A Recommendation System for Preconditioned Iterative Solvers

Preconditioned iterative methods are often used to solve very large sparse systems of linear systems that arise in many science and engineering applications. The performance and robustness of these solvers is extremely sensitive to the choices of multiple preconditioner and solver parameters. Users of iterative methods often encounter an overwhelming number of combinations of choices for solvers, matrix preprocessing steps, preconditioners, and their parameters. The lack of a unified theoretical analysis of preconditioners coupled with limited knowledge of their interaction with linear systems makes it highly challenging for practitioners to choose good solver configurations. In this paper, we propose a novel, multi-stage learning based methodology for determining the best solver configurations to optimize the desired performance behavior for any given linear system. Our solver configuration recommendation system involves three steps of modeling, namely (a) solvability modeling, (b) performance modeling, and (c) performance optimization. We model solvability and performance metrics as response functions associated with dyads of linear systems and solver configurations using classification and regression techniques. The best solver choices are then determined using a fast and efficient technique that performs rank aggregation over the learned performance models. Empirical results over real performance data for the Hypre iterative solver package demonstrates the efficacy and flexibility of the proposed approach.