A Novel Fourier Feature Network for Solving Partial Differential Equations

arXiv:2608.14733 · cs.LG, cs.AI · Submitted 2026-08-13 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-08-13

Updated: 2026-08-13

Terminology

• Activation Function — 27× in this paper · explained in 1 episode
• Accuracy — 22× in this paper · explained in 1 episode
• Random Feature Method — 3× in this paper
• Robustness — 3× in this paper · explained in 5 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Deep Ritz Method — 2× in this paper
• Generalization — 2× in this paper · explained in 13 episodes
• Inverse Problem — 2× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Deep Galerkin Method — 1× in this paper
• DeepONet — 1× in this paper · explained in 2 episodes
• Physics-Informed Neural Network (PINN) — 1× in this paper · explained in 3 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes
• Steering — 1× in this paper · explained in 2 episodes

Sources

• Adam: A Method for Stochastic Optimization
• Operator Learning: Algorithms and Analysis
• The Random Feature Method for Time-dependent Problems
• Randomized Neural Networks with Petrov-Galerkin Methods for Solving Linear Elasticity Problems
• Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases

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