DIESEL: A novel deep learning-based tool for SpMV computations and solving sparse linear equation systems

Sparse linear algebra is central to many areas of engineering, science, and business. The community has done considerable work on proposing new methods for sparse matrix-vector multiplication (SpMV) computations and iterative sparse solvers on graphical processing units (GPUs). Due to vast variations in matrix features, no single method performs well across all sparse matrices. A few tools on automatic prediction of best-performing SpMV kernels have emerged recently and require many more efforts to fully utilize their potential. The utilization of a GPU by the existing SpMV kernels is far from its full capacity. Moreover, the development and performance analysis of SpMV techniques on GPUs have not been studied in sufficient depth. This paper proposes DIESEL, a deep learning-based tool that predicts and executes the best performing SpMV kernel for a given matrix using a feature set carefully devised by us through rigorous empirical and mathematical instruments. The dataset comprises 1056 matrices from 26 different real-life application domains including computational fluid dynamics, materials, electromagnetics, economics, and more. We propose a range of new metrics and methods for performance analysis, visualization, and comparison of SpMV tools. DIESEL provides better performance with its accuracy 88.2%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$88.2\%$$\end{document}, workload accuracy 91.96%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$91.96\%$$\end{document}, and average relative loss 4.4%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4.4\%$$\end{document}, compared to 85.9%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$85.9\%$$\end{document}, 85.31%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$85.31\%$$\end{document}, and 7.65%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.65\%$$\end{document} by the next best performing artificial intelligence (AI)-based SpMV tool. The extensive results and analyses presented in this paper provide several key insights into the performance of the SpMV tools and how these relate to the matrix datasets and the performance metrics, allowing the community to further improve and compare basic and AI-based SpMV tools in the future.