Fermat polynomial-based machine learning algorithm for a few non-linear ship roll damping models arising in ship dynamics

Roll damping significantly influences ship dynamical models, playing a key role in predicting vessel behavior. Recently, in [Ocean Engineering 264 (2022) 112390] discussed the study, which considers a floating production storage and offloading (FPSO) tank model and a barge-like vessel model that consists of two spherical tanks, each governed by different restoring moments and damping coefficients to capture their unique dynamic behaviors. The Lucas wavelet method, along with the multi-layer perceptron approach, has been used for parameter estimations to the observed model. In this study, a machine-learning-based model—multi layer perceptron (MLP)—is employed to predict the roll angle of the ship by incorporating both the restoring moments and damping coefficients results obtained using the fermat polynomial method (FPM). The non-linear differential equations are transformed into simple algebraic equations by considering appropriate collocation points by utilizing derivatives of operational matrices. Accuracy and effectiveness of the proposed FPM-based approximation are validated using experimental data from frozen cargo conditions and validated with the homotopy perturbation method (HPM) results. The obtained solution is compared with a few numerical methods and experimental results. However, the FPM solutions are easy to investigate, straightforward, and convenient algorithms for solving differential equations that are non-linear and arise in ship dynamics.