arXiv:2606. 07385v1 Announce Type: cross Abstract: Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics.
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: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:2308. 08794v4 Announce Type: replace Abstract: Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems.
arXiv:2608. 14716v1 Announce Type: cross Abstract: Abrupt transitions in complex systems are often preceded by early warning signals.
The paper introduces DOODL, a framework that learns a dictionary of spectral dynamics to represent related dynamical systems as points on a low‑dimensional manifold in operator space. By constraining operator estimation to this learned manifold, DOODL provides compact, interpretable embeddings and enables fast, accurate operator estimation from short, partially observed trajectories. Experiments on metastable Langevin dynamics and turbulent plasma simulations show that DOODL achieves one to two orders of magnitude lower errors than independent estimation methods, especially in low‑data regimes.
arXiv:2608.30804v1 Announce Type: new Abstract: Monitoring the health of heterogeneous industrial robot fleets is severely challenged by the multi-modal nature of their operational cycles and a persi...
Autoregressive transformers trained on limited trajectories of nonlinear dynamical systems can extrapolate to unseen parameter regimes, reproducing period-doubling cascades, chaotic dynamics, and attractor structures with high fidelity. In the logistic map, the model captures successive period doublings up to period 128, achieving a scaling ratio within $5 imes10^{-4}$ of the Feigenbaum constant. The study also shows how control‑parameter information is processed via attention, shaping the closed‑loop dynamics during training.
arXiv:2606. 09917v1 Announce Type: new Abstract: Multivariate time series forecasting requires capturing the continuously evolving correlation structure among interacting variables.
arXiv:2607. 19387v1 Announce Type: cross Abstract: Surrogate modeling for high-dimensional nonlinear dynamical systems that exhibit chaos requires mechanisms that preserve not only pointwise accuracy but also the scale-dependent structure of physical fields.
arXiv:2606. 01596v1 Announce Type: cross Abstract: Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics.
arXiv:2606. 20443v1 Announce Type: cross Abstract: Real-time process monitoring requires methods that extract actionable information from high-dimensional time-series data.
The paper introduces Dynafit, a kernel-based method for classifying trajectories produced by distinct nonlinear dynamical systems. It learns a distance metric by approximating the Koopman operator, enabling classification in a feature space without explicit dimensionality. The authors demonstrate Dynafit on logistic map chaos detection, handwritten dynamical pattern recognition, and visual dynamic texture classification.