Mathematical Geoscience manuscript No. (will be inserted by the editor) GPU-accelerated Simulation of Massive Spatial Data based on the Modified Planar Rotator Model Milan Zukoviˇcˇ · Michal Borovsk´y · Mat´uˇs Lach · Dionissios T. Hristopulos Received: date / Accepted: date Abstract 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 assump- tions. Spatial correlations are captured via nearest-neighbor interactions between Milan Zukoviˇcˇ Institute of Physics, Faculty of Science, P. J. Saf´arikˇ University, Park Angelinum 9, 041 54 Koˇsice, Slovakia Tel.: +421-552342544 E-mail:
[email protected] Michal Borovsk´y Institute of Physics, Faculty of Science, P. J. Saf´arikˇ University, Park Angelinum 9, 041 54 Koˇsice, Slovakia Tel.: +421-552342544 E-mail:
[email protected] Mat´uˇsLach Institute of Physics, Faculty of Science, P. J. Saf´arikˇ University, Park Angelinum 9, 041 54 Koˇsice, Slovakia Tel.: +421-552342565 E-mail:
[email protected] Dionissios T. Hristopulos Geostatistics Laboratory, School of Mineral Resources Engineering, Technical University of Crete, Chania 73100, Greece Tel.: +30-28210-37688 arXiv:1811.01604v2 [physics.comp-ph] 18 Oct 2019 Fax: +30-28210-37853 E-mail:
[email protected] 2 Milan Zukoviˇcetˇ al. 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.