Multigrid-Inspired Graph Neural Networks for Selection of Solvers and Preconditioners in Sparse Linear Systems

Xingyu Zhou, Shuzi Niu, Huiyuan Li, Tao Yuan, Ziwei Li

Abstract: Solving sparse linear systems is a fundamental task in science and engineering computing. Multiple iterative solvers have been developed to iteratively refining an initial guess to con-verge to the solution, with preconditioning techniques for better convergence. However, it’s challenging to select a quasi-optimal solver and preconditioner without background knowledge and domain expertise to reduce time and space cost. Meanwhile, a suboptimal selection may incur exponential computational overhead and even solution divergence. We designed a graph neural network model to help select optimal solver and preconditioner for sparse linear systems, where a multigrid-inspired GNN structure was introduced to synergistically aggregate local matrix patterns and global spectral features through hierarchical structure. Experimental results on benchmark sparse matrix collection show that our model outperforms state-of-the-art baseline selectors.

External IDs:dblp:conf/ijcnn/ZhouNLYL25