Field-Level Uncertainty Quantification for AI-Based Ship Hull Surface Pressure Prediction

This study investigates uncertainty quantification for field-level ship hull surface pressure predictions using a U-Net-based data-driven model. A speed-conditioned U-Net is trained on a large CFD dataset covering multiple ship types and velocity conditions to predict pressure distributions on hull surfaces. The model outputs the mean pressure and log-variance at each grid location using a negative log-likelihood loss, allowing aleatoric uncertainty to be estimated, while epistemic uncertainty is quantified by a deep ensemble of independently trained models. The reliability and calibration of the predicted confidence intervals are evaluated at the field level. The results show that calibration stabilizes as ensemble size increases, and coverage slightly exceeds nominal confidence levels. Uncertainty decomposition indicates that aleatoric uncertainty dominates and is insensitive to ensemble size, while epistemic uncertainty primarily affects calibration. Elevated uncertainty is consistently observed near free-surface regions around the bow and stern, reflecting increased prediction difficulty. These findings demonstrate the effectiveness of deep-ensemble-based uncertainty quantification for CFD-driven pressure field prediction models.