# Multi-Scale Residual Depthwise Separable Convolution for Metro Passenger Flow Prediction
## 1 Introduction

Table 1: Overview of studies on passenger flow prediction and its application. methods were statistical methods, followed by machine learning methods. Statistical methods primarily rely on extracting time series patterns from historical data [7; 8]. These methods struggle to meet the requirements for real-time performance and prediction accuracy. Compared with statistical methods, machine learning approaches have higher prediction precision and have more advantages in solving multi-source data integration problems. Moreover, deep nonlinear relationships modeling can be achieved by some models, such as back-propagation neural network (BPNN) [9], gradient boosting decision tree (GBDT) [10], and multilayer perceptron (MLP) [11]. In recent years, deep learning methods have attracted considerable attention as a branch of machine learning, which not only automatically extracts intricate temporal and spatial features but also effectively models high-dimensional data. In the initial stage of deep learning, many models based on recurrent neural networks (RNNs) have emerged, which are widely employed in passenger flow prediction tasks for their superior ability to handle temporal features [12; 13; 14]. As one of the variants of RNN, the gated recurrent unit (GRU) distinguishes itself through its advanced gating mechanism [15; 16]. However, despite the progress made in contemporary passenger flow prediction models, a fundamental limitation of these models is their inability to capture spatial features. Thanks to the excellent properties to extract connections in terms of space, the convolutional neural network (CNN) is widely applied to process spatial data with regular grid structures or Euclidean data [17]. As a supplement to the CNN, the graph convolutional network (GCN) [18] is valuable in capturing network-based spatial dependencies from graph-structured data, and it aggregates the edge features of adjacent nodes to promote global modeling [19; 20; 21]. The spatial dependencies are optimal for metro passenger flow prediction since they can capture the inter-station flow patterns between stations [22]. Considering this, we need to capture not only the local dependencies within each station but also the global interactions between stations throughout the entire metro network. So, some studies focus on multi-station passenger flow prediction, which individually predicts passenger flow for each cluster comprising multiple stations. For instance, [PERSON] et al. [23] employed K-Means to classify all stations into different categories and created a prediction model for the same category in the network. [PERSON] et al. [24] proposed a novel two-step model that predicted the passenger flow for each type of classification result. Unlike stand-alone prediction strategies that only consider interdependencies within a cluster, network-level prediction focuses on interactions across clusters and the flow dynamics of the entire network. In addition to temporal and spatial correlations among stations, the stations are also affected by inter-station correlations measured by geographical connectivity and passenger travel behavior patterns [25]. The inter-station correlations not only exist in local areas but can also occur between geographically distant stations. Nevertheless, some recent models only consider the physical topology of metro networks and neglect the diversity of inter-station dependencies. [PERSON] et al. [26] constructed a geographic topology graph based on the connection relationships in the metro network. Overall, these methods are limited to learning local spatial dependencies between adjacent stations and cannot fully capture the spatial dependencies of long-term passenger flow trends. Therefore, it provides substantial opportunities to improve the accuracy and robustness of passenger flow prediction.