A Machine Learning Model for HTHP Shear-Stress Prediction of Oil-Based Drilling Fluid Using Polynomial-Corrected RBF-CRM

Accurate prediction of the shear stress of oil-based drilling fluids (OBDF) under high-temperature and high-pressure (HTHP) conditions is essential for drilling-hydraulics calculation and safe drilling operations. However, conventional rheological equations and existing data-driven methods still have difficulty in describing the coupled temperature-pressure response of OBDF over a wide HTHP range, especially in low-shear regimes where small stress magnitudes and structural sensitivity increase prediction uncertainty. To address this issue, this study experimentally investigated the effects of temperature, pressure, and density on OBDF shear stress and developed a polynomial-corrected Gaussian radial basis function (RBF) model with complex regularization method (CRM)-based coefficient solving. Three density systems of 1.5, 1.6, and 1.8 g/cm 3 were tested at six shear rates under HTHP conditions. Five conventional rheological models were first evaluated, and the four-parameter model was identified as the most suitable physics-based equation for the tested fluids, although deviations remained under strongly nonlinear conditions. The proposed RBF-CRM framework combines the local nonlinear approximation capability of Gaussian RBF with a polynomial term for global trend compensation, while CRM improves the stability of coefficient estimation. Cross-validation showed smooth error variation with the regularization parameter, indicating robust parameter selection. Across all tested density and shear rate conditions, the proposed model achieved coefficient of determination (R 2 ) values of 0.975–0.999, mean absolute error (MAE) values of 0.165–1.406 Pa, and root mean square error (RMSE) values of 0.227–2.458 Pa. In the medium- and high-shear regimes, the R 2 values were generally higher than 0.995, indicating reliable predictive accuracy under hydraulically relevant shear conditions. These results indicate that the proposed RBF-CRM model provides an accurate and stable approach for OBDF shear-stress prediction under HTHP conditions.