## 2 Materials and Methods
### Predictive Modeling  
The overall dataset used for prediction utilizes the predictors described above and summarized in Table 1, which have the format of time series forming a data sequence for a specific flight. Each of these sequences is assigned exactly one dependent variable, either \(\delta_{LT}\) or \(\delta_{IBT}\), depending on the model being built (either for predicting \(\delta_{LT}\) or \(\delta_{IBT}\)). The dataset contains 1730 flights, with each flight being described by 18 time series. Emphasis was placed on the possibility of using such an approach in real operations, meaning each flight is described by known information at the time of departure. For the purposes of this work, the focus was on predicting \(\delta_{IBT}\) and \(\delta_{LT}\). As discussed in previous sections and considering the nature of the available parameters, a BiLSTM model utilizing a neural network was utilized. Since the goal was to predict potential delays at the final waypoint, whether a runway or parking position, a sequence-to-one approach was identified as the most appropriate. This approach, often referred to as many-to-one, allows the model to process a sequence of inputs and produce a single output. While predicting delays at each point along the route is a potential alternative, such a method would likely require updating the predictive model in real-time during the flight with live data. For this reason, it is more practical to predict a single final delay based on the information available at take-off, including the initial CTFM timestamp and the available FTFM profile. Additionally, historical CTFM flown profiles for the given route could provide further insights and improve the model's accuracy. The BiLSTM network was designed to handle sequential data by leveraging bidirectional processing and regularization. Input data were first normalized using the sequence input layer with zscore normalization, ensuring consistent feature scaling for more stable training. A BiLSTM layer was then employed to capture both forward and backward temporal dependencies. The internal cell states were regulated using the _tanh_ activation function, while the flow of information through the gates was controlled by the _sigmoid_ function. This allowed both past and future context in the sequence to be learned, improving the model's ability to detect patterns. Following the BiLSTM layer, the network integrates an attention mechanism to determine the importance of each feature in making predictions. This mechanism allows the model to focus on the features most relevant to the prediction task, while reducing the impact of less significant ones. By dynamically adjusting the influence of each feature, the attention mechanism helps the model better capture critical patterns in the data, improving both accuracy and interpretability. The attention mechanism operates through two fully connected layers. The first layer learns to assign weights to each of the 18 features during training, representing their relative importance in the prediction process. These weights are updated as the model learns, allowing it to prioritize certain features over others. The second layer then combines these weighted features, generating a scalar value that reflects the overall attention applied to the feature set. This approach enhances the model's ability to concentrate on the most crucial aspects of the data, leading to more robust predictions. The learned features were mapped to higher-level abstractions through a series of fully connected layers. A fully connected layer with 100 units was applied, followed by a dropout layer with a 0.8 dropout rate, which was used to reduce overfitting by randomly deactivating neurons during training. Another fully connected layer with 25 units and a second dropout layer were used to further refine the learned representation while maintaining model robustness. The final output was generated through a fully connected layer.