Comparison among creator variable machine methods: Compressive strength prediction of ultra-high-performance concrete

Ultra-High-Performance Concrete (UHPC) is widely used as a construction material for critical infrastructure. This study presents several equations to design the mixture of UHPC for structural elements. A Dataset of 810 mixtures and their Compressive Strength (CS) was collected from the literature. The white-box AI methods include High Correlated Variables Creator Machine (HCVCM), Modified Stronger Variables Creator Machine (MSVCM), Gene Expression Programming (GEP), and two ensemble methods combining HCVCM with GEP, as well as MSVCM with GEP. A sensitivity analysis for selecting the percentage of training and testing datasets was performed, and based on this analysis, the data were randomly divided into 70% for training and 30% for testing. To ensure robustness, an additional five-fold cross-validation was conducted. Statistical parameters and error terms were computed to compare the accuracy of models. Additionally, SHapley Additive exPlanations (SHAP) and Local Interpretable Model-agnostic Explanations (LIME) were employed as feature sensitivity analysis methods to interpret the predictions of the best-performing model. The results demonstrate that the MSVCM with GEP ensemble model outperforms all others, improving GEP's accuracy in the testing dataset by approximately 3% in the coefficient of determination (from 0.886 to 0.914), 45% in RMSE (from 31.57 MPa to 17.26 MPa), 45% in NMSE (from 0.204 to 0.111), and 31% in MAPE (from 17.32% to 11.93%). The maximum negative error was reduced by about 6 MPa (from –54.56 MPa to –48.44 MPa). Among single models, MSVCM achieves the best performance, with R² = 0.893, RMSE = 20.78 MPa, and NMSE = 0.124 on the testing dataset. Five-fold cross-validation further confirms the robustness of the MSVCM with GEP ensemble (R² = 0.896 ± 0.005, RMSE = 19.94 ± 0.50 MPa), indicating excellent generalisation capability.