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, which requires the evaluation of the expensive Gaussian log-likelihood function. 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. In this paper, we develop 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 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.
|Original language||English (US)|
|Number of pages||1|
|Journal||IEEE Transactions on Parallel and Distributed Systems|
|State||Published - Apr 6 2021|
Bibliographical noteKAUST Repository Item: Exported on 2021-04-08
Acknowledgements: 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, both hosted at the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST).