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    High Performance Multivariate Spatial Modeling for Geostatistical Data on Manycore Systems

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    Type
    Preprint
    Authors
    Salvaña, Mary Lai O.
    Abdulah, Sameh
    Huang, Huang cc
    Ltaief, Hatem cc
    Sun, Ying cc
    Genton, Marc G. cc
    Keyes, David E. cc
    KAUST Department
    Extreme Computing Research Center, Computer, Electrical, and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.
    Extreme Computing Research Center
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Applied Mathematics and Computational Science Program
    Office of the President
    Date
    2020-08-03
    Permanent link to this record
    http://hdl.handle.net/10754/666235
    
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    Abstract
    Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the cokriging technique. The latter requires the evaluation of the expensive Gaussian log-likelihood function, which has impeded the adoption of multivariate geospatial models for large multivariate spatial datasets. However, this large-scale cokriging challenge provides a fertile ground for supercomputing implementations for the geospatial statistics community as it is paramount to scale computational capability to match the growth in environmental data coming from the widespread use of different data collection technologies. In this paper, we develop and deploy large-scale multivariate spatial modeling and inference on parallel hardware architectures. To tackle the increasing complexity in matrix operations and the massive concurrency in parallel systems, we leverage low-rank matrix approximation techniques with task-based programming models and schedule the asynchronous computational tasks using a dynamic runtime system. The proposed framework provides both the dense and the approximated computations of the Gaussian log-likelihood function. It demonstrates accuracy robustness and performance scalability on a variety of computer systems. Using both synthetic and real datasets, the low-rank matrix approximation shows better performance compared to exact computation, while preserving the application requirements in both parameter estimation and prediction accuracy. We also propose a novel algorithm to assess the prediction accuracy after the online parameter estimation. The algorithm quantifies prediction performance and provides a benchmark for measuring the efficiency and accuracy of several approximation techniques in multivariate spatial modeling.
    Sponsors
    The 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).
    Publisher
    arXiv
    arXiv
    2008.07437
    Additional Links
    https://arxiv.org/pdf/2008.07437
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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