## 1 Introduction  
Over the past few years, steady growth of urbanization and rapid economic development have led to the sustained expansion of urban scale, resulting in an increasingly growing demand for travel. Urban rail transit, as a new green, and efficient type of public transportation, has become an important component of transportation due to its continuous growth and improvement in large and medium-sized cities. Under such conditions, passenger flow prediction has been one of the pivotal technologies for ensuring the uninterrupted operations and optimal planning of rail transit systems [1]. Highly accurate short-term traffic forecasting can aid operators in optimizing resource utilization, including proactively managing passenger flow [2], and modifying train schedules well in advance [3, 4]. Moreover, it can help anticipate station congestion, effectively ensuring the safety of passengers and safeguarding their assets [5]. In short, the short-term passenger flow prediction [6] for urban rail transit is of great importance in the fields of daily functioning, refined management planning, and public safety. The development process of rail transit passenger flow prediction can be traced back to the 1970s. The initial prediction methods are mainly based on statistical models to predict future passenger flow trends by analyzing historical data [7]. The Historical Average (HA) model [8] forecasts future values based on the average of past observations. The autoregressive integrated moving average model(ARIMA) [9], as described, combines three steps: the autoregressive, integrated, and moving average, which can flexibly adapt to different time series data and obtain the optimal prediction results by adjusting parameters. Seasonal autoregressive integrated moving average (SARIMA) [10] is an expansion of the ARIMA model which captures seasonal effects by adding additional seasonal differences and seasonal autoregressive terms. However, both require complex parameter selection for the model, and they perform poorly when there are multiple seasonal patterns in the time series. Although statistical methods are simple and feasible, their accuracy is low and cannot meet practical needs because they cannot consider the complexity of the influencing factors and the uncertainty of the data. The development of computer technology has paved the way for the use of innovative techniques like big data and machine learning in predicting passenger flow for rail transit systems [11]. This includes some models like back-propagation neural networks (BPNNs) [12], support vector machines (SVM) [13], and random forest-learning [14], among others. Among them, deep learning, as a subset of machine learning, can automatically discover complex relationships and patterns within data and can be trained on large-scale data. [PERSON] et al. [15] predicted the parameters of a mathematical model of infectious diseases by fusing deep learning models with other temporal prediction methods. [PERSON] et al. [16] fused several deep learning models to propose a new knee angle prediction model. [PERSON] et al. [17] developed a deep learning model to predict traffic flow. Numerous research results [18; 19] demonstrate that deep learning methods provide a good idea to improve prediction accuracy. Recurrent neural network (RNN) is a type of deep learning model that is well-suited for modeling sequential data and can effectively handle passenger flow data with temporal dependencies [20]. Long short-term memory (LSTM) is a kind of RNN capable of capturing both short-term and long-term dependencies and relationships between variables, making it highly effective in passenger flow prediction tasks [21; 22]. In 2014, [PERSON] et al. [23] proposed a lightweight variant of LSTM called gated recurrent unit (GRU), which uses fewer training parameters than LSTM and can achieve comparable or even better results. Concurrently, this model also reduces the training time and computational costs.