovation

• Consistency Learning
• Time-Invariant Operators
• Chaotic Dynamics
• Physics-Informed
• Temporal Extrapolation