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.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
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.
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.
arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
arXiv:2606. 11251v1 Announce Type: new Abstract: Many multivariate dynamical systems are observed only through trajectories, leaving the mechanisms governing their joint dynamics hidden.
Most learning architectures for dynamical systems rely on generic nonlinear function approximation, often requiring high model complexity to capture structured behaviors. In this work, we propose an alternative paradigm in which modeling capability arises primarily from structure rather than from expressive nonlinearities.
arXiv:2606. 19101v1 Announce Type: cross Abstract: Most learning architectures for dynamical systems rely on generic nonlinear function approximation, often requiring high model complexity to capture structured behaviors.
arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.
The paper introduces Newmark‑eta‑DGN, a graph neural network framework that learns coarse‑step dynamics and internal mechanical responses from discretely sampled trajectories. It combines a semi‑implicit update inspired by the Newmark‑eta method with an operator‑weighted virtual hub to capture system‑wide coupling. The model can predict long‑horizon motion and infer unobserved forces and stiffness operators across deformable beams, human gait, and protein dynamics without explicit supervision on mechanical quantities.
arXiv:2606.19101v2 Announce Type: replace-cross Abstract: We investigate a structure-first approach to dynamical learning in which the organization of stateful interactions is prescribed explicitly r...
arXiv:2607. 07425v1 Announce Type: cross Abstract: Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data.
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...