Accelerating Geostatistical Modeling and Prediction With Mixed-Precision Computations: A High-Productivity Approach With PaRSEC

Geostatistical modeling, one of the prime motivating applications for exascale computing, is a technique predicting desired quantities from geographically distributed data, based on statistical models and optimization parameters. Spatial data are assumed to possess properties stationarity or non-stationarity via kernel fitted covariance matrix. A primary workhorse stationary spatial statistics Gaussian maximum log-likelihood estimation (MLE), whose central structure dense, symmetric positive definite matrix dimension number correlated observations. Two essential operations in MLE application inverse evaluation determinant These can be rendered through Cholesky decomposition triangular solution. In this contribution, we reduce precision weakly locations single- half- distance. We thus exploit mathematical migrate three-precision approximation that takes advantage contemporary architectures offering BLAS3-like single instruction extremely fast reduced precision. illustrate application-expected accuracy worthy double-precision majority half-precision computation, context where uniform single-precision by itself insufficient. tackling complexity imbalance caused mixing three precisions, deploy PaRSEC runtime system. delivers on-demand casting precisions while orchestrating tasks movement multi-GPU distributed-memory environment within tile-based factorization. Application-expected maintained achieving up $1.59X$ FP64/FP32 1536 nodes HAWK 4096 Shaheen II , notation="LaTeX">$2.64X$ FP64/FP32/FP16 128 Summit relative FP64-only operations. This translates into 4.5, 4.7, 9.1 (mixed) PFlop/s sustained performance, respectively, demonstrating synergistic combination architecture, dynamic software, algorithmic adaptation applied challenging environmental problems.