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. 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}.
By Joan Bruna
arXiv:2607. 00257v1 Announce Type: new Abstract: Accurate prediction of complex dynamical systems from noisy measurements remains a significant challenge in scientific computing.
By Max Kreider, John Harlim, Daning Huang
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. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
By Yao Cheng Li, Ana Larra\~naga, Steven L. Brunton, Urban Fasel
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.
By Matteo Gallo, Fabio Anselmi, Paolo Lazzari