Some enhancements to DeepKriging

With an increased volume of spatial data, conventional spatial prediction methods have encountered significant challenges in handling complex data structures while maintaining statistical and computational efficiency. Recently, a spatial neural network method called DeepKriging has been proposed, which utilizes a set of basis functions as an embedded input to capture spatial information. In this study, we enhance this approach by using an ordered set of multi‐resolution thin plate spline basis functions, which offers ease of implementation and alleviates the challenges associated with basis function allocation, particularly when the data locations are highly irregular. The proposed method requires only the selection of the number of basis functions based on a validation dataset. In addition, we propose a robust version of DeepKriging, which is resistant to outliers. Several simulation experiments are conducted to show the advantages of our method over conventional statistical methods and the original DeepKriging approach. Finally, we apply the proposed method to a PM 2.5 dataset in Taiwan.