A Neural Network Framework with Embedded Experimental Variograms for Sparse Spatial Interpolation in Geotechnical Site Investigation

Variogram-based spatial correlation remains fundamental in geostatistical analysis, yet traditional approaches face persistent challenges in variogram model selection and parameter estimation. This study presents a novel neural network framework that directly incorporates experimental variograms into the learning process, eliminating the need for explicit variogram model specification. By embedding the empirical variogram structure as a spatial constraint in the neural architecture, the proposed approach preserves the interpretability of geostatistical methods while leveraging the flexibility of machine learning. The proposed method automatically captures spatial correlation patterns from data without requiring manual selection of theoretical variogram models or parameter fitting procedures. Numerical experiments demonstrate that this approach achieves comparable or superior prediction accuracy to conventional geostatistical methods across various spatial correlation structures. The framework shows particular robustness in cases where traditional variogram modeling would be challenging, such as with complex spatial patterns or limited data. The results suggest that direct integration of experimental variograms into machine learning architectures offers a promising direction for automated spatial analysis while maintaining geostatistical interpretability.

Keywords: Spatial prediction, Neural networks, Experimental variogram, Geostatistics, Sparse data, Spatial correlation.