Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions.
arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.
By Ana Larra\~naga, Urban Fasel, Steven L. Brunton
arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.
By Riccardo Cappi, Paolo Frazzetto, Nicol\`o Navarin, Alessandro Sperduti
arXiv:2609.09434v1 Announce Type: cross
Abstract: In recent years, weak-form methods have made significant advances in data-driven discovery of dynamical systems. However, in high-dimensional setting...
By Will Houser, Vanja Dukic, David M. Bortz
The paper introduces a learning method for identifying interaction kernels in particle systems using only single-snapshot observations of collective steady states, rather than trajectory data. By regularizing with empirical distributions from varied, unseen initial conditions, the authors address the ill‑posed inverse problem and demonstrate stable, accurate recovery of interaction laws across several models. The recovered laws enable faithful reproduction of both steady‑state patterns and, in many cases, the preceding dynamics.
By Baoli Hao, Mauro Maggioni, Ming Zhong
arXiv:2606. 07483v1 Announce Type: new Abstract: Many important outcomes unfold as dynamic cascades, including product adoption, disease spread, financial distress, and information diffusion.
By Lei Huang