Explicit wave height prediction model and regularity analysis for floating breakwaters based on deep symbolic regression

The accurate prediction of wave attenuation across floating breakwaters is essential for coastal structure design and nearshore aquaculture safety. This study employs Physical Symbolic Optimization (PhySO) to model the transmission of significant wave height (Hs) and maximum wave height (Hmax) behind a floating breakwater in Lianjiang, Fujian Province. Using in-situ wave data including incident wave height, period, and direction, the dataset is split into 80% training and 20% testing sets, with constraints on expression complexity and physical consistency. Results show that PhySO produces explicit, interpretable formulas with strong generalization ability: the best Hmax expression achieves accuracy comparable to black-box machine learning models, while Hs expressions show slightly lower but still reliable performance. Simple linear scaling expressions exhibit excellent robustness across all wave conditions, and incident wave height is confirmed as the dominant controlling factor. This work demonstrates the value of PhySO in balancing accuracy and physical interpretability, offering a practical and easy-to-use tool for engineering applications.