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.