Wachspress coordinates enable a transfinite interpolant that exactly enforces Dirichlet boundary conditions in PINNs on convex polygons by providing a smooth lift of boundary data into the domain interior.
Fourier PINNs: From strong boundary conditions to adaptive fourier bases.arXiv:2410.03496, 2024
3 Pith papers cite this work. Polarity classification is still indexing.
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beignet replaces random Fourier feature embeddings in PINNs with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy on PDE benchmarks with fewer parameters and near machine precision residuals on the inviscid Burgers blowup using Adam.
MS-SFNN encodes multi-scale Fourier features in a separable product of fixed-weight cosine subnetworks and solves for linear coefficients by least squares, claiming better accuracy than PINN and SV-SNN on high-frequency PDEs.
citing papers explorer
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A Wachspress-based transfinite formulation for exactly enforcing Dirichlet boundary conditions on convex polygonal domains in physics-informed neural networks
Wachspress coordinates enable a transfinite interpolant that exactly enforces Dirichlet boundary conditions in PINNs on convex polygons by providing a smooth lift of boundary data into the domain interior.
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Fourier Feature Pyramids for Physics-Informed Neural Networks
beignet replaces random Fourier feature embeddings in PINNs with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy on PDE benchmarks with fewer parameters and near machine precision residuals on the inviscid Burgers blowup using Adam.
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Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
MS-SFNN encodes multi-scale Fourier features in a separable product of fixed-weight cosine subnetworks and solves for linear coefficients by least squares, claiming better accuracy than PINN and SV-SNN on high-frequency PDEs.