A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.
Preconditioning for physics-informed neural networks
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PINN failure modes are overfitting to collocation points; regularization and double backpropagation over full residuals fix them, achieving SOTA with up to 23x fewer points on standard benchmarks.
Sparse RFNNs with sSVD via Lanczos-Golub-Kahan bidiagonalization maintain accuracy while improving efficiency and robustness for 1D steady convection-diffusion equations with strong advection.
citing papers explorer
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Solving Convolution-type Integral Equations using Preconditioned Neural Operators
A preconditioned neural operator is trained to handle high-frequency error components and hybridized with weighted Jacobi iteration to solve large convolution-type integral equations faster than multigrid or preconditioned conjugate gradient methods.
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PINNs Failure Modes are Overfitting
PINN failure modes are overfitting to collocation points; regularization and double backpropagation over full residuals fix them, achieving SOTA with up to 23x fewer points on standard benchmarks.
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Sparse Random-Feature Neural Networks with Krylov-Based SVD for Singularly Perturbed ODE
Sparse RFNNs with sSVD via Lanczos-Golub-Kahan bidiagonalization maintain accuracy while improving efficiency and robustness for 1D steady convection-diffusion equations with strong advection.