SolverSet: A Large-scale Benchmark Dataset for the Auto-selection of the Optimal Combination of Iterative Solvers and Preconditioners

The combination of iterative solvers and preconditioners is the mainstream approach for solving sparse linear systems of the form [Formula: see text], which are fundamental to many scientific and engineering applications. However, the automatic selection (auto-selection) of the optimal solver–preconditioner combination remains a challenging task. Although machine learning or deep learning methods have been explored for this purpose, their performance has been limited due to the lack of standardized, large-scale datasets. To address this issue, we introduce a large-scale benchmark dataset called SolverSet, designed for the auto-selection of the optimal combination of iterative solvers and preconditioners. We develop a matrix generation tool to produce a wide variety of large-scale sparse matrices, based on which we construct the SolverSet dataset. This dataset now comprises 12,651 large-scale matrices and their corresponding sparse linear systems, effectively overcoming the limitations of prior work — namely, limited size and a small number of systems — making it highly suitable for automatic selection modeling. We evaluate several baseline methods on SolverSet to validate its effectiveness and usability. Furthermore, we analyze key features of sparse linear systems and propose a deep learning based model named DL-Solver to predict the optimal solver–preconditioner combination for a given system. Experimental results demonstrate that SolverSet serves as a valuable benchmark for auto-selection research, and DL-Solver outperforms state-of-the-art method in predictive performance on the test set, achieving improvements of 2.14%, 3.47%, 2.71% and 3.16% in accuracy, macro-precision, macro-recall and macro-F1 score, respectively.