# Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network
## 3 Methods
### Temporal Convolution Module  
The temporal convolution module consists of two Dilated Inception layers. Tanh and Sigmoid activation functions are used after the Dilated Inception layer. One dilated inception layer is followed by an activation function, and Tanh is used as a filter. The sigmoid function of the other layer is used as the gate unit. The gate unit controls the amount of information that the filter propagates to the next module.  
The advantages of the Inception network and Dilated convolution are incorporated into the Dilated Inception layer. Information at different scales can be captured by the Inception network, while the dilated convolutional network ensures that long-term sequences can be processed. First, the receptive field of traditional convolutional networks is limited by the depth of the network and the size of the convolution kernels. Processing long-term sequences requires increasing convolution kernel size and network depth, which increases the cost of computational resources for the problem. For example, for a network with \(L\) one-dimensional convolutions and \(K\) convolution kernels, the size of the receptive field is:  
\[R=(K-1)\times L+1 \tag{6}\]  
In WaveNet [33], stacked dilated convolutions were used to make the network have a very large receptive field. Computational efficiency and input data integrity are guaranteed with only a few layers. In this paper, the dilated convolution method is used to reduce the cost of model computing resources. The dilation factor is doubled for each layer. With the increase in depth, the dilation factor can make the receptive field grow exponentially. For long time series, the advantage of dilated convolution is that the internal data structure can be preserved without reducing the length of the data input. However, models designed based on dilated convolutions also have some problems. Due to the discontinuity of the convolution kernel, all elements cannot be covered in the dilated convolution, so the continuity of information will be lost. Therefore, the Inception network is introduced into the model. Multiple convolution kernels of different sizes are used to cover the receptive field to retain more information.  
In the Inception network, features of multiple scales are obtained by convolution kernels of different sizes. The sparse matrices output by multiple convolutional networks are aggregated into denser submatrices. For the Inception network, the size of the convolution kernel needs to be selected according to the characteristics of the data. According to the periodicity of the time series (2, 3, 6, 7), four convolution kernels are used by the Inception network in this paper. These convolution kernels can be combined to cover multiple time periods of different lengths. The input data \(X\) is processed using four convolution kernels of different scales. The outputs of different scale convolutions are fused to obtain complete temporal information.  
\[X=concat(X\times I_{1\times 2},X\times I_{1\times 3},X\times I_{1\times 6},X \times I_{1\times 7}) \tag{7}\]  
Finally, the convolution results of different lengths are cropped to the same length. In Formula (7), the convolution results are concatenated by the channel dimension. Features of different scales are learned by each layer in the network. The adaptability of the network to different scales of information is increased by the concatenation of channel dimensions.