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Performance Prediction of Multigrid-Solver Configurations

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Software for Exascale Computing - SPPEXA 2013-2015

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 113))

Abstract

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.

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Notes

  1. 1.

    http://www.sac-home.org/

  2. 2.

    http://exastencils.org/

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Acknowledgements

We thank the Jülich Supercomputing Center for providing access to the supercomputer JuQueen. This work is supported by the German Research Foundation (DFG), as part of the Priority Program 1648 “Software for Exascale Computing”, under the contract RU 422/15-1 and AP 206/7-1. Sven Apel’s work is also supported by the DFG under the contracts AP 206/4-1 and AP 206/6-1.

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Authors and Affiliations

  1. University of Passau, Passau, Germany

    Alexander Grebhahn, Norbert Siegmund & Sven Apel

  2. Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany

    Harald Köstler

Authors
  1. Alexander Grebhahn
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  2. Norbert Siegmund
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  3. Harald Köstler
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  4. Sven Apel
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Corresponding author

Correspondence to Alexander Grebhahn .

Editor information

Editors and Affiliations

  1. Technische Universität München Institut für Informatik, Garching, Bayern, Germany

    Hans-Joachim Bungartz

  2. Technische Universität München Institut für Informatik, Garching, Germany

    Philipp Neumann

  3. Technische Universität Dresden, Dresden, Germany

    Wolfgang E. Nagel

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Grebhahn, A., Siegmund, N., Köstler, H., Apel, S. (2016). Performance Prediction of Multigrid-Solver Configurations. In: Bungartz, HJ., Neumann, P., Nagel, W. (eds) Software for Exascale Computing - SPPEXA 2013-2015. Lecture Notes in Computational Science and Engineering, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-40528-5_4

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