## 4 Case Study
### Results  
The trip assignment probability weight was updated 2000 times with a learning rate of 0.01 in the backpropagation-based algorithm. The loss had a downward trend with each update, and dropped sharply within about 200 iterations, as shown in Figure 10. Furthermore, it almost converged to the final value after about 200 iterations. When the probability weight was updated once, the loss was 36,624,504, and the final value decreased to 97,344 after 2000 iterations. This means that the difference between the estimated volume using the backpropagation-based algorithm and the observed volume significantly decreased. The trip assignment results for each HSR station using the backpropagation-based algorithm are presented in Table 3. The results for major HSR stations with more than 1000 passengers are presented by dividing the regions into the Seoul metropolitan area, which had a relatively high concentration of HSR stations, and non-metropolitan areas, which did not. To verify the algorithm's prediction performance, we compared the results found using the optimal strategy algorithm based on the volume at each HSR station. Moreover, the error rate presented in Equation (1) and the mean absolute error (MAE) and mean absolute percentage error (MAPE), expressed as Equation (3) [48], were chosen as the key performance indicators. \[MAE=\frac{\sum_{i}^{n}\left|f_{est}-f_{obs}\right|}{\eta},MAPE=\frac{\sum_{i}^ {n}\frac{\left|f_{est}-f_{obs}\right|}{f_{obs}}\times 100}{\eta} \tag{3}\]  
Figure 10: The loss changes in the backpropagation-based algorithm by iteration. Here,  
\(i\): HSR station (\(\forall i\in Z\));  
\(n\): the number of HSR stations;  
\(f_{est}\): the estimated number of passengers at each station using the trip assignment model;  
\(f_{obs}\): the observed number of passengers at each station. The trip assignment results from the backpropagation-based algorithm show that all stations had an error rate of less than 30%, the reference value stated by the guideline. However, the results from the optimal strategy algorithm show that many stations had an error rate exceeding 30%. The backpropagation-based algorithm results presented a very low error rate, less than 2% for the major stations with more than 10,000 passengers and less than 10% for the minor stations with less than 10,000 passengers. The high error rate at Gangneung Station could be attributed to the PyeongChang Olympic Winter Games. During the Winter Olympics, additional temporary trains that directly connected Incheon International Airport to Gangneung were operated. Accordingly, the observed volume at Gangneung Station was higher than usual; thus, the predicted demand was underestimated because it used the KTDB O/D trip data, estimated based on the average weekday trips. The estimation accuracy using the backpropagation-based algorithm was relatively high compared with the estimation results from the optimal strategy algorithm for stations in both areas, i.e., the Seoul metropolitan area and the non-metropolitan area. However, the results for the Seoul metropolitan area show that the backpropagation-based algorithm's accuracy was overwhelmingly higher than the optimal strategy algorithm's accuracy. In the optimal strategy algorithm, the trip distribution among the adjacent stations was