What question did this study set out to answer?

To develop an explainable AI framework for predicting fracture properties of concrete, specifically Gc and KIC.

March 1, 2026Open Access

From classical machine learning algorithms to modern transformer-inspired neural networks for multi-target prediction of fracture properties in concrete structures

Key Points

To develop an explainable AI framework for predicting fracture properties of concrete, specifically Gc and KIC.
Analyzed a dataset of 330 data points with six input features.
Trained and evaluated 25 machine learning algorithms, including classical and transformer-inspired models.
Performed hyperparameter tuning through grid search and 5-fold cross-validation.
Applied early stopping to neural network models to prevent overfitting.
Conducted SHAP analysis for interpretability of fracture predictions.
TabPFN achieved the highest accuracy of R² = 87.89% on unseen test data.
SHAP analysis revealed Gc is mainly influenced by tensile strength and geometry.
KIC is affected significantly by beam depth and notch length.
Highlighted nonlinear effects that simple correlation analysis missed.

Abstract

• Multi-target prediction of Gc and KIC of concretes using 25 ML algorithms • TabPFN outperforms 24 algorithms with R² = 87.89% on unseen test data • SHAP analysis provides unbiased interpretability of fracture predictions Concrete fracture properties, including fracture energy ( G c ) and Mode I fracture toughness ( K IC ), are critical parameters of structural performance. Accurate prediction of these parameters remains challenging due to their nonlinear dependence on geometric and mechanical factors. This study develops a comprehensive explainable artificial intelligence framework for the simultaneous prediction of G c and K IC of concretes. A dataset comprising 330 data points with six input features, including beam depth, span length, beam width, notch length, tensile strength, and elastic modulus, was analyzed. 25 machine learning algorithms, including 22 classical models and three modern transformer-inspired models (i.e., TabPFN, TabNet, FTTr), were systematically trained and evaluated. Hyperparameter tuning was performed through grid search and 5-fold cross-validation, while early stopping was applied for neural network–based models to prevent overfitting. Results show that the TabPFN algorithm, as the most modern and state-of-the-art transformer-based algorithm, achieved the highest accuracy with an R² of 87.89% on the test set, outperforming all other algorithms. To enhance interpretability, Shapley Additive Explanations (SHAP) analysis was conducted on the test predictions of TabPFN. The results revealed that G c is predominantly governed by tensile strength and ligament-related geometry, whereas K IC is strongly influenced by beam depth and notch length. Importantly, the SHAP results also highlighted nonlinear and interaction-driven effects that were not captured by simple correlation analysis. Overall, the findings demonstrate that advanced transformer-based algorithms combined with explainable AI provide a powerful framework for the multi-target prediction of concrete fracture properties, offering valuable insights for structural design and material optimization.

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Cite This Study

Nikzad et al. (Sun,) studied this question.

synapsesocial.com/papers/69a3d79dec16d51705d2de7b https://doi.org/https://doi.org/10.1016/j.mlwa.2026.100877

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