## 4 Results and Discussion
### Up-Scaling of the Healthy Examples  
Our simulations include four types of RBCs, of which three types have reduced elasticity and are considered sick. Although the ratio of healthy to sick RBCs is 1:3, this does not correspond to the observed ratio in reality [34]. Therefore, we used data augmentation to upscale the minority class and balance the class sizes. As described in Section 3, we used horizontal flip and rotation to add two new training examples for each original example. This augmentation, together with the original healthy examples, makes the healthy class three times larger.  
We train the best performing model from our previous experiments, a four-class classification NN with no additional information, which is then reduced to a two-class classification. We augmented the training dataset and the validation dataset to maintain consistency between the class distribution of the datasets. After training and validating the model on the dataset with the same distribution, we cross-validated the model on the dataset with a different class ratio.  
Table 7 provides a comparison of three models: the original model (O_4x1) and the best-performing model from previous experiments, along with two models trained on datasets with equal ratios of healthy and unhealthy RBCs. The first model uses unmodified class weights (A_3\(1\)1_1), resulting in equal weights for each class. The second model (AW_3\(1\)1_1), on the other hand, uses class weights proportional to the sizes of the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**NN Model** & **Accuracy** \\ \hline
4c\_heatmap & 87.83\% \\
4c\_values & 91.48\% \\
2c\_heatmap & 57.04\% \\
2c\_values & 67.33\% \\
2c\_heatmap & 59.13\% \\
2 cw\_values & 69.78\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: The validation accuracies were evaluated for six distinct classes of models using optimized hyperparameters. The names of these neural network (NN) models consist of two parts. The first part represents the number of classes used during training, while the second part indicates the type of physical information employed for the physics-informed neural network (PINN). The abbreviations “4c”, “2c”, and “2 cw” denote four classes, two classes, and two weighted classes, respectively. Additionally, “Heatmap” and “Values” signify the utilization of heatmap information and velocity vectors from the middle flow layer, respectively.  
classes. We observed that the second model outperforms the first model in terms of classification accuracy.  
The results indicate that the original dataset achieved the highest accuracy on the original dataset for all three models. The O_4x1 model achieved an accuracy of 93.54%, while the A_3\(1\)1_1 and AW_3\(1\)1 models achieved lower accuracies of 88.88% and 81.55%, respectively.  
When comparing the accuracies on the augmented dataset, it can be observed that the A_3\(1\)1_1 model performed slightly better, with an accuracy of 93.91%, compared to the 91.01% accuracy of the O_4x1 model. However, the AW_3\(1\)1_1 model achieved an accuracy of 92.21%, which was slightly lower than both the original dataset and the A_3\(1\)1_1 model.  
Based on these findings, it can be concluded that augmenting the dataset through upsampling had a mixed impact on the model performance. While the A_3\(1\)1_1 model showed a slight improvement, the addition of class weights in the AW_3\(1\)1_1 model did not yield significant improvements and even resulted in a slightly decreased accuracy compared to the original dataset.