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On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Sifan Wang,Hanwen Wang,P. Perdikaris

2020 · DOI: 10.1016/j.cma.2021.113938
arXiv.org · 556 Citations

TLDR

This work investigates how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK, and constructs novel architectures that employ spatio-temporal and multi-scale random Fourier features, and justifies how such coordinate embedding layers can lead to robust and accurate PINN models.