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|Title||Extreme-Scale Task-Based Cholesky Factorization Toward Climate and Weather Prediction Applications|
|Publication Type||Conference Paper|
|Year of Publication||2020|
|Authors||Cao, Q., Y. Pei, K. Akbudak, A. Mikhalev, G. Bosilca, H. Ltaief, D. Keyes, and J. Dongarra|
|Conference Name||Platform for Advanced Scientific Computing Conference (PASC20)|
|Conference Location||Geneva, Switzerland|
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.