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.
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:2511. 08860v2 Announce Type: replace-cross Abstract: The deep learning revolution has spurred a rise in advances of using AI in sciences.
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: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.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
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: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: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:2607. 02203v1 Announce Type: new Abstract: Operator learning has emerged as a powerful tool for modeling complex physical systems in functional spaces.
arXiv:2604. 24662v2 Announce Type: replace-cross Abstract: Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences.
arXiv:2410. 11894v3 Announce Type: replace-cross Abstract: Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum.
Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions.