Physics-Informed Neural Networks for Vessel Trajectory Prediction: Learning Time-Discretized Kinematic Dynamics via Finite Differences
Bibliographic record
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 firstand 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".