Physics-Informed Neural Network Framework for Ship Roll Motion Prediction with Adaptive Loss Balancing

Accurate prediction of ship roll motion is essential for maritime safety and stability assessment. Physics-based methods can provide physically interpretable predictions, but high-fidelity numerical simulations usually require considerable computational resources, limiting their application to efficient and long duration roll motion prediction. In contrast, purely data driven models are computationally efficient but may lack physical consistency. To address these limitations, this study develops a physics-informed neural network (PINN) framework with an adaptive loss-balancing strategy for ship roll motion prediction. An adaptive loss balancing strategy is incorporated to dynamically regulate the relative contributions of the governing equation loss and the data fitting loss during training, thereby integrating physical constraints with available roll response data. The DTMB 5415 hull is selected as a benchmark case, in which the roll motion equation is incorporated as a physical constraint, and time series data under both regular and irregular wave conditions are generated through numerical simulations. Comparative results demonstrate that the proposed PINN-BP (Adaptive) framework achieves the lowest RMSE and MAE among the evaluated models, while maintaining an R2 comparable to that of the standard PINN. The computational results further show that its training cost remains comparable to that of the standard PINN and is substantially lower than that of the LSTM model, while the inference time remains at a low level. The results demonstrate that incorporating adaptive loss balancing into the physics-informed BP neural-network framework can improve roll motion prediction accuracy without introducing a substantial additional computational burden. The proposed framework provides a physically informed and computationally efficient approach for ship roll motion prediction under the investigated wave conditions.