Monotonicity-constrained physics-informed neural networks for concrete compressive strength prediction

Abstract

Accurate prediction of concrete compressive strength is critical for mix design optimization, quality control, and reliable decision-making in modern construction. While data-driven machine learning models have demonstrated strong predictive capability, most existing approaches treat concrete behavior as a purely statistical problem, often neglecting well-established physical relationships among mix constituents and curing conditions. This limitation can lead to physically inconsistent predictions and reduced interpretability, hindering adoption in engineering practice. To address these gaps, this study proposes a new physics-informed neural network (PINN) framework for concrete compressive strength prediction that explicitly embeds domain knowledge into the learning process. The model utilizes eight fundamental mix-design variables and curing age, integrating a conventional data-driven cross-entropy loss with physics-based gradient constraints that enforce known monotonic trends, including strength reduction with increasing water content and strength enhancement with increasing binder content and curing age. A structured hyperparameter search is conducted to identify an optimal network architecture comprising two hidden layers with rectified linear unit activation, dropout regularization, and the Adam optimizer. The optimized PINN achieved a validation accuracy of 0.975 and an independent test accuracy of 0.978. Across the three strength classes, precision ranged from 0.93 to 0.99, recall from 0.97 to 1.00, and F1-score from 0.97 to 0.98. The continuous expected-strength output achieved an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}$$\end{document} of 0.834, an MAE of 5.481 MPa, and an RMSE of 6.758 MPa. Gradient-based evaluation further showed a nonpositive sensitivity to water and nonnegative sensitivities to curing age and the constrained binder components. These results demonstrate that embedding physics-based constraints enhances both predictive performance and interpretability, positioning the proposed PINN framework as a robust and practical tool for mix optimization, quality assurance, and decision support in precast concrete manufacturing. Physics-based gradient constraints enforce physically consistent learning of concrete strength. PINN achieves high classification accuracy and robust continuous strength estimation. Embedded physics enhances generalization and interpretability for practical engineering use. Physics-based gradient constraints enforce physically consistent learning of concrete strength. PINN achieves high classification accuracy and robust continuous strength estimation. Embedded physics enhances generalization and interpretability for practical engineering use.