## 4 Analysis of Prediction Results
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Model** & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**R2**} & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**MAPE**} \\ \hline
**Dataset** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline ADF-GCN & **0.487** & **0.506** & **0.951** & **0.948** & **0.347** & **0.0.378** & **6.389\%** & **6.733\%** \\ AD-GCN & 0.720 & 0.746 & 0.894 & 0.887 & 0.575 & 0.586 & 9.930\% & 10.162\% \\ AF-GCN & 0.866 & 0.916 & 0.845 & 0.830 & 0.678 & 0.704 & 12.080\% & 12.656\% \\ DF-GCN & 0.608 & 0.638 & 0.924 & 0.917 & 0.475 & 0.487 & 8.365\% & 8.670\% \\ D-GCN & 0.786 & 0.851 & 0.872 & 0.854 & 0.608 & 0.642 & 10.743\% & 11.596\% \\ F-GCN & 0.975 & 0.998 & 0.808 & 0.794 & 0.728 & 0.764 & 11.623\% & 11.214\% \\ BiGRU & 1.049 & 1.061 & 0.777 & 0.767 & 0.783 & 0.794 & 13.567\% & 13.619\% \\ BiLSTM & 1.155 & 1.156 & 0.730 & 0.723 & 0.904 & 0.913 & 15.293\% & 15.327\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of the four evaluation indicators of the deep learning models (The bold and underlined values indicate the best results). had better performance. Compared to the adjacency matrix predefined using cosine similarity and covariance, the attention-adaptive adjacency matrix was not influenced by the threshold \(\phi\) for cosine similarity or covariance. This mechanism enabled the predictive model to dynamically acquire the graph structure throughout the training process, which significantly enhanced both the accuracy and robustness of the predictions. The attention-adaptive matrix is sparser than the pre-constructed adjacency matrix, indicating that the attention mechanism concentrated solely on the most pertinent features for forecasting. The attention-adaptive matrix is asymmetric, enabling unbalanced aggregation between adjacent nodes in the deep sequence and feature-related graph. This enabled each node to autonomously collect the most critical logging data components and discard the noise, thereby enhancing accuracy. The AD-GCN model (\(R^{2}=0.8937\)) and D-GCN model (\(R^{2}=0.8723\)), which only considered the deep-sequence-related graph, produced more accurate predictions on the training set than the AF-GCN (\(R^{2}=0.8448\)) model and F-GCN (\(R^{2}=0.8076\)) model, which only considered the feature-related graph, and had higher overall prediction accuracy. Figure 4: Scatter plot of the true and predicted values of the deep learning models on the training set. This indicates that the model captured the non-Euclidean features in the logging data, thereby extracting the inherent spatiotemporal relationships in the formation data, which is more critical for improving the model's accuracy. Therefore, we selected two commonly used models for processing sequences, BiGRU (\(R^{2}\) = 0.7774) and BiLSTM (\(R^{2}\) = 0.7299). The experiments indicate that employing undirected graphs to represent data relationships allows for the efficient detection and integration of closely related logging data. GCNs excel at handling undirected graphs by incorporating their topological structure into the analysis. GCNs use multiple repeated spectral graph convolutional layers to predict logging porosity. Models based on GCNs can extract inherent spatiotemporal relationships when processing formation data, which may be more beneficial than neural network models specifically designed to handle sequences, to better capture complex geological structures for local information processing. Figure 6 shows a scatter plot of the deep learning model's relative error. A central line at 0% relative error was drawn. The proximity of the scatter points to the central line correlates positively with the model's performance. Looking at the distribution of the scatter, the concentration is as follows: ADF-GCN (RMSE = 0.4873) > DF-GCN (RMSE = 0.6080) > AD-GCN (RMSE = 0.7169) > D-GCN (RMSE = 0.7858) > AF-GCN  
Figure 5: Scatter plot of the true and predicted values of the deep learning models on the testing set.