# Joint Geoeffectiveness and Arrival Time Prediction of CMEs by a Unified Deep Learning Framework
## 2 Methods
### Arrival Time Prediction for Geoeffective CMEs
#### 2.2.2 Deep Residual Regression Network Based on Group Convolution  
The architecture of the arrival time prediction network is shown in Table 2. The overall architecture is similar to the geoeffectiveness feature extraction network. First, through the data preprocessing, the original image is scaled, normalized and gray-scale processed in sequence. The first two layers of the network still use the same convolutional layer and max pooling. Next layers are composed of six residual blocks based on group convolution, and the illustration of the residual block is shown in Figure 4. Referring to the idea of Resnext [31], the network introduces group convolution to realize the split-transform-merge strategy. Through group convolution, the floating point operations (FLOPs) of the network can be reduced while increasing the cardinality of the network to improve the performance of the network.  
The residual blocks based on group convolution first splits the input feature map \(F\in\mathbb{R}^{H\times W\times C}\) in the channel dimension to obtain \(group\) sub-feature maps, where \(group\) is a parameter and uses as the default value of 32 in our network. The shape of each sub-feature map is \(\mathbb{R}^{H\times W\times C}/group\). Next, convolution operation with the filter size of \(5\times 5\) is performed on each sub-feature map to transform and learn the features of each sub-feature map. Then the transformed sub-feature maps are reconnected in the channel dimension, and the information of the inter sub-feature maps is merged through the \(5\times 5\) convolution operation. Finally, the merged feature map is added with the shallow input feature maps. There are two purposes using residual connection based on group convolution. One is reducing the FLOPs of the network and speeding up the network. If the parameter of group convolution is \(group\), the FLOPs of group convolution is only \(1/group\) of traditional convolution operation. The other is increasing the cardinality of the network. In addition to  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer Name** & **Layer** & **Output Size** \\ \hline Conv1 & \(11\times 11\), 64, stride 1 & \(256\times 256\) \\ \hline Max Pool & \(3\times 3\), max pool, stride 2 & \(128\times 128\) \\ \hline Conv2\_x & \(\begin{bmatrix}5\times 5,\ 64,\ g=32\\ 5\times 5,\ 64\end{bmatrix}\times 2\) & \(128\times 128\) \\ \hline Conv3\_x & \(\begin{bmatrix}5\times 5,\ 128,\ g=32\\ 5\times 5,\ 128\end{bmatrix}\times 2\) & \(64\times 64\) \\ \hline Conv4\_x & \(\begin{bmatrix}5\times 5,\ 256,\ g=32\\ 5\times 5,\ 256\end{bmatrix}\times 2\) & \(32\times 32\) \\ \hline FC1 & FC, Dropout & \(1\times 256\) \\ \hline FC2 & FC & \(1\times 1\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The illustration of the deep residual regression network based on group convolution.  
the dimensions of depth and width, cardinality is also an essential factor that can improve the performance of the network.  
After extracting the feature map from the input image, the multi-layer perceptron module is followed to obtain the predicted arrival time, which contains two fully connected layers and Dropout [46]. The random inactivation probability of Dropout is 0.2 to prevent the network from overfitting.