A physics-informed machine learning method to evaluate added resistance in waves of arbitrary heading

Paper in proceeding, 2026

A physics-informed Gaussian process regression (PhI-GPR) framework is introduced to enable fast and reliable estimation of wave-added resistance at arbitrary encounter angles. A semi-empirical model is embedded to preserve physical consistency and robust extrapolation. The training datasets span 52 ship types and 288 experiments, totaling 3081 towing-tank records. Inputs comprise geometric and operating descriptors, and the response is added wave resistance. Across benchmark hulls (KVLCC, SCB84, PXBC), PhI-GPR attains lower RMSE than pure GPR and the baseline semi-empirical model, while preserving reasonable curve shapes and delivering credible intervals. Furthermore, the predictive uncertainty of added wave resistance is propagated into estimated time of arrival (ETA) calculations under changing sea states. A planned route is discretized into segments. For each segment, the posterior distribution of added wave resistance is mapped to speed-overground through a resistance–power relation and combined with environmental variability to achieve a sailing time distribution. Aggregation across segments produces a full ETA distribution rather than a single value. ETA confidence intervals are reported to support decision making.