## 2 Materials and Methods
### Predictive Modeling
A regression layer was applied to calculate the loss, making the network suitable for regression tasks by optimizing predictions for continuous values. This architecture's success was achieved through the bidirectional learning of sequential dependencies, effective regularization via dropout layers, and the progressive abstraction of features (see Figure 4). These elements ensured that the network could generalize well while effectively learning complex patterns from sequential data. \begin{table}
\begin{tabular}{l l} \hline \hline
**Predictor** & **Description** \\ \hline POINT\_DIST & Distance of aircraft position from ADEP \\ LAT & Latitude of the aircraft position \\ LON & Longitude of the aircraft position \\ ALT & Altitude (flight level) of the aircraft position \\ FS & Flight speed of the aircraft at a specific waypoint \\ windspd & Wind speed at the current aircraft position \\ winddir & Wind direction at the current aircraft position \\ WindComponent & Wind speed component at the current aircraft position \\ dSIBT\_TO & Difference between scheduled in-block time and estimated time of waypoint arrival (from FTFM) \\ dSOBT\_TO & Difference between scheduled off-block time and estimated time of waypoint arrival (from FTFM) \\ dATOT\_TO & Difference between actual take-off time and estimated time of waypoint arrival (from FTFM) \\ dAOBT\_TO & Difference between actual off-block time and estimated time of waypoint arrival (from FTFM) \\ histDelay\_TO & Difference between historical delay time related to previous flight operations and estimated time of waypoint arrival (from FTFM) \\ histD\_OBIT\_TO & Difference between historical off-block time delay and estimated time of waypoint arrival (from FTFM) \\ histD\_IBT\_TO & Difference between historical in-block time delay and estimated time of waypoint arrival (from FTFM) \\ histD\_LT\_TO & Difference between historical landing time delay and estimated time of waypoint arrival (from FTFM) \\ histFS\_FS & Difference between estimated flight speed and historical flight speed at a given point \\ histWC\_WC & Difference between current wind component and historical wind component at a given point \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptions of the predictors used in the model. The training setup was configured for efficiency and stability using the Adam stochastic optimisation algorithm [39]. A maximum of 300 epochs was set, with validation data used to monitor performance and prevent overfitting. The initial learning rate was set to \(1\times 10^{-3}\), allowing for balanced convergence. The longest sequence length was used to ensure that all sequence data were processed fully, without truncation. Shuffling was disabled to preserve the order of the sequences, while a gradient threshold of 1 was applied to prevent exploding gradients. The network with the best validation loss was automatically saved, ensuring the most generalizable model was retained. The process was executed on a GPU (NVIDIA RTX 3070 Ti with CUDA support (Santa Clara, CA, USA)) for faster computation. After completing the training, predictions on the test data were made using the trained network, with the sequence length kept consistent to ensure reliable inference. To evaluate learning stability, the entire training process, including predictor computation, was repeated 60 times. In each iteration, the data were randomly split into training, validation, and test sets in a 70/15/15 ratio, and the performance of each model was assessed using the test dataset. Specifically, the performance was evaluated by computing the Root-Mean-Square Error \(RMSE\), Mean Absolute Error \(MAE\), the mean of residuals \(rMean\), the standard deviation of residuals \(rSTD\), and \(R^{2}\). This repeated process was employed to avoid bias introduced by a single random selection of data, ensuring the model's performance was not an artifact of a particular dataset split.