# Traffic Prediction of Space-Integrated Ground Information Network Using the GTCN Algorithm
## 3 TCN Neural Network  
The traditional convolutional neural network is not suitable for modeling time series problems such as network traffic prediction. Because of the size limitation of the convolutional kernel, the traditional convolutional neural network cannot capture the lengthy time information in the time series well. Therefore, TCN was developed by [PERSON] in 2018 to solve time series modeling and natural language processing problems [19]. TCN neural network consists of three parts, namely, causal convolution, expansion convolution, and residual linkage. The principle of causal convolution is to produce a value at time t of the upper layer by only depending on the value at time t of the next layer and the value before it. Thus, the time series is subject to strict time constraints and only the observed information is used for feature extraction and prediction. The structure of causal convolution is shown in Figure 1.  
When the input time series is \(\{x_{0},x_{1},x_{2},\ldots,x_{t-1}\}\), to ensure that the input size is the same as the output size, appropriate zero paddings are carried out in front of the input data. The causal convolution formula is as follows:  
\[p(x)=\prod_{t=1}^{T}p(x_{t}|x_{1},\ldots,x_{t-1}) \tag{1}\]  
The prediction is implemented according to the sequence \(\{x_{0},x_{1},x_{2},\ldots,x_{t-1}\}\), so that the prediction result is closer to the actual value. Dilated convolution is introduced based on causal convolution to reduce the number of convolution layers, to avoid the gradient disappearance problem in neural network training, and to make the causal convolution's model length for time series no longer limited by the size of the convolution kernel. The structure of dilated convolution is shown in Figure 2.  
Figure 1: Causal Convolution. Figure 2: Dilated convolution. Unlike causal convolution, dilated convolution allows interval sampling of the input during convolution and the sampling rate is controlled by the Dilation in Figure 2. Dilation = 1 in the lowest layer means that every point is sampled input and Dilation = 2 in the middle layer means that every two points are sampled as input. Generally, the higher the convolution layer, the greater the value of the expansion coefficient, allowing the network to use the least number of layers to obtain a larger receptive field. The expansion convolution formula is as follows:  
\[F(s)=\sum_{i=0}^{k-1}f(i)\cdot x_{s}-d\cdot i \tag{2}\]  
where \(f\) is the convolution kernel calculation, \(k\) is the number of convolution layers, the expansion convolution operates on the element \(s\), and \(d\) is the expansion coefficient. When the number of layers of the neural network is too deep, the gradient disappearance problem often occurs, causing the gradient of the shallow layer to not be updated. The residual network has been proved to be able to solve the deep network degradation and gradient disappearance problems [20]. The residual network structure is shown in Figure 3.  
After the calculation of the first weight on the first layer, the input sequence is adjusted by the ReLU activation function and then enters the next layer's weight. The ReLU activation function can improve both calculation speed and convergence speed. In the residual network structure, the problem of reversed error is changed from F(x) to H(x). In this way, when the error is the lowest, F(x) = 0, is the only requirement to ensure that the network state of the next layer is still in the optimal state. Consequently, we can prevent the neural network from continuing to optimize when the optimal solution is reached, which shall result in degradation. The residual block of a TCN network is shown in Figure 4.  
A TCN network model consists of two layers of expansion convolution and a non-linear mapping. In each layer, a weight normalization and a dropout algorithm are used to regularize the network, which reduces the possibility of overfitting, strengthens the generalization ability, and improves the accuracy of training and prediction.