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This paper proposes Fourier Feature Networks (FENs), a single-hidden-layer neural network architecture using Fourier features to solve partial differential equations, achieving higher accuracy than Extreme Learning Machines without affine transformations.
This paper proposes FALM-PINN, an alternating Levenberg-Marquardt training framework for physics-informed neural networks that uses Fourier-enhanced features to address spectral bias and representation-coefficient coupling, achieving up to two orders of magnitude lower errors on high-frequency and nonlinear PDEs.
The paper introduces beignet, a PINN architecture that replaces random Fourier features with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy and computational efficiency on PDE benchmarks.
Study reveals that diverse language-model architectures independently evolve similar periodic Fourier features for representing numbers, with only some achieving geometric separability for modular arithmetic.