## 5 Conclusions  
We developed a backpropagation-based algorithm to optimize the trip assignment probability, and probability simulations of the access trip pattern from each zone to accessible HSR stations were undertaken. Backpropagation was used when training the artificial neural network; in this problem, the probability could be recognized as the weight optimized in the artificial neural network. Accordingly, the initial value in the backpropagation-based algorithm was a function of the access distance from zones to accessible HSR stations and the train frequency at HSR stations for each zone and line combination. The difference between the estimated volume from the probability and the observed volume was defined as the loss in the optimization process, and the weight was updated in the direction of minimizing this loss. To apply this backpropagation concept, we obtained the loss value using only differentiable calculations provided by PyTorch, a deep learning framework used for artificial neural network learning. To verify the prediction performance of the backpropagation-based algorithm, its trip assignment results were compared with those of an optimal strategy algorithm using network and O/D trip data from the KTDB. A total of 225,495 trips/day generated from 247 zones were assigned to 51 stations on the three HSR lines. The results for 19 major HSR stations with more than 1000 passengers were presented by dividing the regions into the Seoul metropolitan area, which had a relatively high concentration of HSR stations, and a non-metropolitan area, which did not. The backpropagation-based algorithm results show that all stations had an error rate of less than 30%, the reference value stated in the guideline. Furthermore, the results present a very low error rate, less than 2% for major stations with more than 10,000 passengers and less than 10% for minor stations with less than 10,000 passengers. On the other hand, the optimal strategy algorithm results show that many stations had an error rate exceeding 30%. For the stations in the Seoul metropolitan area, the MAE and MAPE indicators found using the backpropagation-based algorithm were 153 and 3.5%, respectively, and those found using the optimal strategy algorithm were 3310 and 53.6%, respectively. This means that the backpropagation-based algorithm was especially superior when applied to an area with multiple HSR stations, simulating the passenger access trip pattern from each zone to multiple stations. Therefore, the backpropagation-based algorithm will improve the accuracy and time efficiency of long-term HSR demand forecasting. A limitation of this study was that the access distance from each zone to the HSR stations was calculated using the Euclidean distance, which was used owing to data acquisition issues and the complexity problem of calculating using input data, such as applying the shortest path algorithm. If it were possible to obtain access distance or time data for each access mode to HSR stations, the algorithm's accuracy would be improved by reflecting more realistic conditions. Lastly, it is necessary to examine the extendibility of the backpropagation-based algorithm by applying it to various HSR networks with different conditions from those in Korea. This research received no external funding. Not applicable. The data are available upon request from the author. The author declares no conflict of interest. The main codes for optimizing the trip assignment probability weight are presented below. They consist of two steps: (1) variable initialization and (2) optimization. 1. Variable initialization
2. Line 105: \"opt_target_tensor\" is the tip assignment probability weight tensor for all stations (\(T_{a}\)) in Figure 5.
3.