Probabilistic Prediction of Rock Strength: Physics-Featured Gaussian Process Regression

Laboratory determination of uniaxial compressive strength (UCS) after in situ sampling is costly and slow. Coupling measurement while drilling (MWD) with machine learning can recover UCS in place. Most such models, however, return point estimates and quantify uncertainty only weakly. This study compiled 161 records from seven sources. Records that recur across sources were removed, leaving 111 unique records, 93 of them soft rock with torque below 100 kN·m. PG-GPR was fitted to these 93 records and checked by five-fold cross-validation with ten random seeds. Against a baseline that used the same kernel on the four raw drilling channels, R2 rose from 0.925 ± 0.011 to 0.964 ± 0.006 and mean absolute error fell from 3.19 ± 0.22 MPa to 2.25 ± 0.15 MPa. At comparable empirical coverage, mean interval width fell from 14.45 ± 0.43 MPa to 8.60 ± 0.25 MPa, and CRPS fell from 2.37 ± 0.12 to 1.65 ± 0.12. Leave-one-source-out scoring of all 93 held-out records together gives R2 = 0.463 and RMSE = 12.11 MPa.