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DeepKriging on the global Data

Hao-Yun Huang, Wen-Ting Wang, Ping-Hsun Chiang, Wei-Ying Wu

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.

DeepKriging on the global Data

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 . 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.

Paper Structure

This paper contains 13 sections, 27 equations, 6 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Spherical multi-resolution thin-plate spline basis functions (Spherical MRTS)
  4. Spherical TPS roughness penalty
  5. Knots and eigen-ordered multi-resolution bases
  6. Neural Network Architecture and Training
  7. Simulation Studies & Real Data Analysis
  8. Simulation
  9. (i) Stationary processes on $\mathbb{S}^2$
  10. Real Data
  11. (a) Temperature Dataset
  12. (b) Windspeed Dataset
  13. Conclusion

Figures (6)

  • Figure 1: Structure of a hidden-layer block in the DeepKriging neural network. Each block consists of an affine transformation followed by batch normalization, ReLU activation, and dropout, and is repeated $L$ times.
  • Figure 2: Realizations of Stationary Gaussian process (i)
  • Figure 3: Realizations of Local Extremes (ii)
  • Figure 4: Realizations of Non-stationary Local Extremes (iii)
  • Figure 5: Temperature data model prediction and residual.
  • ...and 1 more figures