A comparative study of classic, evolutionary, and ensemble machine learning methods for pressuremeter modulus prediction

Accurate determination of the pressuremeter modulus (Ep) is essential for foundation design and settlement analysis in geotechnical engineering, while direct pressuremeter testing remains costly and time-consuming. This study develops and compares five machine learning models from three methodological families for predicting Ep: classic machine learning (Support Vector Regression (SVR) and k-Nearest Neighbors (kNN)), evolutionary computation (Multi-Expression Programming (MEP)), and ensemble learning (Random Forest (RF) and Extreme Gradient Boosting (XGBoost)). The models use four routinely measured index properties, including depth (H), moisture content (ω), bulk density (ρ), and fines content (FC), from 103 pressuremeter tests collected at 103 distinct sites in Mashhad, Iran. Baselines included a mean predictor, ordinary least squares (OLS) regression, and a depth-only linear model. Performance was assessed through three accuracy indices (correlation coefficient, Willmott’s index of agreement, and Nash-Sutcliffe efficiency) and two error-based indicators (mean absolute error and root mean square error), all reported in kg/cm 2 . Under repeated 5-fold cross-validation and leave-one-out cross-validation, OLS, SVR, RF, and XGBoost performed statistically equivalently (LOOCV R 2 ≈ 0.974–0.978), while the depth-only linear model achieved R 2 = 0.969. An ablation analysis excluding depth caused R 2 to collapse to 0.30–0.37 for all models, confirming that depth dominates Ep prediction in this region. MEP evolved a nonlinear depth-only equation (test R 2 = 0.964) that provides comparable accuracy with full transparency and spreadsheet-level implementation. SHAP analysis confirmed the dominance of depth (88.5% importance) and the approximate linearity of the underlying relationship. Jackknife+ conformal prediction produced well-calibrated 95% intervals with 93.5% empirical coverage for both SVR and MEP. The study provides a dual-outcome framework: practitioners can adopt the SVR for maximum accuracy or use the transparent MEP equation for routine engineering calculations, both within the investigated regional conditions.