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.
Learning Neural PDE Solvers with Convergence Guarantees
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Neural operators supply warm-start guesses that cut iteration counts and runtime by up to 90% in Krylov solvers for PDEs while retaining the original methods' convergence guarantees.
ADANNs design ANN architectures and initializations to mimic classical numerical algorithms for parametric PDE operator approximation and report significant outperformance over existing methods in numerical tests.
citing papers explorer
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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.
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NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers
Neural operators supply warm-start guesses that cut iteration counts and runtime by up to 90% in Krylov solvers for PDEs while retaining the original methods' convergence guarantees.
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Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
ADANNs design ANN architectures and initializations to mimic classical numerical algorithms for parametric PDE operator approximation and report significant outperformance over existing methods in numerical tests.