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:2505. 07068v2 Announce Type: replace-cross Abstract: In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data.
By Jinchao Feng, Sui Tang
arXiv:2510.16656v2 Announce Type: replace
Abstract: Modeling dynamical systems and unraveling their underlying structural dependencies is central to many domains in the natural sciences. Various phys...
By Noah El Rimawi-Fine, Adam Stecklov, Lucas Nelson, Mathieu Blanchette, Alexander Tong, Stephen Y. Zhang, Lazar Atanackovic
The paper studies finite‑horizon minimum‑energy steering of inertial swarms under stochastic disturbances, focusing on mean‑field models with Cucker–Smale alignment or Morse attraction–repulsion interactions. It formulates the problem as a Schr"odinger bridge, deriving nonlinear, time‑symmetric optimality systems and proposing nested fixed‑point schemes for numerical solution. Numerical experiments demonstrate that the optimal corrective drift can either exploit or counteract the natural interaction forces, depending on their alignment with the steering objective.
By Asmaa Eldesoukey, Md Zulfiqur Haider, Italo Napolitano, Yongxin Chen, Abhishek Halder
arXiv:2606. 03067v1 Announce Type: cross Abstract: A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior.
By Valentina Kuskova, Dmitry Zaytsev, Michael Coppedge
arXiv:2606. 12365v1 Announce Type: cross Abstract: We propose Ambient Diffusion Policy, a simple and principled method for imitation learning from suboptimal data in robotics.
By Adam Wei, Nicholas Pfaff, Thomas Cohn, Arif Kerem Day{\i}, Constantinos Daskalakis, Giannis Daras, Russ Tedrake