Physics-Informed Neural Networks for Vessel Trajectory Prediction: Learning Time-Discretized Kinematic Dynamics via Finite Differences

Abstract

Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints, leading to forecasts that violate vessel motion dynamics, such as in scenarios with limited or noisy data where sudden course changes or speed variations occur due to external factors. To address this limitation, we propose a Physics-Informed Neural Network (PINN) approach for trajectory prediction that integrates a streamlined kinematic model for vessel motion into the neural network training process via first- and second-order, finite-difference physics-based 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 PINN using real-world AIS datasets that cover diverse maritime conditions and compared it with state-of-the-art models. Our results demonstrate that the proposed method reduces average displacement errors by up to 32% across models and datasets while maintaining physical consistency. These results enhance model reliability and adherence to mission-critical maritime activities, where precision translates into better situational awareness in the oceans.