A New Matrix Feature Selection Strategy in Machine Learning Models for Certain Krylov Solver Prediction

Abstract

Numerical simulation processes in scientific and engineering applications require efficient solutions of large sparse linear systems, and variants of Krylov subspace solvers with various preconditioning techniques have been developed. However, it is time-consuming for practitioners with trial and error to find a high-performance Krylov solver in a candidate solver set for a given linear system. Therefore, it is instructive to select an efficient solver intelligently among a solver set rather than exploratory application of all solvers to solve the linear system. One promising direction of solver selection is to apply machine learning methods to construct a mapping from the matrix features to the candidate solvers. However, the computation of some matrix features is quite difficult. In this paper, we design a new selection strategy of matrix features to reduce computing cost, and then employ the selected features to construct a machine learning classifier to predict an appropriate solver for a given linear system. Numerical experiments on two attractive GMRES-type solvers for solving linear systems from the University of Florida Sparse Matrix Collection and Matrix Market verify the efficiency of our strategy, not only reducing the computing time for obtaining features and construction time of classifier but also keeping more than 90% prediction accuracy.