Physics-guided long short-term memory–Transformer prediction of ship motion and broaching in oblique stern waves

Accurate ship-motion prediction and early identification of unstable navigation states are essential for autonomous vessels operating in following-oblique waves. This study proposes a physics-guided long short-term memory (LSTM)–Transformer encoder–decoder model for joint motion prediction and surf-riding/broaching identification of an autonomous trimaran. Numerical simulation data are generated under different operating conditions, and physics-based state labels are constructed using the ship–wave speed ratio, heading deviation, yaw-rate response and rudder saturation. The proposed framework combines LSTM-based local temporal feature extraction with Transformer-based global dependency modelling. A state-identification branch is further introduced, and a multi-objective loss function is designed by integrating motion prediction, state classification, physical consistency and ordinal risk constraints. Comparative studies with different models and model variants are conducted to evaluate the prediction accuracy, robustness and generalisation capability of the proposed method. The results show that physically meaningful variables and state-related constraints strongly affect the prediction of navigation-state features. The proposed model improves both motion-response prediction and unstable-state identification, providing a more interpretable and reliable short-term forecasting framework for surf-riding and broaching conditions.