Physics-Informed Vessel Trajectory Prediction via Finite Difference Kinematic Losses

Accurate and physically consistent vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, and autonomous navigation. Traditional data-driven models lack real-world physical constraints, leading to forecasts that violate vessel motion dynamics, particularly in scenarios with limited, sparse, or noisy data, or when sudden course changes or speed variations occur due to environmental factors. To address this limitation, we propose a Physics-Informed Neural Network (PINN) framework for trajectory prediction that integrates a streamlined kinematic model of vessel motion directly into the neural network training process via first- and second-order, physics-based finite-difference loss functions. These loss functions, discretized using the first-order forward Euler method, Heun's second-order approximation, and refined with a midpoint approximation based on Taylor series expansion, enforce fidelity to fundamental physical principles by penalizing deviations from expected kinematic behavior. We evaluated the PINN framework using real-world AIS datasets that cover diverse maritime conditions and compared it with state-of-the-art deep learning models. Our results demonstrate that the proposed method reduces average displacement errors by up to 32% across models and datasets while successfully maintaining physical consistency. These findings enhance model reliability and adherence to mission-critical maritime activities, where precision translates into better situational awareness at sea.