Performance‐influence models of multigrid methods: A case study on triangular grids

Abstract

Summary Multigrid methods are among the most efficient algorithms for solving discretized partial differential equations. Typically, a multigrid system offers various configuration options to tune performance for different applications and hardware platforms. However, knowing the best performing configuration in advance is difficult, because measuring all multigrid system variants is costly. Instead of direct measurements, we use machine learning to predict the performance of the variants. Selecting a representative set of configurations for learning is nontrivial, although, but key to prediction accuracy. We investigate different sampling strategies to determine the tradeoff between accuracy and measurement effort. In a nutshell, we learn a performance‐influence model that captures the influences of configuration options and their interactions on the time to perform a multigrid iteration and relate this to existing domain knowledge. In an experiment on a multigrid system working on triangular grids, we found that combining pair‐wise sampling with the D‐Optimal experimental design for selecting a learning set yields the most accurate predictions. After measuring less than 1 % of all variants, we were able to predict the performance of all variants with an accuracy of 95.9 %. Furthermore, we were able to verify almost all knowledge on the performance behavior of multigrid methods provided by 2 experts.

A comparison of performance specialization learning for configurable systems

“…Current practices mainly focus on classification algorithms. Although in the optimization and performance prediction scenarios there are works using regression techniques [13,16,28,29,46], these techniques have not been yet explored for specialization. Also, some additional steps are worth exploring (like feature selection prior to learning).…”

Special issue: Advanced stencil‐code engineering

“…The paper “Performance‐influence models of multigrid methods: A case study on triangular meshes,” authored by Alexander Grebhahn, Carmen Rodrigo, Norbert Siegmund, Francisco J. Gaspar, and Sven Apel, addresses the problem of finding variants with good performance. Among a huge number of variants, how can one predict reasonably accurately which ones will perform well?…”

Interpretability of configurable software in the biosciences

“…Other research has investigated how evolving configuration models affect regression testing [9,16], and how to predict performance [32][33][34][35][36]. There also exist tools for studying and dealing with configurations and variability in software that are not strictly testing related.…”

“…Some recent research has looked at variability in programs that calculate partial differential equations [35,52], numerical solvers [53], and configurable robotics [54]. None of these are in the bioinformatics domain.…”

“…SPL Conqueror is an existing tool for performance-influence modeling [32,33] and has been applied to scientific domains such as stencil codes [34,52] and to multigrid methods, a technique for solving partial differential equations [35] (see Section 2.1 for additional background). Related work investigates how different machine-learning techniques and sampling strategies affect performance prediction models [36,38].…”