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arXiv:2505. 23863v3 Announce Type: replace-cross Abstract: Understanding chaotic dynamics is a fundamental problem across scientific disciplines, including climate science, neuroscience, and fluid dynamics, yet direct experimentation and intervention in such systems are often infeasible.
arXiv:2507. 03631v4 Announce Type: replace Abstract: Extracting interpretable mathematical models from complex dynamical systems is difficult, especially for chaotic dynamics observed with noisy experimental data.
The paper proposes a method for predicting long‑term behavior in chaotic systems by learning a time‑invariant evolution operator that can jump across large time spans in a single evaluation. It derives consistency equations that the operator must satisfy, incorporating differential and compositional objectives tied to physical dynamics. Experiments on five chaotic systems show that this physics‑distilled consistency approach yields more accurate short‑term trajectories and long‑term statistics, survives temporal extrapolation, and requires only one‑tenth the evaluations of autoregressive rollouts.
Neural surrogates for forecasting physical fields from sparse, noisy sensors typically use a spatial window and a temporal history of past snapshots. This study compares the trade‑off between window size and history length against the Bayes‑optimal error, showing that for fields with local dynamics the optimal forecast relies mainly on distant sensors via spatial correlation. Experiments on Burgers flow and the chaotic Kuramoto‑Sivashinsky equation reveal that the benefit of additional snapshots depends on lead time and system stability, leading to design rules that size the window in correlation lengths and split input budgets between window and history based on forecast horizon.
arXiv:2511. 06609v4 Announce Type: replace Abstract: The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines.
arXiv:2507. 09652v2 Announce Type: replace-cross Abstract: Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data.