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This paper introduces a CNN-based approach for single-field spatial interpolation, predicting a complete spatially correlated field from sparse observations. The CNN is trained directly on the partially observed field, learning to predict values at unobserved locations without relying on external data or prior fields. Results demonstrate that this method offers a practical alternative to Kriging and other geostatistical methods by flexibly capturing local spatial patterns in a data-driven manner.
Ditch the variograms: CNNs can interpolate spatial data from a single, sparsely observed field, rivaling Kriging without needing Gaussian process assumptions or domain expertise.
Predicting a complete spatially correlated field from sparse observations is a fundamental challenge in spatial statistics and environmental modelling. Classical interpolation methods such as Kriging rely on Gaussian process assumptions and variography, which can limit their effectiveness in non-stationary settings and require substantial domain expertise. In this work, we leverage an architecture based on convolutional neural networks (CNNs) for spatial interpolation that is trained and applied on a single partially observed field, without access to external data or prior fields. The model is supervised directly on the observed locations and learns to predict values at unobserved points on the user defined grid. Unlike Kriging, our method does not require explicit covariance modelling or variogram estimation, and it can flexibly capture local spatial patterns in a data-driven manner. This work demonstrates the potential of CNNs for single-instance spatial interpolation under sparse supervision, offering a practical alternative to classical geostatistical methods, and extending the use of CNNs to a new problem domain.