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

Abstract

Accurate vessel trajectory prediction is critical for navigational safety, traffic management, search and rescue, and autonomous navigation. Traditional data-driven models often lack adherence to physical constraints, leading to unreliable outputs, particularly in dynamic maritime environments. This work proposes a Physics-Informed Neural Network (PINN) framework that integrates time-discretized vessel kinematics into the learning process through a composite loss function derived from finite difference schemes, including Euler, Heun, and midpoint approximations. By embedding first- and second-order motion laws into the training objective, the model enforces physical fidelity and improves predictive reliability. Evaluated on real-world AIS datasets across diverse conditions, the PINN approach achieves up to 32% reduction in average displacement error compared to baseline models, significantly enhancing trajectory realism and consistency for operational maritime applications.