## 5 Experiment and Analysis  
First, we use simulated data to visually test the quality of the GNN method. The experiment used Python version 3.8, PyTorch version 1.13, and EIDORS version 3.10. The simulated data include 200 training and 100 test samples, as shown in Figure 5. Each simulated model contains 1-4 ellipses with constant resistivity. The model defines these ellipses on the same circular grid with a radius of 140 mm. The circular grid consists of 32 electrodes, each with a width and height of 20 mm, placed at equal intervals. The excitation mode used in the experiment is the adjacent current mode of 2 mA. The data collected for this study come from two different systems: the 32-electrode ACT 3 system and the 16-electrode KIT 4 system [50]. The ACT 3 system utilized a triangular current mode with a maximum amplitude of 0.2 mA and a frequency of 28.8 kHz. The electrodes are uniformly distributed, with a width of 25 mm and a salt height of 16 mm, placed in grooves with a radius of 150 mm. The KIT 4 system, on the other hand, used neighboring current patterns with amplitudes of 3 mA and frequencies of 10 kHz. The circular tank utilized in this system had a radius of 140 mm, and the electrodes were about center, with a width of 25 mm. The tank contained two targets--a large resistor with a conductivity of 0.067 S/m and a small conductor with a conductivity of 0.305 S/m. We placed the target at a height of 45 mm in the salt bath. A chest-shaped slot with a circumference of 1020 mm and an electrode width of 20 mm was used. The reconstructed results of the simulated data are presented in Figure 5, while the evaluation index results can be found in Table 1.  
In this experiment, we use the finite element method to solve a direct EIT problem with approximately 5000 triangular elements. The raster data are on the left side of the Figure 6. In addition, we do not investigate the effect of mesh granularity on the accuracy of different \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Sample 1** & **Sample 2** & **Sample 3** \\ \hline MSE & 155.01 & 438.20 & 361.47 \\ PSNR & 26.23 & 21.71 & 22.55 \\ SSIM & 0.97 & 0.93 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation metrics for simulated data. Figure 5: Some simulation samples. reconstruction techniques. Before training the model, the resulting finite element mesh data must be converted to the graph data format required for neural convolutional graphs. Our work employs the control variable method to compare the results of multiple experiments. The selected parameters for the experiment include \(\lambda_{LM}=0.1\) and a convolutional network with a depth of 2 to train the model. The implementation in PyTorch utilizes a mini-batch of 512 samples. It combines the optimization methods of [PERSON] [51] and limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) [52] to perform minimization training of the iterative loss function for each block. The learning rate is 0.002. Training ends if the validation loss for 100 epochs does not decrease, and the minimum validation loss for the trainable parameters remains unchanged. We simulated static EIT without noise interference. The simulation results were obtained by performing computer numerical calculations, using theoretical voltage data with minimal error. However, noise inevitably influences measurement data, including power frequency interference in practical applications such EIT and other fields. Despite efforts to reduce these interferences through hardware circuits, eliminating them remains challenging. This experiment examines the anti-noise performance of the Newton-based GCN by adding Gaussian noise to the simulated data. Specifically, Gaussian noise with signal-to-noise ratios of 0 dB, 39 dB, 45 dB, and 51 dB is added when calculating the voltage data on adjacent electrodes. These four values cover a wide range of SNR conditions, ranging from very low (0 dB) to very high (51 dB). They can be used to evaluate the performance of the system under different SNR conditions [53].