# Joint Geoeffectiveness and Arrival Time Prediction of CMEs by a Unified Deep Learning Framework
## 4 Results
### Results on the Arrival Time Prediction for Geoeffective CMEs  
On the arrival time prediction of CME events, the evaluation metric adopts mean absolute error (MAE). The MAE formula can be defined as follows:  
\[MAE=\frac{1}{N}\sum_{i=1}^{N}|y_{i}^{predict}-y_{i}^{true}|, \tag{9}\]  
where \(N\) represents the number of CME events in the testing set, \(y_{i}^{true}\) represents the actual arrival time of the \(i\)th CME event, and \(y_{i}^{predict}\) represents the predicted arrival time.  
For comparison with other methods, we chose four well-known CNN models and three machine learning/deep learning methods, which are used in the CME arrival time prediction task. The results are shown in Table 4.  
In addition to the three CNN models mentioned above, we also add ResNext [31] to compare. Resnext repeats a building block that aggregates a set of transformations with the same topology. The mean absolute error of four CNN models is 8.1 h and has been increased 2.3 h in average when compared to our method. The main reasons for the better performance of our method are as follows--firstly, our method uses a more suitable kernel size of the convolution filter; secondly, our method introduces the residual block based on group convolution to train deeper networks and improve network performance by increasing the cardinality of the network; thirdly, our method uses cost-sensitive regression loss function to reduce the error of hard sample.  
Meanwhile, we also compare with the machine learning/deep learning methods used in CME arrival time prediction. [PERSON] et al. [20] uses FCNN to predict the transit time for CME events using the initial velocity of the CME and the central meridian distance of the associated flare as inputs, the MAE is about 11.6 h and is twice the error of our method. CAT-PUMA [21] uses SVM fitting parameters to predict the arrival time for geoeffective partial-/full-halo CME events, the MAE is increased 0.1 h when compared with our method. Moreover, 5.9 h is the best result in a random 100,000 testing set. Both two machine learning methods are necessary to manually collect the parameters and if the relevant parameters are missed, errors of the related CME events will be raised. [PERSON] et al. [23] first uses CNN to predict the arrival time for geoeffective CME events, with an error of 12.4 h. Compared with our method, the error is greatly increased. The main reason is that the network is too simple to capture distinguishing features, and it only uses the observation of the LASCO C2 white light coronagraph as input.  
Finally, we determine the value of \(\beta\) in the cost-sensitive regression loss function through enumeration on the basis of data expansion and deep residual regression network. As shown in Table 5, the MAE is 6.4 h when using L2 Loss. After switching to cost-sensitive regression loss, different \(\beta\) all bring a small improvement, with an average improvement of 0.3 h. Among them, the \(\beta\) value of 3 is the optimal choice and the MAE is only 5.8 h.  
In summary, our proposed arrival time prediction algorithm is effective and is better than well-known machine learning/deep learning methods.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **F1 Score** & \(\boldsymbol{\triangle}\boldsymbol{1}\) & **Accuracy** & \(\boldsymbol{\triangle}\boldsymbol{2}\) \\ \hline ResNet18 & 0.203 & \(-\)0.067 & 59.0\% & \(-\)16.1\% \\ \hline Vgg16 & 0.235 & \(-\)0.035 & 67.4\% & \(-\)7.7\% \\ \hline MobileNetv2 & 0.249 & \(-\)0.021 & 63.4\% & \(-\)11.7\% \\ \hline CNN+LSTM & 0.185 & \(-\)0.085 & 11.5\% & \(-\)63.6\% \\ \hline Ours & 0.270 & - & 75.1\% & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the geoeffectiveness prediction of CME events with other methods.