Performance Prediction of Multigrid-Solver Configurations

Geometric multigrid solvers are among the most efficient methods for solving partial differential equations. To optimize performance, developers have to select an appropriate combination of algorithms for the hardware and problem at hand. Since a manual configuration of a multigrid solver is tedious and does not scale for a large number of different hardware platforms, we have been developing a code generator that automatically generates a multigrid-solver configuration tailored to a given problem. However, identifying a performance-optimal solver configuration is typically a non-trivial task, because there is a large number of configuration options from which developers can choose. As a solution, we present a machine-learning approach that allows developers to make predictions of the performance of solver configurations, based on quantifying the influence of individual configuration options and interactions between them. As our preliminary results on three configurable multigrid solvers were encouraging, we focus on a larger, non-tivial case-study in this work. Furthermore, we discuss and demonstrate how to integrate domain knowledge in our machine-learning approach to improve accuracy and scalability and to explore how the performance models we learn can help developers and domain experts in understanding their system.