The paper introduces Fundamental Dynamical Units (FDUs), signed three‑node interaction patterns that reduce the combinatorial complexity of interaction architectures in networked dynamical systems. By embedding FDU‑regularized structural inference into a physics‑informed neural ODE, the authors jointly recover interaction structure and perturbation‑resolved trajectories, demonstrating the approach on synthetic benchmarks. This framework enables motif‑prescribed intervention design and mechanistically interpretable inference in complex systems.
By Nima Nouri
The paper introduces a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs) using operator coercivity, variational formulations, and non-asymptotic perturbation theory. It proves that minimizing residual losses in Sobolev norms leads to convergence in energy and uniform norms, provides deterministic stability bounds and probabilistic concentration results for sample complexity, and establishes a generalization bound linking residual consistency, projection error, and perturbation sensitivity. Empirical tests on elliptic, parabolic, and nonlinear PDEs validate the predictive accuracy of these theoretical bounds and highlight key structural principles such as operator coercivity, activation smoothness, and sampling admissibility.
By Ronald Katende
arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.
By Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai
arXiv:2606. 15053v1 Announce Type: new Abstract: Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems.
By Matthias Chung, Yutong Bu, Deepanshu Verma
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:2608. 16473v1 Announce Type: new Abstract: Neural PDE training yields a finite checkpoint archive, yet its logged energy errors are inaccessible without the exact solution, while loss-based selection does not necessarily recover the logged energy oracle.
By Karim Bounja, Lahcen Laayouni, Boujemaa Achchab, Abdeljalil Sakat
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
By Qiyao Zhou, Xujia Zhu, Pierre Joli, Yu Cong, Sibo Cheng
arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
By Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer, Andrew B. Duncan
arXiv:2606. 06171v1 Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions.
By Cornelius Otchere, Michael Shields
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:2608.23725v1 Announce Type: new
Abstract: Deep Equilibrium Models (DEQs) compute predictions from a hidden representation unchanged by the model update. Training through this equilibrium uses i...
By Jose Luis Lima de Jesus Silva
The paper introduces SIHA, a method for jointly recovering hidden-agent trajectories and their interaction structures in multi-agent dynamics. It tackles the circular dependency between trajectory reconstruction and structural inference by combining a structure‑agnostic initialization with iterative, structure‑guided refinement using Neural Relational Inference and multi‑strength structural attention. Experiments on benchmark dynamical systems and motion‑capture data show that SIHA improves both visible‑to‑visible structural inference and hidden‑state reconstruction, leading to better future predictions.
By Zhongben Gong, Xiaoqun Wu, Mingyang Zhou, Hui Huang