## 3 Results and Discussion
### Model Testing Using Real Fractures  
The models' performance in estimating fractures in actual rocks was evaluated to determine their ability to generalise, which refers to the their capacity to learn relationships from the training data and apply them effectively to previously unseen data [42]. First, permeability values from the andesite fracture data were predicted by each model. Their performance is shown in Table 8 and Figure 14. The best-performing model was CNN-2 (R\({}^{2}\) value of 0.995 and MAPE of 12.606%), followed by CNN-1, VGG16 and DenseNet201, with Xception having the largest error. The performance of the models in estimating surface roughness is shown in Table 9 and Figure 15, indicating that model predictions were not as accurate for andesite fractures. The models tended to predict higher values than the actual values, with DenseNet201 having the smallest error compared to the other models. The second-best performing model was Xception, followed by CNN-1 and VGG16. CNN-2 had the largest error. The models performed poorly in capturing the variations in surface roughness from the andesite data, which led to a relatively low R\({}^{2}\) value. This can be attributed to the small range of values in the andesite fracture compared to the broader range in the training dataset. Despite this, the models performed reasonably well when evaluated using MAPE, with DenseNet201 having an MAPE of 12.004%. The simpler models, CNN-1 and CNN-2, struggled to generalise the surface roughness of the synthetic data compared to real data, possibly due to the difference in the roughness geometry of the synthetic fracture compared to the real rock fracture. Figure 14: Scatter plot of the predicted permeability versus its actual permeability from the andesite fracture dataset: (**a**) Xception, (**b**) DenseNet201, (**c**) VGG16, (**d**) CNN-1, and (**e**) CNN-2 models. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & \(\mathbf{R^{2}}\) & **MAPE** \\ \hline Xception & \(-42.384\) & \(12.887\%\) \\ DenseNet201 & \(-37.615\) & \(12.004\%\) \\ VGG16 & \(-51.271\) & \(13.996\%\) \\ CNN-1 & \(-45.253\) & \(13.233\%\) \\ CNN-2 & \(-53.800\) & \(14.279\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Model performance in estimating the surface roughness of andesite fracture. The next parameter evaluated was the mean aperture of the andesite fractures. The performance of the models in estimating mean aperture values is depicted in Table 10 and Figure 16, showing that the CNN-2 model has the smallest error compared to other models with an R\({}^{2}\) value of 0.977 and MAPE of 4.583%. The CNN-2 model was the most accurate, followed by VGG16, Xception and CNN-1, with DenseNet201 having the largest error. Next, permeability of the shale oil reservoir fracture dataset was predicted by each model, and their performance is shown in Table 11 and Figure 17. The Xception model achieved the highest R\({}^{2}\) value (0.473) but a high MAPE of 51.414 %, indicating moderate consistency but large absolute errors. VGG16 followed with an R\({}^{2}\) value of 0.393 and a lower MAPE of 38.881%, demonstrating a good balance of predictive accuracy and reliability. CNN-2 showed the lowest MAPE (35.666%), reflecting a minimal absolute error, but its R \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **R\({}^{2}\)** & **MAPE** \\ \hline Xception & 0.958 & 4.879\% \\ DenseNet201 & 0.963 & 5.029\% \\ VGG16 & 0.975 & 4.718\% \\ CNN-1 & 0.971 & 4.973\% \\ CNN-2 & 0.977 & 4.583\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Model performance in estimating the mean aperture of andesite fracture. Figure 15: Scatter plot of the predicted surface roughness versus the actual surface roughness using an andesite fracture dataset: (**a**) Xception, (**b**) DenseNet201, (**c**) VGG16, (**d**) CNN-1, and (**e**) CNN-2 models. value (0.258) indicates a weaker correlation with true values.