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: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:2502. 18959v4 Announce Type: replace Abstract: The architecture of a neural network and the choice of its activation function are both fundamental to its performance.
arXiv:2502. 07209v4 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning.
arXiv:2402. 00152v5 Announce Type: replace Abstract: Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent question.
arXiv:2607. 01694v1 Announce Type: new Abstract: Solving partial differential equations (PDEs) with high-frequency solutions remains a central challenge in physics-informed machine learning due to spectral bias -- the tendency of neural networks to learn low-frequency components preferentially.
arXiv:2608. 05892v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems.
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.
Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems. Two factors underlie this difficulty: spectral bias, the tendency of neural networks to underfit high-frequency features; and representation-coefficient coupling, the entanglement of representation learning and coefficient fitting within a single nonconvex optimization objective.
arXiv:2510. 19399v2 Announce Type: replace Abstract: Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs).
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:2309. 07401v2 Announce Type: replace-cross Abstract: Deep neural networks (DNNs) show great promise for solving partial differential equations (PDEs), but their deep architectures introduce complex, large-scale, non-convex optimization challenges.
arXiv:2601. 07397v2 Announce Type: replace-cross Abstract: In this work, we propose a novel layerwise adaptive construction method for neural network architectures.