Tile low rank cholesky factorization for climate/weather modeling applications on manycore architectures

Kadir Akbudak, Hatem Ltaief*, Aleksandr Mikhalev, Keyes David

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

45 Scopus citations

Abstract

Covariance matrices are ubiquitous in computational science and engineering. In particular, large covariance matrices arise from multivariate spatial data sets, for instance, in climate/weather modeling applications to improve prediction using statistical methods and spatial data. One of the most time-consuming computational steps consists in calculating the Cholesky factorization of the symmetric, positive-definite covariance matrix problem. The structure of such covariance matrices is also often data-sparse, in other words, effectively of low rank, though formally dense. While not typically globally of low rank, covariance matrices in which correlation decays with distance are nearly always hierarchically of low rank. While symmetry and positive definiteness should be, and nearly always are, exploited for performance purposes, exploiting low rank character in this context is very recent, and will be a key to solving these challenging problems at large-scale dimensions. The authors design a new and flexible tile row rank Cholesky factorization and propose a high performance implementation using OpenMP task-based programming model on various leading-edge manycore architectures. Performance comparisons and memory footprint saving on up to 200K × 200K covariance matrix size show a gain of more than an order of magnitude for both metrics, against state-of-the-art open-source and vendor optimized numerical libraries, while preserving the numerical accuracy fidelity of the original model. This research represents an important milestone in enabling large-scale simulations for covariance-based scientific applications.

Original languageEnglish (US)
Title of host publicationHigh Performance Computing - 32nd International Conference, ISC High Performance 2017, Proceedings
EditorsJulian M. Kunkel, Pavan Balaji, David Keyes, Rio Yokota
PublisherSpringer Verlag
Pages22-40
Number of pages19
ISBN (Print)9783319586663
DOIs
StatePublished - 2017
Event32nd International Conference, ISC High Performance, 2017 - Frankfurt, Germany
Duration: Jun 18 2017Jun 22 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10266 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference32nd International Conference, ISC High Performance, 2017
Country/TerritoryGermany
CityFrankfurt
Period06/18/1706/22/17

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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