## 3D Multi-layer Heatmap of Electron Density
### Deep Learning MLP Methodology  
This study developed a deep neural network based on a Multilayer Perceptron (MLP) architecture to achieve nonlinear mapping from macroscale TEC to vertically layered electron density (60-800 km) through the integration of IGS-TEC data, geomagnetic-solar activity parameters, and essential spatiotemporal inputs. Figure 4 illustrates the workflow of the proposed model.  
The model inputs comprise nine dimensional features, including hour of the day (integer), latitude (in radians), sine and cosine of longitude (radian units), altitude, AE, SYM-H, and F10.7. Longitude is transformed into trigonometric representations (sine and cosine encoding) to better capture the periodicity of longitude. The output label is electron density in logarithmic units (In(e/m\({}^{3}\))), which effectively compresses the target variable's dynamic range (spanning multiple orders of magnitude) to mitigate training instability and gradient-vanishing issues. Detailed input-output specifications are provided in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Feature**} & \multicolumn{3}{c}{**Label**} \\ \hline
**Channel Name** & **Unit** & **Channel Name** & **Unit** \\ \hline TEC & TECU & Ne & ln(m\({}^{-3}\)) \\ Latitude & rad & - & - \\ sin(Longitude) & - & - & - \\ cos(Longitude) & - & - & - \\ Altitude & km & - & - \\ AE & nT & - & - \\ SYM-H & nT & - & - \\ F10.7 & SFU & - & - \\ Hour & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of input and output data of decomposition model. The table summarizes the nine input parameters (name and unit) and the single output prediction target (ln(Ne) in ln(m\({}^{-3}\))).  
Figure 3: Histogram and kernel density estimation (KDE) of COSMIC-2 satellite-derived electron density profile altitudes for the period DOY 274–365 in 2019. The histogram illustrates the frequency distribution of valid altitude samples after data cleaning, ranging from 60.0 km to 727.55 km. A KDE curve (red) is overlaid to reveal the continuous density trend, with the mean altitude marked at 416.9 km (\(\sigma\) = 171.10). The distribution reflects COSMIC-2’s high coverage in the F-region ionosphere, supporting its suitability as a benchmark dataset for evaluating the model-reconstructed electron density profiles.  
The network comprises three fully connected hidden layers with 128, 64, and 32 neurons sequentially, each followed by a ReLU (Rectified Linear Unit) activation function to introduce nonlinear expressiveness:  
\[ReLU(x)=\max(0,x) \tag{1}\]  
The model employs mean squared error (MSE) as the loss function and the Adam optimizer with an initial learning rate of 0.001. The model was trained for 25 epochs using a batch size of 4,194,304. A 90-10% split was applied to each year of the training data (2011-2018) to construct training and validation subsets, with a fixed seed of 42 to ensure reproducibility. Input features were preserved in their physically meaningful forms; specifically, longitude was transformed into sine and cosine components to reflect its periodic nature. All other features were used directly in their native units without additional normalization. The logarithmic transformation of the electron density output mitigates dynamic range issues and stabilizes training.  
This study utilized nine years of IGS-TEC data (2011-2019), with 2019 data reserved as the test set and the remaining years allocated to training. During preprocessing, the three physical indices (AE, SYM-H, F10.7) were temporally aligned with global TEC data at hourly resolution through replication-based expansion. The TEC decomposition model was obtained after 25 training epochs.