# Ionospheric TEC Prediction in China Based on the Multiple-Attention LSTM Model
## 3 Experimental Results and Discussion
### Prediction Comparison of Different Months  
This section mainly discusses the prediction performance of the LSTM, GRU, Att BiGRU and MA-LSTM models in different months of the eight regions in Table 1. The training data are 42715 TEC sequences from 0:00 on 1 January 2002 to 18:00 on 30 December 2010, and the test data are TEC sequences from 12 different months in 2011. The mean prediction performance of different models in different months are shown in Table 4 and Figure 9. It can be seen that the fitting index R-square of our model exceeded 0.99 in July, August and September, and the maximum reaches 0.993, which appears in August. The lowest and highest RMSE values of our model are 1.086 TECU and 1.267 TECU, which are lower than those of the comparison models. The minimum MAPE of a single month of our model is 0.042, and the maximum is 0.071, which are significantly lower than those of the comparison model. That is to say, in all selected regions, in all months, in all comparison indicators, our MA-LSTM mode outperforms other comparison models. From Figure 9 we also can see that the R-square of our model is high in July, August and September, which indicates that the predicted value has a good fit with the real value in these three months. In March, April and May, the R-square is slightly low, and the prediction performance of the model is slightly poor, but even at the worst time, the fitting degree between the predicted value and the real value still reaches 0.965.  
Figure 8: Comparison of (**a**) RMSE, (**b**) R-square, (**c**) MAPE values of different models in all regions.  
Figure 9: Comparison of (**a**) RMSE, (**b**) R-square, and (**c**) MAPE values for various models in different months.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Algorithm** & **Indicator** & **January** & **February** & **March** & **April** & **May** & **June** & **July** & **August** & **September** & **October** & **November** & **December** \\ \hline LSTM & & 4.150 & 4.357 & 3.915 & 3.964 & 3.848 & 4.072 & 4.132 & 4.168 & 4.222 & 3.950 & 4.321 & 4.479 \\ GRU & RMSE & 3.848 & 4.006 & 3.675 & 3.703 & 3.589 & 3.818 & 3.866 & 3.917 & 3.907 & 3.664 & 3.998 & 4.118 \\ Att-BEGRU & (TECU) & 1.533 & 1.666 & 1.552 & 1.522 & 1.522 & 1.431 & 1.625 & 1.534 & 1.568 & 1.613 & 1.581 & 1.645 & 1.664 \\ MA-LSTM & **1.202** & **1.115** & **1.184** & **1.122** & **1.086** & **1.206** & **1.145** & **1.195** & **1.202** & **1.150** & **1.154** & **1.267** \\ \hline LSTM & & 0.854 & 0.678 & 0.618 & 0.542 & 0.623 & 0.753 & 0.871 & 0.922 & 0.871 & 0.704 & 0.657 & 0.798 \\ GRU & R-square & 0.874 & 0.730 & 0.665 & 0.603 & 0.678 & 0.786 & 0.889 & 0.931 & 0.890 & 0.749 & 0.708 & 0.829 \\ Att-BEGRU & 0.983 & 0.959 & 0.944 & 0.937 & 0.954 & 0.965 & 0.984 & 0.989 & 0.998 & 0.959 & 0.957 & 0.977 \\ MA-LSTM & **0.989** & **0.981** & **0.967** & **0.965** & **0.973** & **0.981** & **0.991** & **0.993** & **0.991** & **0.978** & **0.979** & **0.986** \\ \hline LSTM & & 0.168 & 0.187 & 0.161 & 0.185 & 0.189 & 0.184 & 0.148 & 0.161 & 0.185 & 0.244 & 0.263 & 0.189 \\ GRU & MAPE & 0.158 & 0.176 & 0.156 & 0.178 & 0.177 & 0.177 & 0.141 & 0.152 & 0.171 & 0.231 & 0.248 & 0.177 \\ Att-BEGRU & 0.064 & 0.072 & 0.069 & 0.079 & 0.076 & 0.075 & 0.061 & 0.065 & 0.072 & 0.101 & 0.108 & 0.074 \\ MA-LSTM & **0.045** & **0.049** & **0.052** & **0.056** & **0.053** & **0.053** & **0.042** & **0.048** & **0.054** & **0.071** & **0.071** & **0.053** \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of prediction performance by month.