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.
arXiv:2606. 10084v1 Announce Type: cross Abstract: This work presents a divide-and-conquer modeling strategy for the CTF-4-Science Lorenz benchmark, which evaluates chaotic-system prediction across twelve hidden scores and five scenario families: clean forecasting, noisy reconstruction, noisy-input forecasting, few-shot learning, and parametric generalization.
arXiv:2608.22112v1 Announce Type: cross Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...
arXiv:2603.13496v2 Announce Type: replace Abstract: Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems...
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
The paper presents a method to enhance one‑dimensional rotating detonation engine (RDE) models by integrating data assimilation and machine learning. Continuous data assimilation (nudging) aligns the low‑order Koch‑Kutz solver with high‑fidelity temperature data, while a Jacobian‑regularized closure is trained on the recorded correction forces. The resulting corrected model, once the observation term is removed, autonomously reproduces the temperature spectrum and key statistical properties of the full high‑fidelity simulation.
The paper presents a method for predicting dynamical behavior across bifurcations by extrapolating trained neural network models. It leverages generalized synchronization to reconstruct unseen chaotic dynamics, deriving a formula that combines pretrained readouts. Using Lagrange interpolation theory, the authors establish rigorous bounds on readout errors and conjugacy residuals, and demonstrate accurate predictions through numerical examples.