arXiv AI
Jun 29
Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
arXiv:2606. 28122v1 Announce Type: cross Abstract: Neural operators provide deep neural networks for learning mappings between function spaces.
SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators
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.
Related stories
arXiv Machine Learning
Jun 9
Fourier Neural Operators with rank-1 lattice points and hyperbolic cross
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 Machine Learning
Jun 16
Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
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 AI
1d ago
A Novel Fourier Feature Network for Solving Partial Differential Equations
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.
arXiv Machine Learning
Jun 30
Spectral Gating via Damped Oscillations for Adaptive Implicit Neural Representations
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.
arXiv Machine Learning
Jun 18
Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems
arXiv:2606. 18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing.
arXiv Machine Learning
Jun 30
Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation
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 Machine Learning
Jun 16
RepNet: Tackling spectral bias in deep neural networks via parameter reparameterization
arXiv:2606. 16575v1 Announce Type: new Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors.
arXiv Machine Learning
Aug 4
Self-composing neural operators for high-frequency and multiscale PDE surrogates
arXiv:2508. 20650v2 Announce Type: replace Abstract: Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framework.
arXiv Machine Learning
Jun 9
SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion
arXiv:2604. 07421v3 Announce Type: replace Abstract: Full-waveform inversion (FWI) is pivotal for reconstructing high-resolution subsurface velocity models but remains computationally intensive and ill-posed.
Hugging Face Trending Papers
Jun 1
Spectral Audit of In-Context Operator Networks
Existing evaluations of neural operators and in-context operator learning rely primarily on prediction error, but accurate output prediction does not guarantee the correct local dynamical structure. A model may match solutions while exhibiting incorrect sensitivities, distorted frequency response, spurious mode coupling, or unstable tangent behavior.
arXiv Machine Learning
Aug 11
End-to-End Neural Decomposition with Koopman Operators for Time-Series Forecasting
arXiv:2608. 08788v1 Announce Type: cross Abstract: Koopman theory offers a linear-operator view of nonlinear sequence dynamics by lifting observations into a space where evolution is governed by a linear time-invariant Koopman operator.