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: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:2412. 12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods.
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: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...
arXiv:2607. 09801v1 Announce Type: new Abstract: Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements.
arXiv:2604. 17121v3 Announce Type: replace Abstract: Transformers encode structure in sequences via an expanding contextual history.
arXiv:2609.37083v1 Announce Type: cross Abstract: We study the problem of recovering the governing ODE of a dynamical system from unstructured, high-dimensional observations such as images. Existing...
The paper introduces an in‑span adaptation technique for reduced‑order models, where the reduced subspace is continually updated using the model’s own predictions via an incremental singular‑value decomposition with a forgetting factor. This creates a trajectory‑informed spectral preconditioner that reweights and realigns the basis without changing the subspace, enabling the model to better absorb future out‑of‑span corrections. The authors demonstrate the method on a 3‑D spiral example and nonlinear PDEs such as viscous Burgers and Fisher–KPP, and relate the approach to in‑context learning in dynamical systems.
arXiv:2308. 13380v3 Announce Type: replace-cross Abstract: Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class?
arXiv:2606. 08956v1 Announce Type: new Abstract: Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displacement, velocity, concentration, and temperature.