Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
DeepONet Based Preconditioning Strategies for Solving Parametric Linear Systems of Equations
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Spectral optimization of admissible entries in fixed-support FSAI preconditioners, using projected Krylov gradients and a detached Rayleigh surrogate, improves performance over Frobenius-based selection on finite-element problems, especially indefinite saddle-point systems.
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.
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.
citing papers explorer
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Hybrid Fourier Neural Operator-Lattice Boltzmann Method
Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
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Factored Sparse Approximate Inverse Preconditioning via Spectral Optimization
Spectral optimization of admissible entries in fixed-support FSAI preconditioners, using projected Krylov gradients and a detached Rayleigh surrogate, improves performance over Frobenius-based selection on finite-element problems, especially indefinite saddle-point systems.
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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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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.