Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings
This addresses a specific problem in computational physics for researchers and engineers using PINNs, though it is incremental as it builds on prior hard-constraining techniques.
The paper tackled the challenge of hard-constraining Neumann boundary conditions in physics-informed neural networks (PINNs) by using Fourier feature embeddings, resulting in improved performance over existing methods, especially in multiscale and high-frequency scenarios.
We present a novel approach to hard-constrain Neumann boundary conditions in physics-informed neural networks (PINNs) using Fourier feature embeddings. Neumann boundary conditions are used to described critical processes in various application, yet they are more challenging to hard-constrain in PINNs than Dirichlet conditions. Our method employs specific Fourier feature embeddings to directly incorporate Neumann boundary conditions into the neural network's architecture instead of learning them. The embedding can be naturally extended by high frequency modes to better capture high frequency phenomena. We demonstrate the efficacy of our approach through experiments on a diffusion problem, for which our method outperforms existing hard-constraining methods and classical PINNs, particularly in multiscale and high frequency scenarios.