GPU-Accelerated Simulation of Massive Spatial Data Based on the Modified Planar Rotator Model

  • Milan ŽukovičEmail author
  • Michal Borovský
  • Matúš Lach
  • Dionissios T. Hristopulos
Special Issue


A novel Gibbs Markov random field for spatial data on Cartesian grids based on the modified planar rotator (MPR) model of statistical physics has been recently introduced for efficient and automatic interpolation of big data sets, such as satellite and radar images. The MPR model does not rely on Gaussian assumptions. Spatial correlations are captured via nearest-neighbor interactions between transformed variables. This allows vectorization of the model which, along with an efficient hybrid Monte Carlo algorithm, leads to fast execution times that scale approximately linearly with system size. The present study takes advantage of the short-range nature of the interactions between the MPR variables to parallelize the algorithm on graphics processing units (GPUs) in the Compute Unified Device Architecture programming environment. It is shown that, for the processors employed, the GPU implementation can lead to impressive computational speedups, up to almost 500 times on large grids, compared to single-processor calculations. Consequently, massive data sets comprising millions of data points can be automatically processed in less than one second on an ordinary GPU.


Spatial interpolation Hybrid Monte Carlo Non-Gaussian model Conditional simulation GPU parallel computing CUDA 



This work was supported by the Scientific Grant Agency of Ministry of Education of Slovak Republic (Grant No. 1/0531/19). We also acknowledge support for a short visit by M. Ž. at the Technical University of Crete from the Hellenic Ministry of Education, Department of Inter-University Relations, the State Scholarships Foundation of Greece and the Slovak Republic’s Ministry of Education through the Bilateral Programme of Educational Exchanges between Greece and Slovakia.


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Copyright information

© International Association for Mathematical Geosciences 2019

Authors and Affiliations

  1. 1.Faculty of Science, Institute of PhysicsP. J. Šafárik UniversityKošiceSlovakia
  2. 2.Geostatistics Laboratory, School of Mineral Resources EngineeringTechnical University of CreteChaniaGreece

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