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: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.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
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: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.
arXiv:2606. 19368v1 Announce Type: cross Abstract: In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations.
arXiv:2607. 27196v1 Announce Type: new Abstract: We present a novel approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment.
arXiv:2508. 12448v2 Announce Type: replace-cross Abstract: In-context learning (ICL) lets large language models (LLMs) solve new tasks from prompts alone, across an ever-widening range of domains, yet the mechanisms underlying this ability remain poorly understood.
arXiv:2604. 19465v3 Announce Type: replace-cross Abstract: Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering.
We present a novel approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment. Specifically, we formulate a general framework for learning nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns.