A PINN framework with separate networks for conductivity and potentials, multiscale wavelet excitations, and FFE recovers dominant conductivity structures from finite DtN data with 3-12% relative error on synthetic tests, with FFE aiding sharp features.
Neural-network-based approximations for solving partial differential equations
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A Fourier neural operator trained on Boussinesq-compressible simulation pairs corrects Boussinesq predictions for natural convection, achieving SSIM near unity and MSE reductions of one to three orders of magnitude.
A PINN-based periodic CFD solver is shown to reach nearly the same accuracy as traditional transient-to-periodic methods but with substantially lower computational time for 2D heat diffusion and fluid flow cases.
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
Side-by-side timing comparison finds BEM solves the scattering problem in ~0.01 s while PINN training takes ~100 s, but trained PINN evaluates interior points ~100x faster than BEM.
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Benchmarking Physics-Informed Neural Networks and Boundary Elements Methods for Wave Scattering
Side-by-side timing comparison finds BEM solves the scattering problem in ~0.01 s while PINN training takes ~100 s, but trained PINN evaluates interior points ~100x faster than BEM.