DeepONet learns the operator from signed distance functions of arbitrary 2D scatterer geometries to the resulting scattered fields for the Helmholtz equation, generalizing to unseen shapes as a surrogate for FEM.
IMA Journal of Applied Mathematics , volume =
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MD-PNOP recasts parameter-induced operator differences as source terms to enable single-configuration neural operator training for extrapolation and acceleration of parametric PDE solvers.
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.
citing papers explorer
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Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries
DeepONet learns the operator from signed distance functions of arbitrary 2D scatterer geometries to the resulting scattered fields for the Helmholtz equation, generalizing to unseen shapes as a surrogate for FEM.
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MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration
MD-PNOP recasts parameter-induced operator differences as source terms to enable single-configuration neural operator training for extrapolation and acceleration of parametric PDE solvers.
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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.