NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
Hybrid iterative solvers with geometry-aware neural preconditioners for parametric PDEs
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2026 2verdicts
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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.
citing papers explorer
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NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
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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.