# Comparison of Deep Transfer Learning Models for the Quantification of Photoelastic Images
## 3 Results and Discussion
### Results of Transfer Learning Models
\[MAE=\frac{1}{n}{\sum_{i=1}^{n}}{|y_{i}-\hat{y_{i}}|} \tag{13}\]  
\[RMSE=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}}(y_{i}-\hat{y_{i}})^{2}} \tag{14}\]  
As mentioned earlier, a higher coefficient of determination indicates smaller MAE and RMSE, reflecting a smaller deviation in predictions. VGG19's MAE was 14.127, and its RMSE was 18.834, making it the best-performing model among those tested. Based on the performance metrics, the models can be ranked in the following order: VGG19, VGG16, ResNet152V2, DenseNet201, InceptionV3, and EfficientNetB7. The R\({}^{2}\), MAE, and RMSE calculated for the training/calibration dataset were evaluated in the same order as those calculated for the test/validation dataset. For the VGG model, which was evaluated as the most superior in performance, both the MAE and the RMSE were calculated to be over 10 N. This makes it challenging to accurately predict the load level for photoelastic images that change in increments of 10 N. This inherent limitation can be attributed to the fact that only photoelastic images with load increments of 100 N were used for training. Therefore, to obtain a more precise quantitative evaluation model for photoelastic responses, training data based on more refined load increments must be secured. The VGG model, which was the first transfer learning model introduced in this study, has the simplest network architecture. One can examine the superior performance of the VGG model compared with more recently introduced transfer learning models with more complex network structures from various perspectives. The simplicity of the VGG model's architecture, composed of 3 \(\times\) 3 convolutional filters and pooling layers, can sometimes result in a more robust and easier-to-train model on specific datasets. Furthermore, when the dataset to be trained on shares similarities with the pre-trained data, using a pre-trained model can greatly enhance feature extraction in the case of transfer learning. Therefore, the performance of deep learning models heavily depends on the characteristics of the dataset, and in this particular study, the photoelastic response images used were suitable for training with the VGG model, which is why it exhibited the best performance. [PERSON] et al. [46] proposed the StressNet model, a convolutional-based autoencoder architecture inspired by the VGG16 model, for analyzing photoelastic images. Several limitations need to be acknowledged in this study. First, the suggested transfer learning model lets you measure the photoelastic response to find out how much force is pressing down on the particles as a whole, but it does not tell you anything about the direction and size of each stress component. Researchers [47; 48; 49] have proposed stress separation techniques in the literature to obtain individual stress components. Similarly, for the transfer learning model, considering individual stress components based on the training data is worth exploring. Secondly, this study limited the number of training \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Training/Calibration Data**} & \multicolumn{3}{c}{**Test/Validation Data**} \\ \cline{2-7}  & \(\mathbf{R^{2}}\) & **MAE** & **RMSE** & **R2** & **MAE** & **RMSE** \\  & & **(N)** & **(N)** & **(N)** & **(N)** \\ \hline VGG-16 & 0.986 & 15.176 & 20.458 & 0.984 & 15.792 & 21.520 \\ VGG-19 & 0.986 & 14.738 & 19.844 & 0.988 & 14.127 & 18.834 \\ InceptionV3 & 0.938 & 35.263 & 42.501 & 0.932 & 36.506 & 44.321 \\ ResNet152V2 & 0.958 & 25.804 & 35.278 & 0.957 & 25.685 & 34.412 \\ DenseNet201 & 0.946 & 31.899 & 39.586 & 0.946 & 31.920 & 39.212 \\ EfficientNetB7 & 0.896 & 44.375 & 54.967 & 0.886 & 48.624 & 58.081 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results of performance metrics for transfer learning models. iterations for the transfer learning model to focus on the accuracy of results obtained within a short time. As mentioned in Section 2.4, models like VGG and ResNet demand significant computational resources.