Automatic variogram inference using pre-trained Convolutional Neural Networks
Mokdad Karim, Koushavand Behrang, Boisvert Jeff · Applied Computing and Geosciences · 2025
A novel approach is presented for inferring covariance functions from sparse data using Convolutional Neural Networks (CNNs). Two workflows are proposed: (1) direct prediction of variogram model parameters, and (2) prediction of experimental variogram values at specified lag distances, which are smooth and easily autofit. Workflow 1 achieves an r-squared of 0.80, while Workflow 2 attains a higher r-squared of 0.96. Data augmentation through rotation improves robustness, and can be used to examine variogram uncertainty; the distribution for each predicted parameter can be obtained and used in uncertainty modeling. The CNNs are pre-trained, ensuring minimal computational time and fully automated processing. The workflows are applicable to sparse or dense data but are currently limited to 2D normal score variograms. • Two novel methodologies for the automatic inference of variograms using pre-trained convolutional neural networks. • (1) The first aims to directly predict the variogram model parameters (e.g. range). • (2) The second aims to predict the experimental variogram values at specified lag distances which outperforms the first workflow. • Both workflows are fully automatic alternatives to variogram modeling and variogram calculations. • User modeling time is reduced. • Minimize user interaction and reduce the number of parameters for traditional geostatistical inference. • Negligible runtime because the CNN is pre-trained.