CNNs replace Kriging for single-field spatial interpolation from sparse data

A new paper on arXiv (2605.30167) by Daniel Tinoco, Raquel Menezes, Carlos Baquero, and Alexandra Silva introduces a convolutional neural network (CNN) architecture for single-field spatial interpolation—a task traditionally dominated by geostatistical methods like Kriging. The key innovation is that the CNN is trained and applied entirely on a single partially observed spatial field, without any external data or prior fields. Supervision comes solely from the sparse observed locations, allowing the model to learn to predict values at unobserved points on a user-defined grid. This removes the need for explicit covariance modeling, variogram estimation, or Gaussian process assumptions, which often limit Kriging in non-stationary environments. The model flexibly captures local spatial patterns in a purely data-driven manner. The paper runs 53 pages with 10 figures, demonstrating the method's potential across various synthetic and real-world examples.

The work presents a practical alternative to classical geostatistics, especially for scenarios where domain expertise in variography is scarce or where spatial processes exhibit strong non-stationarity. By extending the use of CNNs to the new problem domain of single-instance spatial interpolation, the authors show that deep learning can compete with—and in some cases outperform—traditional interpolation techniques without requiring massive training datasets. The method is particularly relevant for environmental scientists, geographers, and engineers who need to reconstruct complete spatial fields (e.g., temperature, pollution, soil properties) from limited sensor readings. This approach could democratize spatial interpolation, making it more accessible to practitioners who are comfortable with deep learning but less familiar with classical geostatistics.