A strip-theory-driven DeepONet surrogate for operator learning of wave-added resistance of advancing monohull ships

Accurate prediction of wave-added resistance is essential during preliminary ship design and performance assessment. This study presents a strip-theory-driven DeepONet surrogate model for predicting the wave-added resistance of advancing monohull ships across a broad range of hull geometries, Froude numbers, heading angles, and incident wave conditions. A consolidated dataset is generated using a strip-theory solver, providing frequency-dependent added-resistance response functions over a discrete frequency range for a diverse series of parameterised ship hulls. Therefore, the calculations haven’t captured strong nonlinear and viscous phenomena. The resulting database comprises 4,500 operational condition cases. Unlike conventional machine-learning approaches that perform pointwise regression, the proposed framework formulates wave-added resistance prediction as an operator-learning problem. Through coupled branch and trunk networks, DeepONet learns a nonlinear operator that maps ship and operational descriptors to complete frequency-dependent added-resistance response functions. By learning the underlying hydrodynamic operator rather than discrete input-output relationships, the model preserves the functional structure of the response and enables unified prediction across diverse hull forms and operational scenarios while maintaining strong generalisation for unseen cases. Hyperparameter tuning is performed using five-fold cross-validation, with learning rates and activation functions systematically evaluated using standard error metrics. The final model achieves a mean RMSE of approximately 0.40 and a mean R 2 exceeding 0.97, while rigorous grouped k-fold cross-validation demonstrates stable predictive performance and strong generalisation across independent validation folds. The DeepONet framework also shows strong capability in reproducing resonance characteristics, spectral shape, and transferability when benchmarked against higher-fidelity references. Furthermore, quantitative comparisons with semi-empirical predictions, RANS simulations, and experimental measurements confirm the robustness and reliability of the proposed methodology for two unseen hulls. Overall, these results highlight DeepONet’s potential as an efficient and accurate operator-learning surrogate for rapid wave-added-resistance prediction from potential-flow-based data on standard hardware, enabling sub-second runtime and supporting future applications in ship-performance assessment, design optimisation, and digital-twin frameworks.