## 2 Methodology
### Improved TimesNet Module
The specific procedural formula is as follows:  
\[X_{2D}^{i}=reshape_{p_{i},f_{i}}(Padding(X_{1D})),i\in\left\{1,\cdots,k\right\} \tag{16}\]  
In the above equation, Padding involves appending zeros to the end of the time series to make it compatible with the reshaping process. \(pi\) and \(f_{i}\) denote the number of rows and columns in the transformed 2D tensors, respectively. Continuing, the following formula can express the input and output process within the TimesBlock module:  
\[X_{1D}^{l}=TimesBlock\left(X_{1D}^{l-1}\right)+X_{1D}^{l-1} \tag{17}\]  
Specifically, when \(l=0\), the following holds true:  
\[X_{1D}^{0}=Embed\left(X_{1D}^{0}\right) \tag{18}\]  
In the TimesBlock module, the softmax function is applied after the FFT for periods to determine the relative importance or weight of each detected frequency (or period) in the input time series. This helps the model to focus on the most relevant periods for further analysis and prediction, ensuring that less significant frequencies do not dominate the output. Specifically, the softmax function ensures that the selected frequencies are normalized, and their values sum to 1, providing a clear probabilistic interpretation of how important each period is in the model's analysis. This probabilistic weighting aids in the final aggregation and prediction process. The various temporal two-dimensional variants from the k reshaped tensors are captured efficiently utilizing parameter-efficient Inception Blocks within the two-dimensional space. These are then fused based on normalized amplitude values (shown in Figure 5). Within the 2D tensors, each column contains time points within a single period, while each row involves time points at the same phase across different periods. This allows for the representation of both intra-period and inter-period variations concurrently in the 2D space. In the Inception Block module of the TimesNet model, the TimesBlock uses a parameter-efficient Inception Block within the 2D space to capture both intra-period and inter-period changes. Using the Inception V1 convolution, Inception Block is a structure from deep learning for visual models that process multi-scale information in parallel, allowing it to effectively capture and learn 2D features. In metro passenger flow prediction tasks, models for processing time series data need to capture complex trends and periodic changes. The traditional Inception V1 module uses convolutional kernels of different sizes to capture features at various scales, thereby improving the model's representation ability [37]. However, this design has limitations, such as a large number of parameters that may lead to overfitting and insufficient adaptability to dynamic changes in features. To overcome these issues, dynamic convolution is introduced, which adapts to the features of the input data by learning a weighted combination of different convolutional kernels, offering advantages in adaptive feature extraction and parameter efficiency [38]. Consequently, the design that concatenates dynamic convolution with the Inception V1 module not only inherits the advantages of both but also more effectively processes time series data. Specifically, the dynamic convolution layer first performs adaptive feature extraction on the input data, adjusting the weights of the convolutional kernels based on the dynamic changes in the data, thereby better capturing the trends and periodic changes in the time series data. Then, the data processed by dynamic convolution pass through the Inception V1 module, which further extracts and fuses features at different scales, enhancing the model's representation ability. Finally, the GeLU activation function introduces nonlinearity, enhancing the model's expressive capability, enabling it to capture more complex feature  
Figure 5: Diagram of the TimesNet model. relationships. In metro passenger flow prediction tasks, this design effectively captures the dynamic features of time series data and performs multi-scale feature fusion, thereby improving the accuracy of predictions.