Data-Driven Performance Modeling of Linear Solvers for Sparse Matrices

Performance of scientific codes is increasingly dependent on the input problem, its data representation and the underlying hardware with the increase in code and architectural complexity. This makes the task of identifying the fastest algorithm for solving a problem more challenging. In this paper, we focus on modeling the performance of numerical libraries used to solve a sparse linear system. We use machine learning to develop data-driven models of performance of linear solver implementations. These models can be used by a novice user to identify the fastest preconditioner and solver for a given input matrix. We use a variety of features that represent the matrix structure, numerical properties of the matrix and the underlying mesh or input problem as input to the model. We model the performance of nine linear solvers and thirteen preconditioners available in Trilinos using 1240 sparse matrices obtained from two different sources. Our prediction models perform significantly better than a blind classifier and black-box SVM and k-NN classifiers.