发表机构
National Taiwan University; California Institute of Technology; University of Washington（国立台湾大学; 加州理工学院; 华盛顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出通过物理蒸馏的一致性学习来学习混沌系统的时间不变演化算子，实现单次评估跨越大时间跨度，在五个混沌系统中提高了短期和长期预测精度，并显著减少评估次数。
AI 中文摘要
加速混沌系统长期行为的预测在科学计算中至关重要。然而，现有方法依赖数值求解器或自回归模型，每次仅推进一小步，这使得长时间跨度的预测成本高昂。我们转而将这一问题视为学习系统的时间不变演化算子，该算子能在单次评估中将状态跨越大的时间跨度。为此，我们推导了时间不变算子必须满足的一致性方程，这些方程包含物理时间中的微分和组合目标。这些方程还将学习到的算子与物理规定的瞬时动力学联系起来，从而在一致性学习中实现物理嵌入。在五个混沌系统中，我们发现物理蒸馏的一致性使短期轨迹和长期统计量都更加准确。学习到的算子能够承受时间外推，并且所需的评估次数仅为自回归展开的十分之一，为混沌动力学的长期模拟提供了一条高效途径。
英文摘要
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.
Comments23 pages, 7 figures, 10 tables. Accepted for the NeurIPS 2026 Workshop on AI for Stochastic Dynamics
