## 4 Simulation Analysis
### Simulation Results
As training continues, the loss curves for both the training and test sets stabilize around similar values, indicating that the model is nearly converging and achieving good training effects. Importantly, the close alignment of the training and test loss curves shows that the model is generalizing well to unseen data without signs of overfitting. The Mean Squared Error (MSE) on the test set ultimately drops to below \(10^{-3}\), confirming the model's effective learning and optimization. The predictive performance is evaluated as shown in Figure 7.  
The predictive model demonstrates robust performance, as evidenced by a Mean Absolute Error (MAE) close to 0.01, specifically 0.010924723. This low MAE indicates that, on average, the absolute difference between the predicted values and the actual values is minimal. Furthermore, the Mean Squared Error (MSE) remains consistently low across all time periods, averaging less than 0.001. This low MSE signifies that the model effectively minimizes large prediction errors, maintaining a high level of accuracy over time. Importantly, there is no observable degradation in predictive performance as the prediction time horizon extends. This stability in error metrics across increasing time periods highlights the model's capability for long-sequence prediction, underscoring its superiority in maintaining accuracy over extended predictions. For the demand prediction of communication satellites, which exhibits clear periodicity, the effectiveness of the prediction is compared, as shown in Figure 8. The method of averaging the demand data over 14 days at each time point in a day is used as a reference. The average and maximum MSE obtained from the proposed method are compared with those from direct prediction. The average MSE is calculated by randomly predicting 5000 times for 288 points of data in a day after the model training is completed, while the maximum value is the largest MSE obtained throughout the process.. Using the average value for prediction leads to significant average errors, primarily because it oversimplifies the historical demand data of a single beam and fails to capture its intricate fluctuations and complex patterns. This approach assumes a uniform distribution of demand over time, overlooking the significant variability and nonlinearity inherent in real-world data. As a result, important details such as sudden spikes or drops in demand are smoothed out, leading to a substantial Mean Squared Error (MSE) of up to 0.03 and prediction fluctuations exceeding 0.3, indicating a high degree of instability. Furthermore, the average method neglects temporal dependencies, such as cyclical trends  
Figure 7: Evaluation of simulation predictive performance. and autocorrelation, which are crucial for accurate forecasting. This lack of insight into the underlying causes of demand variability limits its practical utility for applications requiring reliable and stable predictions. Therefore, while averaging provides a quick and straightforward approach, it is insufficient for capturing the complexity of demand patterns, leading to less accurate and less reliable forecasts. In contrast, when historical demand data for different beams are input separately into the model, the model is able to learn and adapt to the unique characteristics of each beam. This targeted approach allows the model to identify and capture underlying trends, periodicities, and nonlinear relationships that are not evident when using a simple average. Consequently, the model's predictive MSE is slightly lower than that obtained through averaging, demonstrating that the model can make more accurate predictions by effectively utilizing the historical data. The model's ability to maintain a significantly lower maximum MSE fluctuation compared to direct averaging underscores its robustness and stability. This reduction in error volatility is critical for practical use cases, as it implies that the model can provide more consistent and reliable forecasts.