Proposing a hybrid ship maneuvering model through force/moment-level integration of MMG and FNN with output constraints

Abstract With recent advances in autonomous navigation technology, the importance of ship maneuvering models that can predict maneuvering motions with high accuracy and interpretability has increased. This study proposes a hybrid maneuvering model for predicting ship motions using the Maneuvering Modeling Group (MMG) model and the Feedforward Neural Network (FNN). In the proposed model, the modular structure of the MMG model is enhanced through the addition of a complementary FNN module. This approach improves the prediction accuracy while maintaining the interpretability of the model. Furthermore, to prevent the FNN output from depending too heavily on its training data, an output constraint and a mechanism for detecting Out-of-Distribution (OOD) based on k-Nearest Neighbors (kNN) distance are introduced. Numerical verification using multiple maneuvering test datasets demonstrates that the proposed model consistently exhibits higher prediction accuracy than both the MMG-only and the FNN-only models. Specifically, it attains an average reduction of 30–40% in Root-Mean-Squared Error (RMSE) compared to the MMG-only model. In particular, under highly nonlinear maneuvering conditions, such as Turning test and Random maneuver, the model shows up to a 70% RMSE reduction. Additionally, the model exhibits low accuracy degradation over long-term predictions, ensuring stable motion predictions. Based on these results, the proposed hybrid model successfully integrates the characteristics of physical models and data-driven models, providing a practical maneuvering model that offers high accuracy, lower data dependency, and interpretability. This model offers a valuable foundation for applications in autonomous navigation support systems.