Physics-Informed Multi-Task Neural Network (PINN) Learning for Ultra-High-Performance Concrete (UHPC) Strength Prediction

Ultra-high-performance concrete (UHPC) mixtures exhibit tightly coupled ingredient–property relations and heterogeneous reporting, which complicate the data-driven prediction of compressive and flexural strength. We present an end-to-end framework that (i) harmonizes mixture records, (ii) completes numeric features using a dependence-preserving Gaussian copula routine, and (iii) standardizes/encodes predictors with training-only fits. The feature space focuses on domain ratios and concise interactions (water–binder, superplasticizer–binder, total fiber, water–binder, superplasticizer–binder, and fiber normalized by water–binder). A physics-informed multi-task neural network (PINN) is trained in log space with Smooth-L1 supervision and learned per-task noise scales for uncertainty-weighted balancing, while soft monotonicity penalties are applied to input gradients so that predicted strength is non-increasing in water–binder (both targets) and, when available, non-decreasing in fiber content for flexural response. In parallel, histogram-based gradient boosting is fitted per target; a convex combination is then selected on the validation slice and fixed for testing. On the held-out sets, the blended model attains an MAE/RMSE/R2 of 10.86 MPa/14.68 MPa/0.848 MPa for compressive strength and 2.78 MPa/3.67 MPa/0.841 MPa for flexural peak, improving over the best single family by 0.5 RMSE (compressive) and 0.16 RMSE (flexural), with corresponding R2 gains of 0.01–0.02. Residual-versus-prediction diagnostics and predicted–actual overlays indicate aligned trends and reduced heteroscedastic tail errors.