The Neural Green's Operator matches exact coarse-solve iteration counts in two-level preconditioners for diffusion and advection-diffusion problems when inputs are integrated against the output basis.
Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh
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When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning
The Neural Green's Operator matches exact coarse-solve iteration counts in two-level preconditioners for diffusion and advection-diffusion problems when inputs are integrated against the output basis.