# A Model-Assisted Combined Machine Learning Method for Ionospheric TEC Prediction
## 3 Results and Discussion  
In this paper, the MMAAdapGA-BP-NN prediction model is proposed. At the same time, a single BP-NN prediction model (prediction of TEC based on BP neural network) and GA-BP-NN prediction model (prediction of TEC based on neural network optimized by a single mutation and single crossover genetic algorithm) are proposed. As can be seen from Figure 3, 2015 is a year of high solar activity, and 2020 is a year of low solar activity. Data from 2015 and 2020 are taken as test sets, respectively, and other data are taken as training sets to train the model. In this paper, the above three models are all run 50 times, and the running results are analyzed. The performance of the above three models, the IRI model and the SML-based model, is compared and analyzed. The error between each predicted TEC data and the actual observed TEC data \(err_{i}\) is defined in the following formula:  
\[err_{i}=\text{TEC}_{i}^{f}-\text{TEC}_{i}^{r}. \tag{13}\]  
The performance indicators are as follows [41]:  
* Mean Absolute Error (MAE) \[\text{MAE}=\frac{1}{N}\sum_{i=1}^{N}\left|\text{TEC}_{i}^{f}-\text{TEC}_{i}^{r} \right|,\] (14)
* Mean Relative Error (MRE) \[\text{MRE}=\frac{1}{N}\sum_{i=1}^{N}\left|\frac{\text{TEC}_{i}^{f}-\text{TEC} _{i}^{r}}{\text{TEC}_{i}^{r}}\right|\times 100\%,\] (15)
* Root Mean Square Error (RMSE) \[\text{RMSE}=\sqrt{\frac{1}{N}\times\sum_{i=1}^{N}\left(\text{TEC}_{i}^{f}- \text{TEC}_{i}^{r}\right)^{2}},\] (16)
* Correlation Coefficient (\(\rho\)) \[\rho=\frac{\sum\limits_{i=1}^{N}\left(\text{TEC}_{i}^{f}-\overline{\text{ TEC}^{f}}\right)(\text{TEC}_{i}^{r}-\overline{\text{TEC}^{r}})}{\sqrt{\sum \limits_{i=1}^{N}\left(\text{TEC}_{i}^{f}-\overline{\text{TEC}^{f}}\right)^{2} }\sqrt{\sum\limits_{i=1}^{N}\left(\text{TEC}_{i}^{r}-\overline{\text{TEC}^{ r}}\right)^{2}}}.\] (17)  
In Equations (13)-(17), \(\text{TEC}_{i}^{f}\) is the predicted TEC data, and \(\text{TEC}_{i}^{r}\) is the actual observed TEC data. \(\overline{\text{TEC}^{f}}\) is the average value of predicted TEC data, and \(\overline{\text{TEC}^{r}}\) is the average value of actual observed TEC data. The comparison results are shown in Table 1, where SML-F10.7 is the SML-based model for prediction based on the actual observed data of F10.7, and SML-SSN is the SML-based model for prediction based on the actual observed data of SSN. By observing the performance indicators of each model in Table 1, it can be found that:  
1. According to the high solar activity year (2015), low solar activity year (2020) and the mean values of the two years of performance indicators, the IRI model has the largest prediction error; the SML-based model has a slightly better prediction effect than the IRI model; MMAAdapGA-BP-NN has the smallest prediction error and the best effect among all models. 2. The prediction results of all models are generally slightly better in a low solar activity year (2020) than in a high solar activity year (2015). The MAE, MRE, RMSE, and \(\rho\) of MMAAdapGA-BP-NN decreased by 86.21%, 53.91%, 70.07%, and 3.30% in a low solar activity year (2020) compared with high solar activity year (2015). 3. In the year of high solar activity (2015), the MAE, MRE, RMSE, and \(\rho\) of MMAAdapGA-BP-NN decreased by 45.28%, 57.26%, 52.27%, and 21.33% compared with the IRI model. In the year of low solar activity (2020), the MAE, MRE, RMSE, and \(\rho\) of MMAAdapGA-BP-NN decreased by 85.42%, 80.58%, 72.13%, and 20.51% compared with the IRI model. On the whole, the MAE, MRE, RMSE, and \(\rho\) of MMAAdapGA-BP-NN decrease by 58.87%, 51.84%, 58.01%, and 21.05% compared with the IRI model. Based on the above data, it is concluded that MMAAdapGA-BP-NN is reliable for a long period of time. 4. In the year of high solar activity (2015), the MAE, MRE, RMSE, and \(\rho\) of MMAAdapGA-BP-NN decreased by 25.91%, 27.86%, 28.82%, and 10.98% compared with BP-NN. In the year of low solar activity (2020), the MAE, MRE, RMSE, and \(\rho\) of MMAAdapGA-BP-NN decreased by 31.71%, 41.39%, 24.11%, and 14.63% compared with BP-NN.