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

arXiv: https://arxiv.org/abs/2605.30167 · HTML: https://mlsanity.com/paper/2605.30167/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 41 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 1 of 1)

- [Review: Nonstationary Spatial Modeling, with Emphasis on Process Convolution and Covariate-Driven Approaches](https://mlsanity.com/paper/1610.02447/) (2016)

## Abstract (arXiv)

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.