A U-Net-Based Prediction of Surface Pressure and Wall Shear Stress Distributions for Suboff Hull Form Family

Abstract

Recent developments in machine learning have enabled prediction models that estimate not only hydrodynamic force coefficients but also full CFD fields. Unlike conventional surrogate models that focus primarily on integrated quantities, such approaches can provide real-time predictions of pressure and wall shear stress distributions, making them highly promising for applications in ship hydrodynamic design where detailed surface flow characteristics are essential. In this study, we address the low prediction accuracy observed near protruding appendages in U-Net-based field prediction models by introducing a positional encoding (PE)-enhanced data processing scheme and evaluating its performance across a dataset of 500 SUBOFF variants. While PE enhances prediction accuracy, especially for the sail, its effectiveness is constrained by the boundary discontinuity introduced at the 12 o’clock seam. To resolve this structural limitation and ensure consistent accuracy across components, the projection seam is relocated to the 6 o’clock position, where high-gradient flow features are less concentrated. This modification produces clear quantitative gains: the drag-integrated MAPE decreases from 3.61% to 1.85%, and the mean field-level errors of $∆{\mathrm{C}}_{\mathrm{p}}$ and $∆{\mathrm{C}}_{\mathrm{f}}$ are reduced by approximately 5.6% across the dataset. These results demonstrate that combining PE with seam relocation substantially enhances the model’s ability to reconstruct fine-scale flow features, improving the overall robustness and physical reliability of U-Net-based surface field prediction for submarine hull forms.