## 2 Related Work
### Metro Flow Prediction Models  
Methods for predicting metro flow have usually been classified into traditional statistical approaches and machine learning techniques. The traditional statistical method ARIMA comprises a linear combination of time-lagged variables and error terms. It has found extensive application in predicting traffic-related data including, but not limited to,metro flow, traffic flow, travel time, speed, and occupancy [34; 35; 36]. For instance, [PERSON] et al. used ARIMA and focused on determining the most appropriate parameters of ARIMA to predict short-term metro flow [37]. The traditional statistical approaches demonstrate strong and consistent performance in modeling time series that exhibit linearity and stationarity. However, metro flow data often exhibits nonlinearity, thereby limiting the predictive accuracy of models based on linear assumptions. To capture nonlinear dependencies within metro flow data, researchers have explored a range of machine learning approaches, including multilinear regression, support vector machines, random forest regression, hidden Markov models, backpropagation neural networks, hybrid methods, and so on. For instance, [PERSON] et al. proposed a least-square support vector approach to handle the complex fluctuations in holidays and predicted passenger flow for a metro system [12]. [PERSON] et al. proposed an innovative approach for predicting metro flow, employing a random forest regression model and leveraging multi-source data [38]. Nevertheless, these conventional machine learning methods are constrained in their ability to capture only shallow nonlinear dependencies, neglecting the long-term time series patterns and deeper nonlinear dependencies inherent in the data. Recently, deep learning has evolved into an advanced machine learning technique, holding considerable promise for predicting metro flow. Deep learning methods possess the ability to automatically model intricate spatial and temporal dependencies within data. Moreover, the reliance on manual feature engineering can be mitigated by employing deep neural networks. For instance, deep neural networks are designed to intricately and abstractly extract nonlinear features embedded in their inputs [39]. [PERSON] et al. used a convolutional neural network (CNN) model for metro passenger flow prediction employing spatial-temporal data fusion. The dynamics of spatial-temporal passenger flow were transformed into a two-dimensional time-space matrix that characterized the temporal and spatial relationships of passenger flow. Then, the optimal hyperparameter combinations for the CNN were determined by the grid search algorithm [40]. Recurrent neural networks (RNNs) are able to model temporal dependencies. However, they face challenges such as gradient vanishing and explosion during long-term prediction. Long short-term memory (LSTM) networks and gated recurrent units (GRUs), as specialized RNN variants, effectively address the severe gradient problem. They excel in capturing long-term dependencies in sequential data, with the added advantage of faster model training for GRUs. [PERSON] et al. proposed a novel ensemble learning model assembling LSTM, support vector regression (SVR), and a sparrow search algorithm to deal with long term metro passenger flow prediction [41]. Moreover, several advanced deep learning approaches have been applied to metro flow prediction, such as attention mechanism-based approaches, graph neural network-based approaches, and some hybrid deep learning approaches. For example, [PERSON] et al. proposed a novel deep learning method combining a graph convolutional network (GCN) and a three-dimensional convolutional neural network (3D-CNN) enhanced by the incorporation of a residual module and an attention mechanism [42]. Due to their self-attention mechanism, transformer-based deep learning architectures are applied for traffic prediction widely, and are capable of sequential data modeling.