Reliability-based mix design for concrete compressive strength using a physics-prior residual-learning surrogate with calibrated uncertainty - Pengfei Qu; Lei Song; Sihan Wang (PLoS ONE, 2026)
An integrated framework is presented for concrete compressive strength prediction and reliability-based mix design under data-scarce conditions, in which a physics-prior residual surrogate and uncertainty decomposition are combined. A physics-consistent baseline is constructed from an effective water-to-binder ratio with age effects, time-dependent reactivity of supplementary cementitious materials and the influence of superplasticizer on effective water demand, and is globally calibrated on the training data. A small residual neural network is then superposed on this baseline with explicit regularization, so that remaining nonlinear interactions are learned while the physical scale and monotonicity are preserved. SHAP values and partial dependence curves are used to confirm the dominant positive roles of age and cementitious content, the negative effect of water, and physically plausible nonlinear effects of admixtures and aggregates. The framework is evaluated on a publicly available high-performance concrete strength dataset containing 1,030 mixtures and 8 input variables; the hybrid Physics+Data model attains R 2 = 0.9252 and RMSE = 4.39 MPa on an independent test set and maintains similar accuracy when only 40% of the training samples are used. Five-fold cross-validation confirms the stability of these results. Refined uncertainty quantification is carried out by combining mild Monte Carlo dropout, feature and physics-parameter perturbations and a single scaling factor for coverage calibration, yielding nominal 95% prediction intervals with about 95.1% empirical coverage and showing the physics sub-model as the dominant source of variance. On the calibrated surrogate, 28-day reliability-based design maps in the w / b – C plane for a 40 MPa strength target are produced, from which mix recommendations such as w / b ≈ 0.33 –0.36 and C ≈ 340 –360 kg/m 3 for P ≥ 0.80 are derived.