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:2608.22112v1 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...
By Nibodh Boddupalli, Jeff Moehlis
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: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
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.
By Christof Sch\"otz, Niklas Boers
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.
By Conrad Ainslie, Pedram Hassanzadeh, Michael W. Mahoney, Ashesh Chattopadhyay