Probabilistic characterization of 3D geotechnical variability by fusion of multi-fidelity measurements using Gaussian Process Regression

Characterization of three-dimensional (3D) subsurface geotechnical properties is essential for the safe design and analysis of geotechnical infrastructures. Due to the complex geological formation process, these properties exhibit strong spatial variability. However, because of time and budget constraints and/or limited technical access, high-fidelity measurements (e.g., standard penetration test, SPT) are typically sparse. Directly interpreting a 3D subsurface profile from such sparse high-fidelity data can lead to significant statistical uncertainty, which may propagate and compromise project safety. Meanwhile, although various low-fidelity measurements (e.g., geophysical data, measurements at similar geotechnical sites) are often available, they are not fully utilized in practice. This study proposes a Gaussian Process Regression (GPR)–based framework to fuse information from multi-fidelity measurements to facilitate the accurate characterization of site-specific 3D variability. The proposed method first trains separate Gaussian process models on each low-fidelity dataset and uses their combined predictions in a linear regression to approximate high-fidelity values. Next, a new GPR is used to fit the residuals to correct remaining discrepancy, producing a final calibrated estimate. The method is demonstrated on a synthetic 3D subsurface case and a real-world case. The results show the proposed method yields much lower prediction errors and uncertainty compared to using only the high-fidelity measurements, with R² values improved by approximately 50%/443% and MSE reduced by about 36%/72% in the numerical/real-life case. A sensitivity study further verifies the robustness of the proposed framework, showing that the method proposed in this study is capable of accurately and efficiently characterizing 3D geotechnical variability by fusing of multi-fidelity measurements.