## 5 Results
### The Results of the Short-Period Prediction using the LSTM Model  
First, we selected 90-day data (90 days since 1 January 2015) and 1096-day data (three years since 1 January 2015) as the training data to test the performance of the LSTM model for short-term (one-hour ahead) prediction, which aims to compare influences on the prediction accuracy at different learning rates and lengths of training data. The learning rate directly affects the degree of parameter changes after training; the more minor  
Figure 5: The overall structure of the EMD-LSTM model. the parameter, the lower the amplitude of change during each training, and the more training times are needed to achieve the ideal fitting effect. Usually, the learning rate is chosen to be \(10^{-3}\), \(10^{-4}\), \(10^{-5}\), or even smaller. Since the number of training times directly affects the training time, \(10^{-3}\), \(10^{-4}\), and \(10^{-5}\) are the learning rates used to compare the prediction results. Here, we list the predictions based on 90 days with different learning rates and trainings. Figures 6-8 and Table 2 show the one-hour ahead prediction of a 7-day length (168 h) using the 90-day data. As the learning rate decreases, the training number increases by around 400% to keep the close prediction error; the RMSE only decreases by 0.07 nT, the CC increases by 0.01, and the learning rate decreases from \(10^{-3}\) to \(10^{-5}\). The predictions based on 1096-day data are as follows. Figures 9-11 and Table 3 show the one-hour ahead prediction results for a 7-day length using three years of data since 2015. The situation is similar to the 90-day results: the RMSE only decreases by 0.03 nT, while the learning rate changes from \(10^{-3}\) to \(10^{-5}\). In addition, the prediction error decreases by about 1.3 nT on average relative to the RMSE of the 90-day data, and the CC improves by 0.03, which suggests that increasing the prediction data can effectively improve the accuracy. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Learning Rate** & **Trainings** & **RMSE (nT)** & **CC** \\ \hline \(10^{-3}\) & 650 & 3.27 & 0.91 \\ \(10^{-4}\) & 3400 & 3.29 & 0.91 \\ \(10^{-5}\) & 20,000 & 3.20 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The 7-day length prediction using 90-day data. Figure 8: The model prediction through 20,000 trainings with a learning rate of \(10^{-5}\). Figure 9: The model prediction through 650 trainings with a learning rate of \(10^{-3}\). However, the above figures show that the model-predicted values have a noticeable lag using different training data lengths. This lag phenomenon has also been observed in other studies using LSTM for prediction, such as [PERSON] et al. [27] and [PERSON] et al. [28]. This stems from the fact that when using the LSTM model for time-series prediction, the model algorithm is calculated using the values in the fixed time window as samples. In order to minimize the error, using the value at moment \(t\) as the prediction value of moment \(t+1\) not only requires no additional operations, but the error is very tiny, and the algorithm tends to use the value at moment \(t\) or \(t-1\) as the prediction value, thus generating a lag in the final prediction. Commonly used solutions include increasing the training data length and indirect prediction. To take advantage of the feature of the EMD-LSTM method and obtain segmented average values and then perform LSTM prediction, we use Figure 9 as an example and perform tests as follows. Figure 11: The model prediction through 18,000 trainings with a learning rate of \(10^{-5}\). Figure 10: The model prediction through 3300 trainings with a learning rate of \(10^{-4}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Learning Rate** & **Trainings** & **RMSE (nT)** & **CC** \\ \hline \(10^{-3}\) & 650 & 1.97 & 0.94 \\ \(10^{-4}\) & 3300 & 1.95 & 0.94 \\ \(10^{-5}\) & 18,000 & 1.94 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The 7-day length prediction using 1096-day data.