Technical Papers Archive

Reshaping Geostatistical Modeling and Prediction for Extreme-Scale Environmental Applications

Authors: Qinglei Cao (University of Tennessee, Innovative Computing Laboratory); Sameh Abdulah and Rabab Alomairy (King Abdullah University of Science and Technology (KAUST)); Yu Pei (University of Tennessee, Innovative Computing Laboratory); Pratik Nag (King Abdullah University of Science and Technology (KAUST)); George Bosilca (University of Tennessee, Innovative Computing Laboratory); Jack Dongarra (University of Tennessee, Innovative Computing Laboratory; Oak Ridge National Laboratory (ORNL)); and Marc Genton, David Keyes, Hatem Ltaief, and Ying Sun (King Abdullah University of Science and Technology (KAUST))

Abstract: 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 tile-based 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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