A Robust Polynomial-Based Machine Learning Algorithm for the Ship Roll Equations Under Different Wave Excitation: A Hybrid Approach

Abstract Accurate modeling of ship roll dynamics under varying wave excitations remains challenging due to nonlinear system behavior and measurement noise. This study presents a physics-informed neural network (PINN) for high-fidelity identification of roll motion parameters with physical interpretability. By leveraging automatic differentiation, the proposed PINN avoids the numerical instability typically encountered with discrete differentiation. Training data are generated using the Fermat polynomial method (FPM). Extensive simulations under varying noise levels (2–5%) reveal PINN’s superior robustness compared to support vector regression (SVR), achieving 45–48% lower root mean square error (RMSE) in roll trajectory prediction with consistently narrower uncertainty bands across both regular and stochastic wave excitations. To enhance learning efficiency for periodic motion, a novel Snake activation function is incorporated within the PINN architecture. Performance is validated using frozen cargo experimental measurements from full-scale sea trials, with 70% of the data used for training and 30% reserved for independent validation, demonstrating 47% lower RMSE compared to SVR. The results highlight the proposed PINN’s capability to accurately and robustly predict ship roll dynamics under diverse excitation conditions.