arXiv:2511. 08860v2 Announce Type: replace-cross Abstract: The deep learning revolution has spurred a rise in advances of using AI in sciences.
By Zakhar Shumaylov, Peter Zaika, Philipp Scholl, Gitta Kutyniok, Lior Horesh, Carola-Bibiane Sch\"onlieb
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.
By Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
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.
By Illia Horenko
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.
By Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
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.
By Zhou Fang, Gianmarco Mengaldo
arXiv:2609.13197v1 Announce Type: new
Abstract: Algorithmic Information Dynamics (AID) studies systems by perturbing them and measuring changes in algorithmic complexity, but its usual estimator, the...
By Luan Ozelim, Hector Zenil