Data-driven governing equation identification of near terminal air traffic flow dynamics

Efficient air traffic management (ATM) relies on accurately understanding and predicting air traffic patterns and delays. While deep learning methods have shown promise in prediction tasks, they often lack interpretability and require large volumes of data. This paper presents a novel, data-driven framework to model and predict near-terminal traffic flow and flight delays by identifying the underlying partial differential equations (PDEs) that govern air traffic dynamics. Our approach leverages aircraft trajectory patterns and density distributions to estimate probability density functions (PDFs) of travel times. Using sparse regression for system identification, we learn the governing equations that capture the temporal evolution of density and travel time distributions. These equations are then embedded into a Physics-Informed Neural Network (PINN) for integrated prediction. Experiments with real-world data validate the framework’s effectiveness in accurately identifying governing PDEs and forecasting flight delays. By combining physical modeling with deep learning, the proposed method improves both the interpretability and generalizability of AI applications in ATM, offering practical value in enhancing airport efficiency and operational decision-making.