# Ionospheric TEC Prediction in China Based on the Multiple-Attention LSTM Model
## 3 Experimental Results and Discussion
### Prediction Comparison of Different Stations  
This paper first discusses the situation of TEC prediction at the second hour. The MA-LSTM model proposed in this paper is compared with the classical time series models LSTM, GRU and Att-BiGRU (in terms of structure, the LSTM is a three-layer gate structure, the GRU is a two-layer gate structure, and the Att-BiGRU is a two-layer gate structure in both directions). In the selected eight regions, samples were made according to the method described in Section 2.2. A total of 90% of the samples were used for training models and 10% for testing. The training data are 42715 TEC observations from 0:00 on 1 January 2002 to 18:00 on 30 December 2010, and the test data are 4747 TEC observations from 20:00 on 30 December 2010 to 24:00 on 31 December 2011. The predictive performance of each model is shown in Figure 8. The specific values are shown in Table 3.  
As can be seen from Figure 8 and Table 3, the performance of the models with attention mechanism (MA-LSTM and Att-BiGRU) is significantly better than those of the models without attention mechanism (LSTM and GRU). The multiple-attention mechanism model proposed in this paper (MA-LSTM) is superior to the single attention mechanism model (Att-BiGRU). In the eight selected regions, the average RMSE of the MA-LSTM model proposed in this paper is 1.171 TECU, which is reduced by 253.29, 228.44 and 35.01%,  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Optimal Value** \\ \hline input\_dim & 13 \\ optimizer & Adagrad \\ loss & “RMSE” and “R-Square” \\ activation & “Relu”and “Softmax” \\ activity\_regularizer & L1(0.01) \\ learning rate & 0.01 \\ batch\_size & 64 \\ num of hidden units & 64 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Optimal parameters of the MA-LSTM model gained by grid search.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Algorithm** & **Indicator** & **Mean** & **Beijing** & **Guangzhou** & **Harbin** & **Tibet** & **Yushu** & **Ziyang** & **Hangzhou** & **Heeze** \\ \hline LSTM & & 4.137 & 2.962 & 4.683 & 6.834 & 2.745 & 3.880 & 4.561 & 4.225 & 3.208 \\ GRU & RMSE & 3.846 & 3.221 & 4.613 & 6.676 & 2.683 & 3.031 & 4.392 & 3.487 & 2.664 \\ Att-BiGRU & (TECU) & 1.581 & 0.801 & 1.867 & 4.244 & 0.650 & 0.957 & 1.354 & 1.445 & 1.331 \\ MA-LSTM & & **1.171** & **0.718** & **1.550** & **3.377** & **0.602** & **0.934** & **1.283** & **0.543** & **0.358** \\ \hline LSTM & & 0.857 & 0.860 & 0.856 & 0.874 & 0.877 & 0.831 & 0.850 & 0.850 & 0.855 \\ GRU & R-square & 0.874 & 0.839 & 0.860 & 0.880 & 0.880 & 0.890 & 0.859 & 0.893 & 0.895 \\ Att-BiGRU & 0.979 & 0.988 & 0.974 & 0.953 & 0.992 & 0.987 & 0.985 & 0.980 & 0.972 \\ MA-LSTM & & **0.988** & **0.991** & **0.982** & **0.970** & **0.993** & **0.988** & **0.986** & **0.997** & **0.998** \\ \hline LSTM & & 0.188 & 0.153 & 0.217 & 0.268 & 0.149 & 0.183 & 0.205 & 0.184 & 0.150 \\ GRU & MAPE & 0.179 & 0.166 & 0.214 & 0.267 & 0.153 & 0.143 & 0.200 & 0.154 & 0.135 \\ Att-BiGRU & 0.100 & 0.139 & 0.191 & 0.166 & 0.047 & 0.051 & 0.065 & 0.069 & 0.072 \\ MA-LSTM & & **0.054** & **0.037** & **0.075** & **0.136** & **0.034** & **0.047** & **0.061** & **0.024** & **0.018** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of prediction performance of different models.  
respectively, compared with LSTM, GRU and Att-BiGRU. The average R-square is 0.988, increased by 15.29, 13.04 and 0.01%, respectively. The average MAPE of our model is 0.054, which is increased by 248.15, 231.48 and 85.19%, respectively.