Automatic variogram inference using pre-trained Convolutional Neural Networks

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.