Reshaping Geostatistical Modeling and Prediction for Extreme-Scale Environmental Applications

TitleReshaping Geostatistical Modeling and Prediction for Extreme-Scale Environmental Applications
Publication TypeConference Proceedings
Year of Publication2022
AuthorsCao, Q., S. Abdulah, R. Alomairy, Y. Pei, P. Nag, G. Bosilca, J. Dongarra, M. G. Genton, D. Keyes, H. Ltaief, and Y. Sun
Conference Name2022 International Conference for High Performance Computing, Networking, Storage and Analysis (SC22)
Date Published2022-11
PublisherIEEE Press
Conference LocationDallas, TX
ISBN Number9784665454445
Keywordsclimate/weather prediction, dynamic runtime systems, high performance computing., low- rank matrix approximations, mixed-precision computations, space-time geospatial statistics, Task-based programming models

We extend the capability of space-time geostatistical modeling using algebraic approximations, illustrating application-expected accuracy worthy of double precision from majority low-precision computations and low-rank matrix approximations. We exploit the mathematical structure of the dense covariance matrix whose inverse action and determinant are repeatedly required in Gaussian log-likelihood optimization. Geostatistics augments first-principles modeling approaches for the prediction of environmental phenomena given the availability of measurements at a large number of locations; however, traditional Cholesky-based approaches grow cubically in complexity, gating practical extension to continental and global datasets now available. We combine the linear algebraic contributions of mixed-precision and low-rank computations within a tilebased Cholesky solver with on-demand casting of precisions and dynamic runtime support from PaRSEC to orchestrate tasks and data movement. Our adaptive approach scales on various systems and leverages the Fujitsu A64FX nodes of Fugaku to achieve up to 12X performance speedup against the highly optimized dense Cholesky implementation.

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