Extreme-Scale Task-Based Cholesky Factorization Toward Climate and Weather Prediction Applications

Qinglei Cao, Yu Pei, Kadir Akbudak, Aleksandr Mikhalev, George Bosilca, Hatem Ltaief, David E. Keyes, Jack Dongarra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

29 Scopus citations


Climate and weather can be predicted statistically via geospatial Maximum Likelihood Estimates (MLE), as an alternative to running large ensembles of forward models. The MLE-based iterative optimization procedure requires the solving of large-scale linear systems that performs a Cholesky factorization on a symmetric positive-definite covariance matrix—a demanding dense factorization in terms of memory footprint and computation. We propose a novel solution to this problem: at the mathematical level, we reduce the computational requirement by exploiting the data sparsity structure of the matrix off-diagonal tiles by means of low-rank approximations; and, at the programming-paradigm level, we integrate PaRSEC, a dynamic, task-based runtime to reach unparalleled levels of efficiency for solving extreme-scale linear algebra matrix operations. The resulting solution leverages fine-grained computations to facilitate asynchronous execution while providing a flexible data distribution to mitigate load imbalance. Performance results are reported using 3D synthetic datasets up to 42M geospatial locations on 130, 000 cores, which represent a cornerstone toward fast and accurate predictions of environmental applications.
Original languageEnglish (US)
Title of host publicationProceedings of the Platform for Advanced Scientific Computing Conference
ISBN (Print)9781450379939
StatePublished - Jun 18 2020


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