## 3 Results and Discussion
### Model Testing Using Real Fractures
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & \(\mathbf{R^{2}}\) & **MAPE** \\ \hline Xception & \(-17.738\) & \(6.599\%\) \\ DenseNet201 & \(-10.114\) & \(4.493\%\) \\ VGG16 & \(-22.038\) & \(7.516\%\) \\ CNN-1 & \(-43.365\) & \(7.948\%\) \\ CNN-2 & \(-24.718\) & \(6.553\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Model performance in estimating the Hurst exponent of shale oil reservoir fracture. Figure 18: Scatter plot of the predicted Hurst exponent versus the actual Hurst exponent using a shale oil reservoir fracture dataset: (**a**) Xception, (**b**) DenseNet201, (**c**) VGG16, (**d**) CNN-1, and (**e**) CNN-2 models. CNN-2 performed the best when predicting physical parameters from synthetic fractures. Its performance in predicting real rock fractures had a noticeable drop in accuracy. This highlights the difference between the synthetic data used during training and real rock fractures used during testing. The andesite fractures still closely resemble synthetic data, with their permeability and mean aperture prediction being quite accurate with CNN-2. While the models struggled with having reasonable accuracy on permeability (MAPE = 35.666%) and exhibited a drop in accuracy regarding the mean aperture (MAPE = 10.014%) on shale oil reservoir fractures, this could be due to shale oil reservoir fractures having greater complexity with varying apertures, which could not be captured using a two-dimensional composite image. Predictions for surface roughness were less accurate for both real rock fractures due to the difference in geometry roughness between synthetic fractures and real rock fractures. Synthetic data generated using the fBm method featured geometric structures with uniform apertures and similar roughness geometry on both surfaces, which does not closely approximate the complexity of fractures in actual \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **R2** & **MAPE** \\ \hline Xception & 0.727 & 9.782\% \\ DenseNet201 & 0.719 & 9.689\% \\ VGG16 & 0.748 & 9.580\% \\ CNN-1 & 0.721 & 9.846\% \\ CNN-2 & 0.708 & 10.014\% \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Model performance in estimating the mean aperture of shale oil reservoir fracture. Figure 19: Scatter plot of the predicted mean aperture versus the actual mean aperture using a shale oil reservoir fracture dataset: (**a**) Xception, (**b**) DenseNet201, (**c**) VGG16, (**d**) CNN-1, and (**e**) CNN-2 models. rocks. This shows the challenges that models face when trained using synthetic datasets due to the differences in their characteristics, such as geometry and roughness. The results also show that a pre-trained model has less accuracy, likely due to its generalisation capabilities being optimised for datasets other than fractures. Some pre-trained models, such as DenseNet201 and VGG16, outperformed CNN-2 in predicting real rock fracture parameters, suggesting that a simpler model like CNN-2 might struggle with the complexity difference between synthetic data and real rock fractures. Testing the models using real rock fractures demonstrates the significant potential of the CNN for estimating the physical parameters of fractures, such as permeability, surface roughness, and mean aperture, in three-dimensional models. By achieving high accuracy with synthetic datasets, the models, especially CNN-2, show promise for rapid and efficient analysis of fracture properties. ML-based approaches offer a cost-effective alternative by reducing reliance on repeated numerical simulations once models are trained, traditionally requiring resource-intensive methods like laboratory testing or numerical simulations. This scalability allows for large-scale evaluations of fracture datasets. While aperture estimation from binary fracture images can be performed using straightforward counting algorithms, ML-based approaches showcase the power of ML to streamline fracture characterizations by predicting all properties directly from the input data.