Multi-horizon vessel trajectory prediction with a physically constrained TCN–KAN framework

Accurate vessel trajectory prediction is essential for maritime situational awareness, traffic management, and autonomous navigation. However, existing data-driven methods often struggle to simultaneously represent temporal dependencies at different scales, nonlinear maneuver-induced deviations, and kinematic consistency, particularly as the forecasting horizon increases. This study proposes TCN–KAN–PINN, a unified framework combining a multi-scale causal Temporal Convolutional Network (TCN), a parallel Linear-KAN predictor, and physics-informed training. The TCN encoder uses hierarchical dilated residual blocks and sample-specific scale fusion to extract complementary temporal features from historical AIS observations. The Linear Base Pathway models the dominant motion trend, whereas the KAN Residual Pathway learns nonlinear corrections associated with vessel maneuvers. A time-discretized kinematic residual further penalizes discrepancies between predicted coordinate increments and expected displacements derived from vessel motion states, while Relative Loss Balancing with Random Lookback (ReLoBRaLo) adaptively balances the data and physics objectives. The model directly generates a complete 30-step future trajectory, with the 5 min, 15 min, and 30 min results evaluated as prefixes of the same output. Experiments on a real-world AIS dataset show that the proposed framework achieves the best overall trajectory accuracy among representative kinematic and deep learning baselines while maintaining favorable speed and course consistency and practical inference efficiency. Results reported as mean ± standard deviation over five independent runs indicate stable predictive performance. Ablation studies further show that kinematic supervision benefits prediction from the early forecasting steps, whereas the contribution of the KAN pathway becomes more pronounced at medium and long horizons.