## 4 Simulation Analysis
### Simulation Results  
Real aviation data are used in this study, divided into different beams based on the coverage range of each beam as training input data. As shown in Figure 5, the aviation traffic demand at 8 a.m. is depicted. Specifically, 14 days of data for thirty-seven beams are used as input, with data averaged every five minutes to form a single data point. A total of 5000 samples are utilized for training, with \(B\) set to 37, \(N\) to 14, \(t\) to 5, and \(M\) to 5000. The training process involves 300 epochs, each batch comprising 20 samples. The model architecture consists of three layers with 128 hidden units, and the learning rate is set to 0.001. It is important to note that these parameters were not arbitrarily chosen. They were determined through a detailed parameter tuning process involving extensive experimentation and cross-validation. Various combinations of hyperparameters were tested to identify the optimal settings for achieving the best performance in terms of prediction accuracy and model stability. Specifically, when selecting the parameter \(t\), we experimented with a range of values. We found that when \(t\) was too small, the sequence became overly noisy, which hindered the training process. Conversely, when \(t\) was too large, there was a risk of losing significant variability in demand, which could negatively impact the model's ability to accurately capture fluctuations. Among the various configurations tested, the initial training process involved 200 epochs, with each batch comprising 20 samples. The model architecture was initially set to one layer with 32 hidden units, and the learning rate was set to 0.001. With this lower-complexity model, convergence was achieved after training for 200 epochs. The Mean Squared Error (MSE) on the test set dropped below \(10^{-2}\), indicating a good prediction  
Figure 4: ACF plot. performance. When examining the MSE over 288 prediction time points, it was observed that the MSE stabilized as the number of epochs increased. Comparing the 1 st epoch to the 200 th epoch, the model's MSE for each prediction time point remained stable and did not worsen with increasing prediction horizons. This demonstrates the model's superiority in long-sequence predictions. Due to the use of only one layer and 32 hidden units, the model had a relatively low parameter count, resulting in a fast convergence. While this simple model provided satisfactory performance, increasing the model complexity could potentially yield more accurate predictions and lower MSE values, albeit at the cost of increased training time. To improve prediction accuracy, the model complexity was increased by using two layers with 64 hidden units, and the number of training epochs was extended to 500. This adjustment in model complexity resulted in a reduction in the MSE to around \(10^{-3}\), demonstrating a significant improvement in prediction accuracy. Further increasing the model complexity, the architecture was set to three layers with 128 hidden units. After training the model on the demand of thirty-seven beams for three hundred epochs, the predictive results are illustrated in Figure 5(a). This led to the following prediction results: with higher model complexity, the results showed further convergence and a further decrease in MSE, indicating an enhanced model performance. Figure 5: Illustration of aviation traffic demand at 8 a.m.  
Figure 6: Simulation predictive results: (**a**) forecast results; (**b**) algorithm convergence. The loss, calculated by measuring the difference between the model's predicted values and the actual labels, is used to monitor the convergence during training, as depicted in Figure 6b. The provided MSE loss graph demonstrates that as the number of training epochs increases, the deep learning model progressively learns and optimizes, which is evident from the decreasing trend of the loss curve. During the initial epochs, both the training and test losses drop rapidly, suggesting that the model is quickly learning the underlying patterns in the data.