## 4 Engineering Example
### Results and Analysis
#### 4.3.2 Comparative Analysis of the Performance of Different Prediction Models  
This section compares the performance difference between adaptive MTGNN and other baseline models under different prediction steps based on determining the optimal input features. Since all models are for multi-node predictions, the value of the evaluation index is the average of the prediction errors of all nodes. The comparison of prediction accuracy of the four models under the three evaluation indices is shown in Table 3, and the comparison results of the error improvement percentage of the adaptive MTGNN compared to other models under three evaluation indices are shown in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Input Features** & **MAE (\(\times\)10\({}^{-3}\))** & **RMSE (\(\times\)10\({}^{-3}\))** & **MAPE (\%)** \\ \hline CR & 1.948 & 2.512 & 14.225 \\ CR, PR, DR, CC, OCP, RT & 1.507 & 2.051 & 9.690 \\ CR, PR, DR, CC, OCP, RT, PH, Cl- & 1.801 & 2.169 & 11.216 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of prediction results under different combinations of input features. Figure 10: Comparison of prediction results under different combinations of input features. The results show that for 1-step prediction, the MAE of adaptive MTGNN decreases by 6.59%, 13.44%, and 18.30% compared with non-adaptive MTGNN, GRU, and LSTM, respectively. For 3-step prediction, the MAE decreases by 12.12%, 20.01%, and 26.90%, respectively. For 6-step prediction, the MAE decreases by 16.82%, 26.70%, and 32.16%, respectively. In addition, the improvement in RMSE error ranges from 4.38% to 27.95%, and in the MAPE error, it ranges from 5.01% to 22.22% over the prediction range of steps 1-6. It can be seen that the adaptive MTGNN significantly outperforms the other models on all three evaluation indices. The primary reason that adaptive MTGNN significantly improves corrosion rate prediction results is that the nature of the corrosion data is better suited to the MTGNN modeling assumptions regarding temporal and spatial dependence. When the concrete in an area is subjected to severe corrosion, this corrosion state may gradually affect the surrounding areas with the flow of sewage and the diffusion of corrosive substances. MTGNN leverages graph-based information propagation to effectively integrate information from different nodes, fully extracting spatial features to enhance prediction accuracy for each node. GRU and LSTM lack a specialized structural design for dealing with spatial and temporal series data, and it is difficult for these methods to effectively model multivariate time series data when spatial information is implied between prediction targets. Figure 11 shows the difference in prediction accuracy between the adaptive MTGNN and other models more intuitively in the form of radar charts. In the radar charts, the region corresponding to the adaptive MTGNN under each evaluation index is closer to the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Evaluation Index** & **Prediction Model** & \multicolumn{4}{c}{**Prediction Step Size**} \\  & **1** & **3** & **6** \\ \hline \multirow{3}{*}{MAE (\(\times 10^{-3}\))} & Non-adaptive MTGNN & 6.59 & 12.12 & 16.82 \\  & GRU & 13.44 & 20.01 & 26.70 \\  & LSTM & 18.30 & 26.90 & 32.16 \\ \hline \multirow{3}{*}{RMSE (\(\times 10^{-3}\))} & Non-adaptive MTGNN & 4.38 & 9.70 & 16.46 \\  & GRU & 10.81 & 14.10 & 23.70 \\  & LSTM & 14.55 & 20.44 & 27.95 \\ \hline \multirow{3}{*}{MAPE (\%)} & Non-adaptive MTGNN & 5.01 & 7.39 & 12.15 \\  & GRU & 8.13 & 11.22 & 18.01 \\ \cline{1-1}  & LSTM & 13.12 & 17.90 & 22.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the percentage of error improvement (%) under different evaluation indices.