Visual Spatial Learning: Single-Field Spatial Interpolation Using Convolutional Neural Networks

2026-05-28

AI Summary

This study addresses the limitations of traditional Kriging in non-stationary environments, where performance is hindered by its reliance on covariance modeling. To overcome this, the authors propose an end-to-end spatial interpolation method based on convolutional neural networks (CNNs). Requiring only a single partially observed field, the approach is trained under sparse supervision on user-defined grids without external data, prior assumptions, or explicit variogram estimation. As the first work to apply CNNs to single-instance, sparsely supervised spatial interpolation, it effectively captures local spatial patterns and demonstrates significantly superior performance over conventional Kriging in non-stationary settings, thereby highlighting the potential of deep learning to establish a new paradigm in spatial statistics.

Abstract

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.

Problem

• spatial interpolation
• non-stationary fields
• sparse observations
• geostatistics
• spatial prediction

Innovation

• convolutional neural networks
• spatial interpolation
• single-field learning
• non-stationary spatial data
• data-driven geostatistics