## 5 Discussion  
Our comprehensive experimental results demonstrate that the proposed StochasticTrajectory model consistently outperforms all comparison methods, including both traditional approaches (physics-based, ARIMA, KalmanFilter) and deep learning methods (LSTM, Attention, SimpleRNN, MLP). This superior performance validates our integrated approach that combines Lyapunov stability constraints with attention-based weather modeling in a probabilistic framework. Ablation studies further confirm the critical importance of each component, both stability constraints and weather attention mechanisms providing substantial contributions to model performance, as evidenced by the 600+% error increases when these components are removed at SR = 1. These findings demonstrate that our stochastic approach not only provides substantial benefits in terms of uncertainty quantification and stability, but also maintains competitive or superior accuracy across most operational scenarios. These advantages are particularly valuable in the nontowed airport environment, where safety margins and risk assessment are critical considerations. The proposed trajectory prediction system targets specific operational needs in general aviation, particularly at non-towed airports. Primary applications include: (1) Enhanced situational awareness for pilots operating in busy traffic patterns, where our uncertainty-aware predictions can highlight potential conflicts before they become critical; (2) Decision support for flight training operations, where instructors can use trajectory predictions to assess student performance and intervene when deviations exceed safe bounds; (3) Ground-based safety monitoring at airports without tower services, providing automated alerts when aircraft trajectories suggest potential runway incursions or pattern conflicts; and (4) Weather-related go-around prediction, where the system's weather attention mechanism can anticipate when current conditions may force missed approaches. The system's 5.86 ms inference time enables real-time deployment through integration with existing ADS-B infrastructure, while the probabilistic outputs provide confidence intervals essential for safety-critical decision making. Initial deployment would focus on high-traffic training air \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Model** & **Test MSE** & **68\% Coverage** & **95\% Coverage** & **Mean Uncertainty** & **JS Divergence** \\ \hline \hline \multicolumn{6}{c}{Sampling Rate = 1} \\ \hline StochasticTrajectory & 0.0000678 & 0.878 & 0.973 & 0.0116 & 0.2314 \\ LSTM & 0.000163 & 0.416 & 0.659 & 0.0056 & 0.4814 \\ Attention & 0.000229 & 0.509 & 0.755 & 0.0075 & 0.1929 \\ SimpleRNN & 0.00313 & 0.257 & 0.497 & 0.0184 & 0.5977 \\ GRU & 0.00136 & 0.414 & 0.660 & 0.0043 & 0.2568 \\ MLP & 0.000561 & 0.923 & 0.997 & 0.0577 & 0.3134 \\ \hline \hline \multicolumn{6}{c}{Sampling Rate = 2} \\ \hline StochasticTrajectory & 0.000849 & 0.857 & 0.986 & 0.0768 & 0.1634 \\ LSTM & 0.00152 & 0.360 & 0.599 & 0.0188 & 0.2666 \\ Attention & 0.00225 & 0.292 & 0.541 & 0.0201 & 0.2844 \\ SimpleRNN & 0.00653 & 0.246 & 0.464 & 0.0250 & 0.2057 \\ GRU & 0.00137 & 0.338 & 0.625 & 0.0173 & 0.2959 \\ MLP & 0.00551 & 0.586 & 0.936 & 0.1224 & 0.3524 \\ \hline \hline \multicolumn{6}{c}{Sampling Rate = 4} \\ \hline StochasticTrajectory & 0.0218 & 0.772 & 0.982 & 0.1200 & 0.1407 \\ LSTM & 0.0212 & 0.241 & 0.467 & 0.0289 & 0.1920 \\ Attention & 0.0238 & 0.315 & 0.546 & 0.0270 & 0.4010 \\ SimpleRNN & 0.0390 & 0.159 & 0.318 & 0.0411 & 0.1600 \\ GRU & 0.0177 & 0.305 & 0.554 & 0.0289 & 0.1285 \\ MLP & 0.0434 & 0.719 & 0.913 & 0.1421 & 0.3304 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Detailed performance comparison: accuracy and uncertainty metrics. ports where the combination of diverse pilot experience levels and concentrated operations creates the greatest safety benefit. Our approach, while demonstrating strong performance, has several important limitations that must be acknowledged.