arXiv:2606. 11518v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations.
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arXiv:2606. 28122v1 Announce Type: cross Abstract: Neural operators provide deep neural networks for learning mappings between function spaces.
arXiv:2606. 08871v1 Announce Type: cross Abstract: The \emph{Fourier neural operator} (FNO) is a neural network architecture that learns mappings between function spaces.
arXiv:2605. 31027v2 Announce Type: replace Abstract: We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs).
arXiv:2608. 14733v1 Announce Type: cross Abstract: Building on the foundation of single-hidden-layer neural networks, Fourier Feature Networks (FENs) are proposed, which incorporate Fourier features using $\cos$, $\sin$, or a combination of both.
The paper introduces a method that combines Fourier Neural Operators with wavelet-based encodings to learn and predict multiple eigenmodes of the elastic wave equation in metamaterials. By encoding PDE inputs with wavelets, the model can deterministically select eigenmodes for both continuous and binary geometries, and it explains how prediction accuracy depends on geometric discontinuities. The surrogate model achieves a three‑order‑of‑magnitude speedup over finite element analysis while maintaining high fidelity, offering a powerful tool for accelerating metamaterial design.
arXiv:2606. 23129v2 Announce Type: replace-cross Abstract: Implicit Neural Representations (INRs) have been proven successful in encoding continuous signals through coordinate-based networks, yet facing a spectral dilemma: periodic activations capture fine details but act as all-pass filters that memorise noise, while spatially compact activations regularise effectively but suffer from low-frequency bias.