NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, the location/values of the applied Dirichlet/Neumann boundary conditions, body forces and material properties, among others. We have previously introduced hybridization of classical linear iterative solvers with neural operators for specific geometries, but they tend to not perform well on geometries not previously seen during training. We partially addressed this challenge by introducing the deep operator network Geo-DeepONet and hybridizing it with Krylov-based iterative linear solvers, which, despite learning e...
| Authors | Francesc Levrero-Florencio, Youngkyu Lee, Jay Pathak et al. |
|---|---|
| Primary category | math.NA |
| Published | 8 May 2026 |
| Last updated at source | 11 May 2026 |
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