# Deep-Learning-Powered GRU Model for Flight Ticket Fare Forecasting
## 4 Experiments and Discussion
A high value of R\({}^{2}\) means that the model could explain a large portion of the variance in the target variable, while a low value of R\({}^{2}\) suggests that the model cannot capture much of the variation in the data. In summary, R\({}^{2}\) is a useful metric for comparing regression models so as to determine the overall fit of a model. Figure 9 depicts a comparison of the convergence speed of the GRU, LSTM, and MLP models. As can be observed from Figure 9, the GRU model outperformed the others in RMSE. The loss of the GRU model was significantly lower than that of the others. Figure 9: Convergence of loss for GRU, LSTM, and MLP models. The plots show how the loss function decreased during training, indicating how well each model fit the data. The superior performance of GRU in this study is due to its ability to capture long-term dependencies in input data. GRU has internal memories, allowing it to remember past inputs and incorporate them into current predictions. Such a capability is crucial for predicting ticket fares, as the pricing of tickets can be influenced by temporal factors such as the day of the week. GRU's ability to capture these factors and incorporate them into predictions could result in more accurate fare predictions, as demonstrated by the lower root mean square error for the GRU model. Additionally, GRU's predictive power was compared with those of LSTM and MLP based on mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R\({}^{2}\)), as presented in Table 6. As can be observed from Table 5, MLP was the worst in performance since it had the highest MAE and RMSE values and the lowest value of R\({}^{2}\). The GRU model was superior in making accurate predictions, making it a reliable reference for the airline transport industry, both for travelers and aviators. The overall performance of GRU stands out as it surpassed both MLP and LSTM. When compared with MLP, the GRU model shows a decrease in MAE from 43.50 to 3.76, a decrease in RMSE from 64.93 to 5.93, and an increase in the coefficient of determination (R\({}^{2}\)) from 0.60 to 0.98. When compared to LSTM, the GRU model shows a decrease in MAE from 8.67 to 3.76, a decrease in RMSE from 13.99 to 5.93, and an increase in R\({}^{2}\) from 0.70 to 0.98. Furthermore, the experimental results of two popular machine learning approaches, autoregressive integrated moving average (ARIMA) and support vector regression (SVR), are listed in Table 6 for comparison. ARIMA is a combination of the autoregressive model, which captures the dependency of the current observation output on the previous observations, and the moving average model, which captures the dependency on the current and previous inputs. The ARIMA model can be characterized as ARIMA (\(p\), \(d\), \(q\)), where \(p\) is the degree of autoregression, \(d\) is the degree of differencing, and \(q\) is the degree of moving average. In this study, we utilized the setting of ARIMA (5, 1, 1) to forecast future prices. In addition, for SVR, the kernel was set as a radial basis function (RBF). It can be observed from Table 6 that the GRU model stands out as a clear choice in fare prediction, providing the airline transport industry with a trustworthy reference. Furthermore, the average of the predicted ticket fares for one flight based on the three different prediction models, GRU, LSTM, and MLP, were compared with the average of the actual fares in Table 7. The results in Table 7 indicate that the average of the predicted ticket fares for GRU is much closer to the actual average fares than those for LSTM and MLP. This suggests that GRU is a more accurate model for predicting ticket fares. Overall, the above results provide evidence of the superiority of the GRU model in predicting flight ticket fares and suggest that it is a promising approach for further study in this field.