DeKNN: Decompositional Kriging Neural Network for efficient and interpretable spatiotemporal interpolation

Spatiotemporal interpolation is a fundamental task in geographic information science and a key component of Earth observation data analysis, supporting applications such as meteorological monitoring, air quality assessment, hydrological analysis, and transportation. Incomplete sampling leads to different types of data scarcity. Missing at random (MAR) refers to sparse missing values scattered across observed locations and timestamps, whereas missing completely at location (MCAL) denotes the absence of complete time series at specific locations. Compared with MAR, MCAL is more challenging because there is no temporally contiguous data available for direct interpolation. Existing geostatistical methods provide theoretical interpretability but often lack the capacity to capture complex data structures. Deep learning methods can model nonlinear spatiotemporal patterns, but they commonly suffer from opaque decision-making processes and high computational costs. To address these challenges, this study proposes a Decompositional Kriging Neural Network (DeKNN) for efficient and interpretable MCAL interpolation. The core idea of DeKNN is to shift interpolation from the original high-dimensional spatiotemporal field to a compact latent spatial space. First, a decomposer based on position-aware gated network maps spatiotemporal observations into latent spatial features. Second, a latent-space Kriging neural network estimates latent features at unsampled locations by learning distance-aware covariance structures. Third, a dual-branch reconstructor recovers the complete time series from the interpolated latent features, preserving high accuracy while providing interpretable temporal basis vectors. This decomposition–interpolation–reconstruction design reduces the computational burden of high-dimensional spatiotemporal interpolation while retaining geostatistical interpretability. In addition, the adjoint Kriging mechanism links forward interpolation with backward parameter learning under the same Kriging system. Experiments on two real-world datasets show that DeKNN achieves the best accuracy among the compared baselines and substantially improves computational efficiency. The learned latent spatial features and covariance structures further illustrate the interpretability.