# Multivariate Time Series Deep Spatiotemporal Forecasting with Graph Neural Network
## 4 Experiment Analysis
### Experimental Setup  
This section describes the hardware and software environment of the experiment and the configuration of related parameters. Our models are built with the Pytorch open source deep learning library. The device configuration used in the experiment is Intel core i5 10400F 2.9 GHz, the GPU is NVIDIA GeForce RTX 3060 12 G, and the memory is 16 GB.  
The four datasets are divided by time into training set (60%), validation set (20%), and test set (20%) in this paper. According to the performance difference of the model among different hyperparameters, the optimal hyperparameters are selected to validate the performance of the model on the test set.  
The key hyperparameter settings of MDST-GNN are shown in Table 2. In this paper, the model adopts four graph convolution modules, four temporal convolution modules, and one down-sampling convolution module. Adam is used as the optimizer, and the gradient clipping is 5. The network model is converged to the optimal solution by the learning rate decay technique. The input sequence window length is 168, and the output sequence length is 1. Train the model to predict future target intervals (Horizon) 3, 6, 12, and 24. The starting 1 \(\times\) 1 convolution has 1 input channel and 16 output channels. The activation function saturation rate of the graph learning module is 3, and the node-embedding dimension is 40. In the dataset Electricity, Traffic, and Solar Energy, the Number of neighbors (K of Formula (5)) of each node is set to 20. Neighboring node information is not considered for the Exchange Rate. The dilation factor of the convolutional network in the temporal convolution module is 2. A dropout of 0.3 is employed after each temporal convolution module. Layer Norm is used after each graph convolution module. The propagation depth of the Attention Mixed propagation layer is 2. The information retention rate of the propagation layer is 0.05. Both the graph convolution module and the temporal convolution module have 16 output channels. The number of layers (Num layers) of the down-sampling convolution module is shown in Table 2. The input channel of the down-sampling convolution module is 16, and the dropout is 0.3. Two skip connection layers have 32 output channels. In the output part of the model,two standard \(1\times 1\) convolutional networks with 64 output channels and 1 output channel are used. The training Epoch is 30. More detailed hyperparameters can be found in Table 2.  
Hyperparameters are obtained by changing the research parameters and fixing other parameters to obtain the optimal hyperparameters in this paper. Each experiment was repeated 5 times with 30 Epochs per run, and the hyperparameter that minimized the RRMSE among the 5 experiments was chosen. We investigate the hyperparameters that affect the results of the MDST-GNN model. The number of neighbors and layers were selected from the parameters. The parameters are analyzed by the results obtained from 5 experiments on the dataset Exchange Rate. Figure 8 shows the experimental results of the parameters. It can be seen from Figure 8 that fewer related nodes have better results, which indicates that the spatial dependence among multiple exchange rates is weak, and increasing the information of adjacent nodes will only increase the noise. Figure 8 shows that increasing the number of layers can achieve good results, but the change in the RRMSE tends to be flat when the number of layers is greater than 4, which is because the overfitting phenomenon occurs when the number of layers is too large.