## 3 DST-LEO Satellite-Traffic Prediction Model
### Model Architecture
#### 3.4.2 Spatial Dependency Extraction Model  
The model employs 64 graph convolutional network (GCN) layers to process the traffic volume and link connectivity. The parameters of each GCN layer are as follows: hidden_channels = 64 and activation = \"relu\". After each GCN layer, there is a BatchNorm1d layer for normalization and a dropout layer to prevent overfitting.  
The principle of the graph convolutional network (GCN) is to construct a filter in the Fourier domain and process the graph nodes and their first-order domain through this filter, in order to obtain the spatial features of the nodes in the graph. Finally, the spatial dependency extraction model is established through the superposition of 64 convolutional layers. In this paper, the low Earth orbit (LEO) constellation network traffic model matrix  
Figure 4: Schematic diagram of the data format for training.  
was used as the node features, and 64 convolutional layers were designed to process the graph structure. The formula is as follows:  
\[H^{(l+1)}=ReLU\Bigg{(}\widetilde{D}^{-\frac{1}{2}}\widetilde{A}\widetilde{D}^{- \frac{1}{2}}H^{(l)}W^{(l)}\Bigg{)},l=0,1,2,\ldots,63 \tag{1}\]  
Here, \(H^{(l)}\) is the input feature matrix with the shape of (N, F1), where \(N\) represents the number of nodes in the graph. Specifically, for 104 satellite links, N = 104. F1 is the number of input features, which mainly depends on the selection of node features. For example, in this paper, the traffic volume and the link on-off data were selected.. The output feature matrix of the 64 th layer is \(H^{(64)}\) with the shape of (N, F64), where F64 is the dimension of the output features. \(\widetilde{A}=A+l\widetilde{A}\) is the adjacency matrix with self-loops added, where \(A\) is the original adjacency matrix and \(l\) is the identity matrix. \(\widetilde{D}=\sum_{j}\widetilde{A}_{ij}\widetilde{D}\) is the degree matrix of \(\widetilde{A}\). \(W^{(l)}\) is the learnable weight matrix of the \(l\)-th layer, with a shape of (F\({}_{l}\), F\({}_{l+1}\)). The rectified linear unit (ReLU) activation function is selected, which plays a crucial role. Firstly, by introducing nonlinearity, it enhances the model's ability to learn nonlinear data. Secondly, _ReLU_ can alleviate the vanishing gradient problem and accelerate the model's convergence. Finally, _ReLU_ enables sparse activation. While reducing redundant computations, it can also automatically select important features. \(\widetilde{L}=\widetilde{D}^{-\frac{1}{2}}\widetilde{A}\widetilde{D}^{-\frac {1}{2}}H^{(l)}\) represents the normalized Laplacian matrix, that is, the graph convolution operator.  
The BatchNorm normalization technique and residual connections were used to stabilize the training process. The meanings of the symbols are the same as those in Formula (1). Normalization can accelerate the convergence of the model and improve its generalization ability and performance. The formulae are as follows:  
\[H^{(l+1)}=Norm\Bigg{(}ReLU\Bigg{(}\widetilde{D}^{-\frac{1}{2}}\widetilde{A} \widetilde{D}^{-\frac{1}{2}}H^{(l)}W^{(l)}\Bigg{)}+H^{(l)}\Bigg{)},l=0,1,2, \ldots,63 \tag{2}\]