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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.
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.
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.
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.
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.
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.