A physics-informed probabilistic machine learning framework for mix design optimisation of waste-based cementitious composites: Uncertainty quantification, SHAP interpretability, and multi-objective pareto analysis

Cement production contributes approximately 8% of global anthropogenic CO₂ emissions, motivating the development of low-carbon concrete through supplementary cementitious materials (SCMs) including fly ash, GGBS, and calcined clays. Existing machine learning models primarily rely on raw mixture proportions as predictors, limiting mechanistic interpretation of feature importance and rarely incorporating structural reliability during optimisation. This study presents a physics-informed probabilistic machine learning framework that transforms raw mixture proportions into five chemistry-derived descriptors grounded in cement hydration kinetics and particle packing theory. The framework trains a heteroscedastic gradient-boosted model to predict both mean compressive strength and its uncertainty, applies SHAP analysis including interaction-level attribution, and performs reliability-constrained multi-objective Pareto optimisation balancing strength, embodied carbon, and waste utilisation. The framework was developed and evaluated using the Yeh (1998) benchmark dataset, the five-feature model achieves a test R² of 0.923 (RMSE = 4.46 MPa, five-fold CV R² = 0.916 ± 0.009), comparable to an eight-variable raw-input model with 40% fewer predictors. A dedicated calibration analysis revealed the initial heteroscedastic variance estimates were overconfident (77.7% empirical coverage against a 95% nominal target); a scalar recalibration factor of 1.95 restored coverage to 95.6% and was propagated through the optimisation stage. Hybrid GGBS-fly ash blends exhibit 27.7% higher predicted uncertainty than plain cement mixtures. Under the calibrated framework, a structural reliability index of β ≥ 3.0 eliminates 19.7% of nominally feasible mixtures, and the Pareto front reveals a trade-off of approximately 25 MPa per 100 kg CO₂/m³ of embodied carbon. SHAP interaction analysis identifies the effective water-to-binder ratio and maturity index as the strongest interacting predictors. Benchmarking against Random Forest, Support Vector Regression, and Artificial Neural Network models confirms the adopted architecture as the strongest performer. The framework provides a transparent, uncertainty-aware, reliability-constrained tool for sustainable mix design, and its calibration methodology offers a template for honest uncertainty reporting in probabilistic machine learning applications to cementitious materials.