# A Model-Assisted Combined Machine Learning Method for Ionospheric TEC Prediction
## 3 Results and Discussion
Overall, the MAE, MRE, RMSE, and \(\rho\) of MMAAdapGA-BP-NN decreased by 26.58%, 29.07%, 36.60%, and 9.52% compared with BP-NN. Based on the above data, it can be seen that the optimization effect of MMAAdapGA on BP-NN is very obvious. Moreover, the optimization effect of MMAAdapGA on BP-NN in a high solar activity year (2015) is more obvious than that in a low solar activity year (2020). We record the operation results of BP-NN, GA-BP-NN and MMAAdapGA-BP-NN TEC prediction models, respectively. The results of each model are recorded 50 times, as shown in Figures 7 and 8. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Year** & **Performance** & **IRI-2020** & **SML-F10.7** & **SML-SSN** & **BP-NN** & **GA-BP-NN** & **MMAAdapGA-BP-NN** \\ \hline High Solar & MAE/TECU & 3.71 & 3.54 & 3.63 & 2.74 & 2.11 & 2.03 \\ Activity Year & MRE/\% & 34.00 & 31.33 & 31.56 & 20.14 & 16.75 & 14.53 \\ (2015) & RMSE/TECU & 5.95 & 5.34 & 5.35 & 3.99 & 3.51 & 2.84 \\  & \(\rho\) & 0.75 & 0.79 & 0.77 & 0.82 & 0.85 & 0.91 \\ \hline Low Solar & MAE/TECU & 1.92 & 1.51 & 1.56 & 0.41 & 0.34 & 0.28 \\ Activity Year & MRE/\% & 18.23 & 16.12 & 16.24 & 6.04 & 5.27 & 3.54 \\ (2020) & RMSE/TECU & 3.05 & 2.87 & 2.96 & 1.12 & 1.03 & 0.85 \\  & \(\rho\) & 0.78 & 0.81 & 0.79 & 0.82 & 0.87 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performances of each model in a high solar activity year (2015) and a low solar activity year (2020). It can be observed from Figures 7 and 8 that:  
1. MMAAdapGA-BP-NN results of 50 runs generally have smaller RMSE, larger \(\rho\), and better prediction accuracy. 2. In the year of high solar activity (2015), the average number of iterations converging for 50 running times of MMAAdapGA-BP-NN, GA-BP-NN, and BP-NN are 19.5, 32.7, and 40.3, respectively. In the year of low solar activity (2020), the average number of iterations converging for 50 running times of the three models are 15.0, 23.3, and 33.5, respectively. MMAAdapGA-BP-NN has fewer iterations and faster training speed. 3. In the year of high solar activity (2015), the standard deviations of iterations converging for 50 running times of MMAAdapGA-BP-NN, GA-BP-NN, and BP-NN are 3.71, 3.95, and 4.12. The standard deviations of RMSE of the three models are 1.46, 2.15, and 3.57. The standard deviations of \(\rho\) of the three models are 0.08, 0.14, and 0.34, respectively. In the year of low solar activity (2020), the standard deviations of iterations converging for 50 running times of the three models are 2.14, 2.34, and 5.02. The standard deviations of RMSE of the three models are 0.74, 1.03, and 1.46. The standard deviations of \(\rho\) of the three models are 0.06, 0.12, and 0.23, respectively. Compared with GA-BP-NN and BP-NN, MMAAdapGA-BP-NN has a lower standard deviation of performance indexes, and the training effect is more stable. Moreover, the three models are generally more stable in the low solar activity year (2020) than in the high solar activity year (2015). Figure 7: In the high solar activity year (2015), the scatter diagram and normal distribution diagram of the performance indicators of BP-NN, GA-BP-NN, and MMAAdapGA-BP-NN after running 50 times: (**a**) the scatter diagram of the performance indicators of BP-NN, GA-BP-NN, and MMAAdapGA-BP-NN running 50 times; (**b**) the normal distribution diagram of iteration times when the three models running 50 times; (**c**) the normal distribution diagram of RMSE when the three models running 50 times; and (**d**) the normal distribution diagram of \(\rho\) when the three models running 50 times. We calculated the mean value of the results of 50 runs of MMAapGA-BP-NN, GA-BP-NN, and BP-NN, which are used as the average prediction results of the three models. The curve graph of actual observed TEC data and the scatter graph of predicted data of each model in a high solar activity year (2015) are shown in Figure 9a. The curve graph of the prediction error of the corresponding models is shown in Figure 9b.