Conditioning Aircraft Trajectory Prediction on Meteorological Data with a Physics-Informed Machine Learning Approach

TL;DR

This work tackles probabilistic aircraft trajectory prediction under epistemic uncertainties from meteorology and operator procedures in en-route airspace. It introduces a physics-informed machine learning pipeline that learns altitude-dependent thrust and calibrated airspeed and feeds them into the Base of Aircraft Data (BADA) model, with a reduced-order, fPCA-based representation of the learned terms. Contextual features are mapped to a distribution $p(oldsymbol{y}|oldsymbol{x})$ via Gaussian Processes and Deep Ensembles, enabling conditioned trajectory generation and calibration assessed with $CRPS$-based skilfulness; a rejection test ensures physical plausibility. Across ten aircraft types and six metrics, the approach yields approximately 20–22% improvements over a baseline, identifying 14 informative features that link meteorological and operational context to climb performance, and highlighting the trade-offs between GP and DE in data-sparse versus data-rich regimes.

Abstract

Accurate aircraft trajectory prediction (TP) in air traffic management systems is confounded by a number of epistemic uncertainties, dominated by uncertain meteorological conditions and operator specific procedures. Handling this uncertainty necessitates the use of probabilistic, machine learned models for generating trajectories. However, the trustworthiness of such models is limited if generated trajectories are not physically plausible. For this reason we propose a physics-informed approach in which aircraft thrust and airspeed are learned from data and are used to condition the existing Base of Aircraft Data (BADA) model, which is physics-based and enforces energy-based constraints on generated trajectories. A set of informative features are identified and used to condition a probabilistic model of aircraft thrust and airspeed, with the proposed scheme demonstrating a 20% improvement in skilfulness across a set of six metrics, compared against a baseline probabilistic model that ignores contextual information such as meteorological conditions.

Figures (9)

• Figure 1: Schematic of the proposed PIML model.
• Figure 2: BADA prediction of B738 climbs, compared to 50 trajectories observed in real-world operations.
• Figure 3: Mean forecast wind and temperature field, overlaid with trajectories of climbing aircraft originating at London airports for a 3 hour period from 07:30UTC to 10:30UTC on 3 July 2019 between FL150 and FL300.
• Figure 4: Feature importances for predictions of the first coefficient in the reduced-order representation of sub-trajectories for the B738.
• Figure 5: Difference in skilfulness score between the Deep Ensemble and Gaussian Process model. Points above the grey dashed line indicate a higher score for the Deep Ensemble. The correlation ($R$) is given in the legend for each metric.