Physics based operators speed up long term chaotic system forecasts
Physics is the Best Teacher: Consistency Learning for Time-Invariant Operators of Chaotic Dynamics
Machine Learning
Summary
Predicting how chaotic systems behave over a long time usually takes many small steps, which is slow. The authors propose teaching a computer model to jump forward big time steps in one go by learning rules that always apply to the system. They connect these rules to known physics laws to make the predictions more accurate. This new method predicts complex systems faster, using fewer steps while keeping good accuracy.
What this means in practice
- •For climate modelers: Run longer climate forecasts with fewer computational steps by using learned time-invariant operators consistent with physical laws.
- •For engineering simulation teams: Accelerate simulations of chaotic fluid or mechanical systems by replacing step-by-step solvers with physics-informed jump operators.
Authors
Lufang Chiang, Jiachen Yao, Thomas Y. L. Lin, Anima Anandkumar
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.