Accurate aircraft trajectory prediction is critical for air traffic management, airline operations, and environmental assessment. This paper introduces NODE-FDM, a Neural Ordinary Differential Equations-based Flight Dynamics Model trained on Quick Access Recorder (QAR) data. By combining analytical kinematic relations with data-driven components, NODE-FDM achieves a more accurate reproduction of recorded trajectories than state-of-the-art models such as a BADA-based trajectory generation methodology (BADA4 performance model combined with trajectory control routines), particularly in the descent phase of the flight. The analysis demonstrates marked improvements across altitude, speed, and mass dynamics. Despite current limitations, including limited physical constraints and the limited availability of QAR data, the results demonstrate the potential of physics-informed neural ordinary differential equations as a high-fidelity, data-driven approach to aircraft performance modelling. Future work will extend the framework to incorporate a full modelling of the lateral dynamics of the aircraft.