Improved predictive formulae for wave overtopping at sloped breakwaters using interpretable machine learning models.

Area of Science:

• Coastal Engineering
• Machine Learning Applications
• Hydraulic Modelling

Background:

• Accurate prediction of mean wave overtopping discharge is critical for designing safe and cost-effective coastal defence structures.
• Traditional models are important, but Machine Learning (ML) offers a powerful complementary approach for enhanced predictive capabilities.

Purpose of the Study:

• To develop and evaluate an ML-based framework for predicting mean wave overtopping discharge at sloped breakwaters.
• To focus on both predictive accuracy and model interpretability for practical engineering applications.
• To translate ML findings into simplified mathematical expressions for enhanced usability.

Main Methods:

• Evaluated five ML algorithms: Random Forest (RF), Gradient Boosted Decision Trees (GBDT), Artificial Neural Networks (ANN), Support Vector Regression (SVR), and Gaussian Process Regression (GPR).
• Trained and validated models using the EurOtop (2018) dataset for sloped breakwaters.
• Employed polynomial regression and Genetic Programming (GP) to derive simplified predictive formulae.

Main Results:

• Gaussian Process Regression (GPR) demonstrated the best predictive performance with an R² of 0.80 and lowest error metrics.
• Relative Freeboard and Freeboard Deficit (FD) were identified as the most influential parameters across all evaluated ML models.
• Developed new simplified formulae based solely on Freeboard Deficit (FD) to estimate mean overtopping discharge (q).

Conclusions:

• The ML framework, particularly GPR, provides accurate predictions of mean wave overtopping discharge.
• The derived simplified formulae offer coastal engineers a rapid, interpretable, and reliable tool for design and decision-making.
• This study advances the integration of ML into coastal infrastructure design, promoting adaptive and climate-resilient defence systems.