Data-driven sparse learning of three-dimensional subsurface properties incorporating random field theory

Geotechnical engineers rely on accurate soil property information for engineering analyses. However, it is challenging for spatial learning of soil attributes because in-situ geotechnical testing is typically performed sparsely at discrete locations, and soil properties also exhibit inherent spatial variability. Traditional geostatistical methods for predicting spatial properties at these unsampled locations exhibit high computational complexity and require pre-determination of hyper-parameters, while pure data-driven methods fail to integrate geotechnical knowledge. In this study, a hybrid and parameter-free framework that uses random field theory and machine learning is proposed to model 3D subsurface field with reduced computational complexity. The framework constructs site-specific basis functions for characterizing the spatial variations of soil properties by decomposing a correlation matrix through principal component analysis. To further reduce the computational complexity involved in processing high-dimensional correlation matrices, a sparse sampling strategy is adopted to map correlation matrix onto lower-rank principal component space. A series of synthetic random field examples are generated to illustrate the impact of scale of fluctuation and autocorrelation functions on the accuracy and sensitivity of subsurface modeling. The performance of the proposed method is further validated using both synthetic cases and two real case histories. It is demonstrated that the proposed method generally achieves higher R² and lower root mean square error (RMSE) and mean absolute percentage error (MAPE) compared to state-of-the-art methods, such as Kriging and Bayesian compressive sensing. Moreover, the proposed method facilitates the explicit quantification of uncertainty associated with the subsurface models, providing valuable insights for engineering design and analysis. The data and code used in this study are available at https://github.com/Data-Driven-RFT/Sparse-Learning.