Machine Learning-Based Recursive Prediction and Application of Green’s Function of Water-Wave Radiation and Diffraction

The frequency-domain free-surface Green’s function method is widely used in solving ship hydrodynamic problems, with its core challenge lying in the computation of the Green’s function and its partial derivatives. This study analyzes the relationship between the free-surface Green’s function and its derivatives, proposing a machine learning-based recursive prediction method termed the pulsating source recursive prediction method. The accuracy and efficiency of this method under various parameter settings are investigated, and its application to the hydrodynamic calculations of container ship S175 and a bulk carrier is demonstrated. Results show that the predicted Green’s function achieves an accuracy of 3–6 decimals, with computational efficiency surpassing numerical methods and matching analytical approaches. The hydrodynamic results are reliable, confirming the method’s practical value.