## 4 Results and Discussion
### Adding Physical Information  
In order to enhance the performance of the network, we added information about the underlying physics--specifically, about the velocity of the fluid flowing in the channel. Our hypothesis was that by adding the physical information, the NN would be able to learn to classify the RBCs better than without it. First, using ESPReSso, we calculated the velocities of each point of the fluid (which is represented as a mesh; more information is available in [33]) in the empty channel--the channel with no RBCs in it. We obtained a 3D data of velocities, since the channel is a 3D object. Then, we took a layer \(H\times W\times\lfloor D/2\rfloor\) that corresponds to the velocities in the middle of the channel along the depth axis. This information can be used in two ways: we can either use it as it is, meaning 3D data with dimensions \(W\times H\times 3\), where 3 represents the \(x\), \(y\), and \(z\) components of a velocity vector, or we can create a heatmap where the colors represent the velocity of the flow. In both options, we added the physical information by creating a new branch of our NN that has the physical information about the flow as input. This information is passed through a Rescale layer, three 2D convolution layers with a number of filters 32, 16, 8, followed by a max pooling layer, a flattening layer, and a dense layer with 1024 hidden units. Then, it is concatenated with the penultimate output of the main branch of our NN, which is passed to the last dense layer. Generally, it is not effective to add the same information to each training example for a NN. The reason for this is that NNs learn patterns and relationships in the data through the variations and differences between the examples. When all examples contain the same information, the network is unable to distinguish between them and may not learn the relevant patterns that are necessary for accurate predictions. However, there may be some cases where adding the same information to each training example can be helpful. For example, if the added information provides some contextual or background information that is relevant to all examples, it may help the network learn more effectively. In general, it is important to carefully consider the information that is added to each training example and how it may affect the network's ability to learn and generalize. We trained both versions of PINNs using the optimized hyperparameters described in Table 5, with the best performing model being EfficientNet v2 B0 with the Adam optimizer. The final results are presented in Table 6.  
Figure 6: The confusion matrix represents the classification results of the validation set, which consists of samples belonging to 2 classes. The classification was performed using the EfficientNet v2 B0 model, which was optimized with the Adam optimization algorithm. The classes of healthy and sick are represented by the labels 0 and 1, respectively. The obtained results highlight several important observations regarding the performance of different classification approaches. Firstly, when comparing the two-class classification (whether weighted or unweighted) to the four-class classification converted to two-class classification, it is evident that the latter achieves significantly better results. This suggests that the additional information present in the four-class classification helps to improve the overall accuracy of the model. Furthermore, the inclusion of physics-related information in the form of a heatmap appears to be less effective than the use of velocity vectors as input. This implies that the velocity vectors carry more meaningful and discriminative information for accurate classification. The use of velocity vectors as input likely allows for the model to capture dynamic patterns and better understand the motion characteristics of the analyzed data. However, it is interesting to note that even though velocity vector information is incorporated, it does not lead to a substantial improvement in the final accuracy of the network.