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<p>Accurate prediction of energy dissipation in stepped spillways remains a pivotal challenge in hydraulic engineering. This study proposes a novel Artificial Intelligence (AI)-driven framework that integrates cutting-edge machine learning architectures—namely the Tabular Prior-Data Fitted Network (TabPFN) and the Self-Attention and Intersample Attention Transformer (SAINT)—to estimate the relative energy dissipation percentage (ΔE%) in Streamlined Stepped Spillways (StSSs). Alongside these, traditional models such as Natural Gradient Boosting (NGBoost) and Random Forest (RF) were enhanced via the Osprey Optimization Algorithm (OOA) to improve predictive accuracy and computational efficiency. Model performance was rigorously evaluated in both training and testing phases using multiple statistical indicators, including the Coefficient of Determination (<i>R</i>²), Root Mean Square Error (RMSE), Variance Accounted For (VAF), and Normalized Mean Bias Error (NMBE). The OOA-optimized NGBoost exhibited the highest training accuracy (<i>R</i>² = 0.992, RMSE = 0.862), while the OOA-TabPFN demonstrated superior generalization during testing (<i>R</i>² = 0.981, RMSE = 1.276). Comprehensive model comparisons using Taylor Diagrams and Normalized Discrepancy Analysis affirmed the strong predictive capabilities of both TabPFN and NGBoost across various flow conditions. To evaluate predictive uncertainty, confidence interval (CI) width and uncertainty ratio (R-Factor) were used, revealing that the OOA-RF model performed best with the narrowest CI and lowest R-Factor. Additionally, sensitivity analyses using Shapley Additive Explanations (SHAP) and the Explainable Boosting Machine (EBM) identified the ratio of critical flow depth to chute height (<i>d</i><sub><i>C</i></sub><i>/P</i><sub><i>S</i></sub>) as the most influential predictor variable. Overall, this study showcases the potential of next-generation AI models, particularly TabPFN and NGBoost, in achieving robust and interpretable predictions of energy dissipation in StSSs, paving the way for more informed and optimized hydraulic design strategies.</p>

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Assessment of accuracy and uncertainty in metaheuristic-optimized state-of-the-art AI models for predicting energy dissipation in streamlined stepped spillways

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Abbas Moradi-Eshgafti,
  • Sara Shahrokhi,
  • Alireza Yousefi-Kebria,
  • Pourya Nejatipour,
  • Ehsan Afaridegan,
  • Arezoo Ghannad

摘要

Accurate prediction of energy dissipation in stepped spillways remains a pivotal challenge in hydraulic engineering. This study proposes a novel Artificial Intelligence (AI)-driven framework that integrates cutting-edge machine learning architectures—namely the Tabular Prior-Data Fitted Network (TabPFN) and the Self-Attention and Intersample Attention Transformer (SAINT)—to estimate the relative energy dissipation percentage (ΔE%) in Streamlined Stepped Spillways (StSSs). Alongside these, traditional models such as Natural Gradient Boosting (NGBoost) and Random Forest (RF) were enhanced via the Osprey Optimization Algorithm (OOA) to improve predictive accuracy and computational efficiency. Model performance was rigorously evaluated in both training and testing phases using multiple statistical indicators, including the Coefficient of Determination (R²), Root Mean Square Error (RMSE), Variance Accounted For (VAF), and Normalized Mean Bias Error (NMBE). The OOA-optimized NGBoost exhibited the highest training accuracy (R² = 0.992, RMSE = 0.862), while the OOA-TabPFN demonstrated superior generalization during testing (R² = 0.981, RMSE = 1.276). Comprehensive model comparisons using Taylor Diagrams and Normalized Discrepancy Analysis affirmed the strong predictive capabilities of both TabPFN and NGBoost across various flow conditions. To evaluate predictive uncertainty, confidence interval (CI) width and uncertainty ratio (R-Factor) were used, revealing that the OOA-RF model performed best with the narrowest CI and lowest R-Factor. Additionally, sensitivity analyses using Shapley Additive Explanations (SHAP) and the Explainable Boosting Machine (EBM) identified the ratio of critical flow depth to chute height (dC/PS) as the most influential predictor variable. Overall, this study showcases the potential of next-generation AI models, particularly TabPFN and NGBoost, in achieving robust and interpretable predictions of energy dissipation in StSSs, paving the way for more informed and optimized hydraulic design strategies.