## 1 Introduction  
With the acceleration of urbanization, the airport express line, as an important part of the modern transportation system, is showing a rapid development trend [1]. Its convenient and efficient transportation characteristics mean that more and more passengers choose to travel between the airport and the urban area through the airport express line, which also makes the accurate prediction of the passenger flow of the airport express line a crucial task in the transportation field [2]. Passenger flow forecasting has a profound impact on the operation and management of the airport express line and the optimal allocation of traffic resources [3]. Accurate passenger flow prediction can help operators plan capacity allocation, personnel arrangement, and other preparations in advance so as to better meet passenger travel needs and improve service quality. At the same time, it also helps to rationally plan transportation resources, improve resource utilization efficiency, and avoid the occurrence of the idle or excessive use of resources [4]. However, the prediction of airport express passenger flow is not easy, and it involves many challenges. Passenger flow is affected by many factors, such as flight take-off and landing times, holidays, working days, weather conditions, and major urban activities. These factors mean that passenger flow shows complex time series characteristics. Traditional prediction methods often have limitations in dealing with such complex time series data, and it is difficult to accurately capture the change law of passenger flow, resulting in inaccurate prediction results [5]. There have been many studies on traditional forecasting methods in airport express passenger flow forecasting, such as the moving average method [6] and exponential smoothing method [7] in time series analysis. The moving average method calculates the mean value of passenger flow in a certain time window to predict the future value. Although it can smooth random fluctuations, it struggles to capture long-term trends and seasonal changes. The exponential smoothing method gives a higher weight to recent data and has a slightly stronger adaptability to dynamic changes. It also struggles to accurately grasp the internal law when facing complex passenger flow changes with multi-factor interweaving. Due to the limitations of its own technology and algorithm logic, the traditional method struggles to capture the subtle changes in passenger flow at different time nodes, resulting in poor prediction accuracy and the inability to provide effective decision support for operators. With the development of science and technology, deep learning algorithms have emerged in the field of passenger flow prediction. Among them, recurrent neural networks (RNNs) [8] and their variants have unique advantages in processing time series data. The RNN is designed for sequence data and transmits information at different time steps through cyclic connections, which can better capture the time dependence of data. For example, in airport express passenger flow prediction, the future value can be predicted by combining past passenger flow with flight take-off and landing, weather, and other factors. However, an ordinary RNN processing long sequence data is prone to gradient disappearance or explosion problems. For this purpose, long short-term memory (LSTM) [9] networks and gated recurrent units (GRUs) [10] are derived. LSTM effectively controls information transmission and forgetting by means of a gating mechanism and is good at dealing with the long-term dependence of long sequence data. The structure of GRUs is relatively simple, which simplifies the model complexity while maintaining a good performance.