Leveraging Deep Learning for Automated Experimental Semivariogram Fitting

The variogram function is a crucial tool for quantifying spatial correlation and a key component of Kriging interpolation, directly influencing the accuracy of interpolation results. However, traditional variogram fitting methods, such as least squares and weighted polynomial regression, often face limitations when handling complex or non-stationary spatial structures, which can lead to unstable fitting outcomes. To address these challenges, this paper proposes an automatic fitting method for experimental variogram functions based on deep learning. The variogram fitting process is inherently a nonlinear optimization problem, where the goal is to optimize the alignment between experimental and theoretical variogram functions. In this study, we construct a deep learning model designed to capture the nonlinear characteristics of experimental variograms with the objective of minimizing fitting errors and improving both the accuracy and stability of the fitting process. Extensive experimental results demonstrate that the proposed neural network model can effectively learn to fit a variety of experimental variograms and accurately represent different theoretical variogram functions. Compared to traditional methods, this approach consistently achieves superior fitting performance across multiple datasets, validating its effectiveness and robustness under diverse conditions. The stronger generalization capability and improved accuracy of the proposed method significantly enhance the automatic fitting of experimental variogram functions.