## 3 Results
### Comparison with COSMIC-2 Satellite Observations  
To validate the model's generalization capability, preprocessed COSMIC-2 radio occultation data--including spatiotemporal coordinates (longitude, latitude, altitude, UTC time)--along with contemporaneous TEC, AE, SYM-H, and F10.7 parameters were fed into the decomposition model to obtain predicted electron densities. For comparative analysis, IRI-2020 outputs were generated under identical input conditions, with COSMIC-2 observations serving as the benchmark for dual-model performance evaluation.  
Due to significant measurement noise from observational instruments, a moving average filter with a window size of 180 was applied to all three Ne datasets (predicted/IRI-2020/observed), effectively suppressing small-scale ionospheric irregularities and mitigating outlier impacts. Figure 6 displays comparative results during a representative time window (19:00-22:00 UTC on 2019 DOY 355).  
The metrics applied in this section are defined as follows:  
\[absolute\;error=|y-\hat{y}| \tag{4}\]  
\[MAE=\frac{1}{n}\underset{i=1}{\sum}\underset{i=1}{\sum}|y_{i}-\hat{y_{i}}| \tag{5}\]  
\[MSE=\frac{1}{n}\underset{i=1}{\sum}\underset{i=1}{\sum}(y_{i}-\hat{y_{i}})^{2} \tag{6}\]  
In these equations,  
* Equation (4) represents the absolute error for individual data points.
* Equations (5) and (6) correspond to the mean absolute error (MAE) and mean squared error (MSE), respectively.
* \(y_{i}\): Predicted values from either the decomposition model or IRI-2020.
* \(\hat{y_{i}}\): Observed values from COSMIC-2.  
Detailed metric values are provided in Table 2.  
Figure 5: Model performance on the 2019 test set. (**a**) Vertical profiles of R\({}^{2}\) (coefficient of determination, red) and RMSE (root mean square error, yellow) scores, evaluating the agreement between the predicted and ground truth ln(Ne) as a function of altitude (60–800 km). Ionospheric regions (D, E, F) are indicated. (**b**) Comparison of global ln(Ne) maps (units: ln(m\({}^{-3}\))). Side-by-side plots compare the ground truth (“Reconstructed”) electron density patterns with the model’s predictions (“Predicted”) at selected altitudes (300, 500, 700 km) and specific times (2019-03-21 12:00 UT and 2019-09-23 20:00 UT).  
Long-term statistical metrics for 2019 (encompassing all COSMIC-2 observational data from that year) are presented in Figure 7. Each point along the satellite orbital trajectory represents an individual observation event, with color coding reflecting the magnitude of the absolute error values.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Statistics and Metrics** & **COSMIC-2** & **Decomposition Model** & **IRI-2020** \\ \hline Mean & 11.3987 & 11.2849 & 11.4355 \\ Std & 0.9806 & 1.1236 & 1.1418 \\ Max & 13.3330 & 13.4746 & 13.6078 \\ Min & 9.0494 & 9.2830 & 8.2590 \\ MSE & - & 0.1389 & 0.3202 \\ RMSE & - & 0.3726 & 0.5659 \\ MAE & - & 0.3037 & 0.4269 \\ Std of Abs Error & - & 0.2159 & 0.3714 \\ R\({}^{2}\) & - & 0.8574 & 0.6675 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Metrics of Ne among COSMIC-2, decomposition model, and IRI-2020.  
Figure 6: (**a**) A line graph showing the comparison between the predicted electron density by the decomposition model, the predicted electron density by IRI-2020 and the observed data from 19:00 to 22:00 on the 355 th day of 2019. Lines represent Ne\({}^{\text{pred}}\) (blue), Ne\({}^{\text{abs}}\) (orange), and Ne\({}^{\text{IRI}}\) (green). (**b**) Satellite orbit display of the same time period, with colors corresponding to the magnitude of the absolute error. The corresponding mean absolute error (MAE = 0.3037 ln(m\({}^{-3}\))) is shown.