arXiv:2607. 28080v1 Announce Type: cross Abstract: We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems.
arXiv:2609. 10767v1 Announce Type: cross Abstract: We develop an exact almost-sure learning theory for smooth parametric models trained by regularly weighted empirical risk minimization on long-range dependent data.
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:2607. 03347v1 Announce Type: new Abstract: We consider the Multiscale Single-Index Model (MSIM), first introduced in \cite{oymak2021learning}, as a stylized model for hierarchical learning with \emph{scale separation}.
The paper introduces a method called model‑constrained randomized Jacobian matching to enforce second‑order consistency when learning chaotic dynamical systems. By comparing Jacobians at randomly perturbed inputs, the approach implicitly penalises Hessian mismatch without computing full Hessian tensors, achieving $O(d^2)$ memory cost. Experiments on Lorenz 63 and Lorenz 96 show that this second‑order supervision reduces invariant‑measure error, improves Lyapunov‑spectrum accuracy, and avoids spurious attractors that plague first‑order methods.
arXiv:2608. 22277v2 Announce Type: replace Abstract: Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts.
arXiv:2607. 00257v1 Announce Type: new Abstract: Accurate prediction of complex dynamical systems from noisy measurements remains a significant challenge in scientific computing.
arXiv:2511. 08860v2 Announce Type: replace-cross Abstract: The deep learning revolution has spurred a rise in advances of using AI in sciences.
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:2607. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
arXiv:2607. 18490v1 Announce Type: new Abstract: Symbolic discovery of governing equations from data is limited not only by algorithm design and data volume, but by the geometry of the attractor: what the long-run dynamics allow to be recovered.
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.
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.