Explainable Machine Learning Framework with Experimental Validation for Strength Prediction of Magnesium Phosphate Cement

Abstract Magnesium Phosphate Cement (MPC) is recognized as an effective rapid repair material, with compressive strength serving as a key mechanical property indicator for its mortar formulations. Nevertheless, due to MPC's complex composition and formulation, predicting its compressive strength remains a significant challenge. In this study, a comprehensive database was developed, incorporating four key input variables: the magnesium-to-phosphate (M/P) molar ratio, water-to-cement (W/C) mass ratio, sand-to-binder (S/B) weight ratio, and the borax-to-magnesia(B/M) weight ratio. This dataset was used to train and validate eight machine learning models, including the Lightweight Gradient Boosting (LGB) algorithm, Support Vector Machine (SVM), Decision Tree (DT), Extreme Gradient Boosting (XGB), Ridge Regression (RR), Random Forest (RF), Backpropagation Neural Network (BP), and Gradient Boosting (GB) models. The eight machine learning models were evaluated using performance metrics, including Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), Correlation Coefficient, and Root Mean Square Error (RMSE), to identify the optimal model, which was then optimized via the Gray Wolf Optimizer (GWO). The most accurate prediction of MPC compressive strength was attained using the XGB model, with the GWO-optimized XGB model showing enhancement in MAPE, MAE, R2, and RMSE by 21.8%, 60.6%, 43.9%, and 55.3% respectively, relative to the unoptimized XGB model. Employing Shapley Additive exPlanations (SHAP) values and Partial Dependence Plots (PDP), this study facilitates the identification of the most influential input variables and quantifies their effects on MPC compressive strength. The optimized model was validated against experimental data, demonstrating robust and conservative prediction behavior. While the model is trained solely to predict compressive strength, its interpretability enables rational insights into how formulation variables influence strength, thereby supporting informed mix design decisions. This framework offers a reliable and transparent computational tool for preemptive strength assessment of MPC and guides the optimization of mechanical performance in structurally demanding applications.