arXiv:2607. 19387v1 Announce Type: cross Abstract: Surrogate modeling for high-dimensional nonlinear dynamical systems that exhibit chaos requires mechanisms that preserve not only pointwise accuracy but also the scale-dependent structure of physical fields.
arXiv:2607. 11974v1 Announce Type: cross Abstract: Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen.
arXiv:2512. 09165v2 Announce Type: replace Abstract: Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs).
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.
arXiv:2607. 17990v1 Announce Type: new Abstract: Highly nonlinear chaotic dynamical systems remain difficult to model due to fundamental trade-offs between complexity, expressivity, and data efficiency.
arXiv:2607. 03347v1 Announce Type: new Abstract: We consider the Multiscale Single-Index Model (MSIM), first introduced in \cite{oymak2021learning}, as a stylized model for hierarchical learning with \emph{scale separation}.
arXiv:2607. 03692v1 Announce Type: new Abstract: Spectral methods are widely used to construct representations from the geometry of data, but they often rely on a fixed kernel, graph Laplacian, or manually selected feature scaling.
arXiv:2608. 13827v1 Announce Type: new Abstract: Machine-learned physical surrogate models have become promising alternatives to mesh-based numerical solvers.
arXiv:2608. 08003v1 Announce Type: cross Abstract: As machine learned models increase in complexity and expressive power, features of simpler models, such as interpretability and control over the shape of the modeled function are lost.
arXiv:2602. 09530v2 Announce Type: replace-cross Abstract: We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization.
arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.
arXiv:2606. 07385v1 Announce Type: cross Abstract: Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics.
arXiv:2605. 27756v2 Announce Type: replace-cross Abstract: Linear dimensionality reduction methods such as proper orthogonal decomposition (POD) make high-dimensional data amenable to analysis by identifying the principal components, or modes, that capture the most variance, or energy, in the data and constructing a low-dimensional representation in the subspace they span.