A comprehensive review of modelling and prediction methods for nonlinear ship roll dynamics

Ship roll motion prediction is essential to ensure maritime performance and safety, particularly under varying and harsh sea conditions. While significant progress has been made, existing methods are still lacking in offering physical interpretability, computational efficiency and responsiveness to non-stationary sea dynamics simultaneously. Analytical → Numerical → Empirical (data-driven) methods, each serving different purposes depending on the complexity of the problem and the availability of data. Advanced high-fidelity CFD and fluid–structure interaction models produce precise simulations but remain computationally expensive. Time-frequency techniques such as wavelet transforms and empirical mode decomposition effectively identify non-stationarity, whereas machine learning models such as LSTM and ensemble schemes provide adaptive short-term prediction. As an original contribution, this paper introduces graph-based polynomial spectral methods as a new and promising method for the prediction of the initial roll motion of ships. These methods transform governing equations into algebraic systems at graph-based collocation points with spectral accuracy and ease in model nonlinear and high dimensional dynamics. This review concludes that hybrid physical data-driven paradigms and digital twin systems hold significant potential for real-time monitoring and control, leading to more accurate and adaptive prediction of ship roll motion in challenging sea conditions.