[HG_AP] Hybrid Preconditioning for Accelerated Linear and Nonlinear PDE Solvers
ABSTRACT
In this talk, we present a hybrid preconditioning strategies that combine neural operators (NOs) with numerical iterative solvers to efficiently solve partial differential equations (PDEs). By leveraging the complementary strengths of NO’s spectral bias for representing low-frequency components and iterative methods’ efficiency at resolving high-frequency modes, the proposed preconditioner balances convergence rates across eigenmodes. To demonstrate the effectiveness of the proposed strategies, we present numerical experiments on various parametric PDEs.
