## 1 Introduction  
Trajectory prediction in general aviation represents a critical component in improving safety and operational efficiency in non-towered airports [1]. Unlike controlled airspace with structured traffic management systems, non-towered airports rely heavily on pilot situational awareness and voluntary compliance with recommended traffic patterns. With approximately 20,000 airports in the United States alone, of which more than 80% are not towered, the ability to accurately predict aircraft trajectories becomes paramount for collision avoidance, traffic management, and emergency response planning [2]. General aviation (GA) encompasses a diverse range of aircraft operations, including personal flights, flight training, aerial surveys, and agricultural applications, among others. The heterogeneity of aircraft types, pilot proficiency levels, and operational objectives introduces significant complexity into trajectory prediction tasks. Traditional deterministic approaches that work well in commercial aviation contexts with standardized procedures and consistent aircraft performance often falter when applied to the more dynamic and unpredictable nature of general aviation operations. Current research in aviation trajectory prediction has focused primarily on commercial aviation within controlled airspace, where constraints and procedures are well defined [34]. Methods ranging from physics-based models to machine learning approaches have demonstrated success in these structured environments [5]. Physics-based models leverage aircraft performance specifications and flight dynamics to predict trajectories, but often struggle with real-time computational demands and sensitivity to environmental variations. Data-driven approaches, including traditional machine learning and neural networks, have shown promise in learning patterns from historical data [6; 7], but often fail to capture the uncertainty and rare events critical for safety applications [8]. The application of these existing methods to general aviation presents several distinct challenges. First, weather conditions significantly affect small aircraft more severely than commercial aircraft, introducing a higher degree of variability that must be taken into account in prediction models. Second, the diversity of pilot behaviors, from student pilots practicing maneuvers to experienced pilots executing precise approaches, creates a wide spectrum of potential trajectories that defy simple modeling approaches. Third, while general aviation regulations specify standard traffic patterns, adherence varies considerably among pilots, particularly at non-tovered airports where pattern compliance is not actively enforced. Fourth, the sparse data problem in GA trajectory prediction stems from the comparative rarity of recorded flights at any single non-tovered airport, limiting the volume of training data available for machine learning approaches. Furthermore, uncertainty quantification remains a critical gap in current trajectory prediction systems [9]. For safety-critical applications, deterministic predictions alone are insufficient; understanding the confidence level and potential variability of predictions is essential for risk assessment and decision making [10]. This uncertainty comes from multiple sources: measurement errors in collected data, stochastic environmental factors, inherent unpredictability in pilot decision-making, and limitations in model capabilities. Our approach addresses these challenges by fundamentally reimagining trajectory prediction as a stochastic process rather than a deterministic one [11]. We take advantage of recent advances in deep learning architectures combined with probabilistic modeling to develop a system capable of generating trajectory distributions that capture both the most likely path and the associated uncertainty [12].