Graph Neural Multilevel Preconditioners for Iterative Solvers
The paper tests whether an AMG-style hierarchy actually helps learned preconditioners on broad sparse-matrix workloads.
Zhang, Li, and Saad propose a Graph Neural Multilevel Preconditioner that learns smoothing, restriction, and interpolation operators inside an AMG-like structure. It is designed as a drop-in preconditioner for standard Krylov solvers on general sparse systems. The benchmark covers more than 800 sparse matrices and compares GMP with classical AMG, ILUT, and existing GNN preconditioners. The authors report both convergence gains and cases where the multilevel structure adds overhead against strong single-level baselines. ArXiv · AI/CL/LG's note
Zhang, Li, and Saad propose a Graph Neural Multilevel Preconditioner that learns smoothing, restriction, and interpolation operators inside an AMG-like structure. It is designed as a drop-in preconditioner for standard Krylov solvers on general sparse systems. The benchmark covers more than 800 sparse matrices and compares GMP with classical AMG, ILUT, and existing GNN preconditioners. The authors report both convergence gains and cases where the multilevel structure adds overhead against strong single-level baselines. ArXiv · AI/CL/LG's note
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