# Bivariate DeepKriging for Large-scale Spatial Interpolation of Wind Fields

arXiv: https://arxiv.org/abs/2307.08038 · HTML: https://mlsanity.com/paper/2307.08038/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 75 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 11 of 11)

- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks](https://mlsanity.com/paper/1907.04595/) (2019)
- [DeepKriging: Spatially Dependent Deep Neural Networks for Spatial Prediction](https://mlsanity.com/paper/2007.11972/) (2020)
- [Deep Compositional Spatial Models](https://mlsanity.com/paper/1906.02840/) (2019)
- [Valid model-free spatial prediction](https://mlsanity.com/paper/2006.15640/) (2020)
- [Deep Distribution Regression](https://mlsanity.com/paper/1903.06023/) (2019)
- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [Variational Inference to Measure Model Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/1902.10189/) (2019)
- [Cross-Covariance Functions for Multivariate Geostatistics](https://mlsanity.com/paper/1507.08017/) (2015)
- [Nearest-Neighbor Neural Networks for Geostatistics](https://mlsanity.com/paper/1903.12125/) (2019)
- [Interpretable Architecture Neural Networks for Function Visualization](https://mlsanity.com/paper/2303.03393/) (2023)

## Built on by (most cited first, 2 of 2)

- [Modeling nonstationary spatial processes with normalizing flows](https://mlsanity.com/paper/2509.12884/) (2025)
- [Deep classifier kriging for probabilistic spatial prediction of air quality index](https://mlsanity.com/paper/2512.23474/) (2025)

## Abstract (arXiv)

High spatial resolution wind data are essential for a wide range of applications in climate, oceanographic and meteorological studies. Large-scale spatial interpolation or downscaling of bivariate wind fields having velocity in two dimensions is a challenging task because wind data tend to be non-Gaussian with high spatial variability and heterogeneity. In spatial statistics, cokriging is commonly used for predicting bivariate spatial fields. However, the cokriging predictor is not optimal except for Gaussian processes. Additionally, cokriging is computationally prohibitive for large datasets. In this paper, we propose a method, called bivariate DeepKriging, which is a spatially dependent deep neural network (DNN) with an embedding layer constructed by spatial radial basis functions for bivariate spatial data prediction. We then develop a distribution-free uncertainty quantification method based on bootstrap and ensemble DNN. Our proposed approach outperforms the traditional cokriging predictor with commonly used covariance functions, such as the linear model of co-regionalization and flexible bivariate Mat'ern covariance. We demonstrate the computational efficiency and scalability of the proposed DNN model, with computations that are, on average, 20 times faster than those of conventional techniques. We apply the bivariate DeepKriging method to the wind data over the Middle East region at 506,771 locations. The prediction performance of the proposed method is superior over the cokriging predictors and dramatically reduces computation time.