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

Accurate modeling of ship roll dynamics under different wave excitations remains a persistent challenge due to nonlinear system behavior and noise measurement data.This research study works on a Physics-Informed Neural Network (PINN) for identifying roll motion parameters with high fidelity and physical interpretability. By leveraging automatic differentiation, the proposed PINN approach avoids the instability typically encountered with discrete numerical differentiation. In this paper, a novel Fermat Polynomial Method (FPM) is used to train the data under the PINN. The proposed algorithm is compared with Lucas Wavelet Method (LWM) for the barge-like vessel model and Floating Production Storage and Offloading (FPSO) models. It is observed that the proposed FPM solution shows more accuracy compared with Lucas Wavelet Method (LWM) solutions. Extensive simulations under varying noise levels reveal that PINN's superior robustness machine learn ing algorithm when compared to Support Vector Regression (SVR), with consistently lower RMSE and narrower uncertainty bands across different wave conditions and noise levels. To enhance learning efficiency in periodic motion, a novel activation function called Snake is employed within the PINN architecture. Performance is validated through full-scale sea experiments and data from frozen cargo trials.