Visual Spatial Learning: Single-Field Spatial Interpolation Using Convolutional Neural Networks
For geostatisticians and environmental modelers, this provides a data-driven alternative to Kriging that avoids explicit covariance assumptions, though it is an incremental application of existing CNNs to a new domain.
This work introduces a CNN-based method for spatial interpolation from a single partially observed field, achieving competitive accuracy without requiring covariance modeling or external data. The method outperforms Kriging in non-stationary settings, as demonstrated on synthetic and real-world datasets.
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.