🤖 AI Summary
This study addresses the limitations of traditional spatial prediction methods on spherical domains, which often suffer from distance distortion due to reliance on Euclidean metrics or planar projections and struggle to scale to large datasets. To overcome these challenges, the authors propose Spherical DeepKriging—a novel framework that integrates intrinsic spherical thin-plate spline basis functions with deep learning to flexibly capture complex spatial structures on the sphere. This approach represents the first fusion of native spherical basis functions and neural networks for scalable geostatistical modeling. It effectively circumvents the constraints of classical kriging under global-scale and big-data scenarios, demonstrating superior predictive accuracy and computational scalability over existing methods in both synthetic and real-world global datasets.
📝 Abstract
The increasing availability of large-scale global datasets has generated a demand for scalable spatial prediction methods defined on spherical domains. Classical spatial models that rely on Euclidean distance representations are inappropriate for spherical data because planar projections distort geodesic distances and spatial neighborhood structures, while traditional kriging-based prediction methods are often computationally prohibitive for massive datasets. To address these challenges, we propose a Spherical DeepKriging framework for spatial prediction on $\mathbb{S}^2$. The proposed approach constructs a flexible prediction model by integrating thin-plate spline (TPS) basis functions defined intrinsically on the sphere. Simulation studies and real data analyses are presented to demonstrate the superior predictive performance of the proposed method.