Geostatistical Modeling and Prediction Using Mixed Precision Tile Cholesky Factorization
KAUST DepartmentExtreme Computing Research Center
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Office of the President
Permanent link to this recordhttp://hdl.handle.net/10754/666233
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AbstractGeostatistics represents one of the most challenging classes of scientific applications due to the desire to incorporate an ever increasing number of geospatial locations to accurately model and predict environmental phenomena. For example, the evaluation of the Gaussian log-likelihood function, which constitutes the main computational phase, involves solving systems of linear equations with a large dense symmetric and positive definite covariance matrix. Cholesky, the standard algorithm, requires O(n^3) floating point operators and has an O(n^2) memory footprint, where n is the number of geographical locations. Here, we present a mixed-precision tile algorithm to accelerate the Cholesky factorization during the log-likelihood function evaluation. Under an appropriate ordering, it operates with double-precision arithmetic on tiles around the diagonal, while reducing to single-precision arithmetic for tiles sufficiently far off. This translates into an improvement of the performance without any deterioration of the numerical accuracy of the application. We rely on the StarPU dynamic runtime system to schedule the tasks and to overlap them with data movement. To assess the performance and the accuracy of the proposed mixed-precision algorithm, we use synthetic and real datasets on various shared and distributed-memory systems possibly equipped with hardware accelerators. We compare our mixed-precision Cholesky factorization against the double-precision reference implementation as well as an independent block approximation method. We obtain an average of 1.6X performance speedup on massively parallel architectures while maintaining the accuracy necessary for modeling and prediction.
CitationAbdulah, S., Ltaief, H., Sun, Y., Genton, M. G., & Keyes, D. E. (2019). Geostatistical Modeling and Prediction Using Mixed Precision Tile Cholesky Factorization. 2019 IEEE 26th International Conference on High Performance Computing, Data, and Analytics (HiPC). doi:10.1109/hipc.2019.00028
SponsorsThe authors would like to thank NVIDIA Inc., Cray Inc., and Intel Corp., the Cray Center of Excellence and Intel Parallel Computing Center awarded to the Extreme Computing Research Center (ECRC) at KAUST. For computer time, this research used GPU-based systems as well as Shaheen supercomputer hosted at the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST).
Conference/Event name26th Annual IEEE International Conference on High Performance Computing, HiPC 2019