Spatial Interpolation With Locally Varying Anisotropy Using Deep Neural Networks

ABSTRACT In spatial interpolation, both distance and direction play critical roles. While Euclidean distance captures only isotropic spatial characteristics, extended methods have introduced non‐Euclidean metrics to better reflect spatial anisotropy. However, most existing approaches primarily address global anisotropy, typically assuming that anisotropic parameters—such as scaling and principal direction—are spatially uniform. Consequently, these methods are often inadequate in scenarios where anisotropic properties vary across space. To address this limitation, we propose a novel interpolation model—LVANN (Locally Varying Anisotropy Neural Network for Spatial Interpolation)—which explicitly incorporates locally varying anisotropy into a deep neural network model. Our approach reformulates the representation of anisotropic spatial distance as a structural design and optimization problem within a geographic neural architecture, enabling the model to more effectively capture complex and nonlinear spatial dependencies. We conduct extensive experiments to evaluate the performance of LVANN under both globally and locally anisotropic conditions. Under global anisotropy, LVANN reduces mean absolute error (MAE) by an average of 27% compared to state‐of‐the‐art baselines. Under locally varying anisotropy, it achieves a performance improvement of approximately 10% over the best existing method. These results demonstrate that LVANN is a powerful tool for modeling spatial anisotropy by leveraging the capabilities of deep neural networks.