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

Geostatistical modeling is an efficient technique for climate and environmental analysis and prediction. A primary computational kernel of stationary spatial statistics is the evaluation of the Gaussian maximum log-likelihood estimation (MLE) function, whose central data structure is a dense, symmetric, and positive-definite covariance matrix of the dimension of the number of correlated observations. The MLE approach requires the application of its inverse and evaluation of its determinant, rendered through the Cholesky decomposition and triangular solution. In this paper, we migrate geostatistics to three precisions approximation by exploiting the mathematical structure of the dense covariance matrix. We illustrate application-expected accuracy worthy of double-precision from a majority half-precision computation, in a context where all single precision is by itself insufficient. We deploy PaRSEC runtime system with high productivity in mind to tackle the complexity and imbalance caused by the mixed three precisions. PaRSEC delivers within a solo Cholesky factorization on-demand casting of precisions while orchestrating tasks and data movement on heterogeneous environments. We maintain the application-expected accuracy while achieving against FP64-only operations up to 2.64X by mixing FP64-FP32-FP16 operations with various HPC systems. We deliver up to 9.1 (mixed) PFlop/s sustained performance, demonstrating the effective synergism between PaRSEC and environmental HPC applications.