## 3 Results
### Strain Map Prediction Accuracy  
This section evaluates the accuracy of mapping 2D cross-sectional images of arterial walls to their corresponding strain maps. Figure 7a,b showcased the actual (simulated via FEM) and predicted strain maps using U-Net and cGAN. Figure 7a displays a test data image, then compares the actual strain map (calculated using FEM) and the ones generated by U-Net and cGAN. U-Net outperforms cGAN in strain prediction, achieving an SSIM of 0.822 and a mean error percentage of 6.35, while cGAN achieves an SSIM of 0.803 and a mean error percentage of 5.34. Figure 7b compares strain map predictions made by the basic U-Net model and cGAN and the best U-Net and cGAN models obtained through ensemble techniques. The results for all models, including those utilizing ensemble methods, are presented in Table 4. The best ensemble model for U-Net is achieved by combining different U-Net architectures, as previously described. We employed one U-Net model with 8 layers and another with 10 layers (adding a layer with 32 channels at the beginning and end of the networks). This ensemble yields the best results for U-Net, with a mean SSIM of 0.830. For cGAN, we applied the same technique to the generator layers and then combined it with a basic cGAN. This ensemble of two architectures also results in the best cGAN performance (mean SSIM of 0.803). We then chose the best models and compared their predictions to those of the basic U-Net model and cGAN in Figure 7b. The ensemble technique for U-Net produces superior predictions in this case, with an SSIM of 0.833. Based on the numerical results we observed here and more, though cGAN and its ensemble version did not deliver the best numbers in terms of SSIM, they do have the best performance visually. In Table 4, we display the SSIM and MSE values for the U-Net and cGAN models, which were trained using pre-trained weights from U-Net and cGAN models based on von Mises stress data. It was observed that both models led to an increase in SSIM and a decrease in MSE. Additionally, Figure 8 compares the average SSIM and MSE values for stress and strain between the actual and predicted stress-strain maps across all 600 validation images, substantiating the high precision of our model's predictive capabilities. In Figure 8a, we compared the MSE of predicted von Mises stress maps among six networks: a simple U-Net, an ensemble method with various hyperparameters, an ensemble using two distinct U-Net architectures, a simple cGAN, an ensemble method with various hyperparameters in the cGAN generator model, an ensemble using two distinct cGAN generator architectures. The box plots reveal that employing an ensemble with two cGAN architectures results in a lower MSE than other models. Moreover, Figure 8b indicates that the SSIM of an ensemble cGAN with two generator architectures is superior. Figure 8c examines the MSE of eight strategies for predicting strain maps. A comparison of the U-Net and cGAN with a basic network, ensembles, and transfer learning reveals that an ensemble method with various hyperparameters in the cGAN generator model exhibits a narrower MSE range than other \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **\#of Models** & **Metrics** & **Min** & **Max** & **Mean** \\ \hline U-Net & \(1\) & MSE & 0.008 & 0.039 & 0.019 \\  & & SSIM & 0.773 & 0.902 & 0.842 \\ \hline cGAN & \(1\) & MSE & 0.008 & 0.036 & 0.017 \\  & & SSIM & 0.787 & 0.895 & 0.850 \\ \hline \multirow{3}{*}{Ensembling (U-Net)} & \multirow{3}{*}{2} & MSE & 0.008 & 0.038 & 0.018 \\  & & SSIM & 0.771 & 0.903 & 0.845 \\  & & MSE & 0.007 & 0.038 & 0.017 \\  & & SSIM & 0.778 & 0.906 & 0.854 \\ \hline \multirow{3}{*}{Ensembling (cGAN)} & \multirow{3}{*}{2} & MSE & 0.005 & 0.023 & 0.010 \\  & & SSIM & 0.821 & 0.909 & 0.884 \\ \cline{1-1}  & & MSE & 0.003 & 0.024 & 0.008 \\ \cline{1-1}  & & SSIM & 0.823 & 0.924 & 0.890 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Different approaches for predicting von Mises stress maps on the testing data. approaches.