@conference {, title = {Extreme-Scale Task-Based Cholesky Factorization Toward Climate and Weather Prediction Applications}, booktitle = {Platform for Advanced Scientific Computing Conference (PASC20)}, year = {2020}, month = {2020-06}, publisher = {ACM}, organization = {ACM}, address = {Geneva, Switzerland}, abstract = {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.}, doi = {https://doi.org/10.1145/3394277.3401846}, author = {Qinglei Cao and Yu Pei and Kadir Akbudak and Aleksandr Mikhalev and George Bosilca and Hatem Ltaief and David Keyes and Jack Dongarra} } @conference {1452, title = {Performance Analysis of Tile Low-Rank Cholesky Factorization Using PaRSEC Instrumentation Tools}, booktitle = {Workshop on Programming and Performance Visualization Tools (ProTools 19) at SC19}, year = {2019}, month = {2019-11}, publisher = {ACM}, organization = {ACM}, address = {Denver, CO}, author = {Qinglei Cao and Yu Pei and Thomas Herault and Kadir Akbudak and Aleksandr Mikhalev and George Bosilca and Hatem Ltaief and David Keyes and Jack Dongarra} }