## 2 Methodical Approach
### CNN Architecture  
After explaining the classification procedure and the dataset, this chapter will focus on applied CNNs. A total of four architectures were investigated: Vgg19, ResNet, Inception-V3, and MobileNet-V2. Figure 9 shows a simplified comparison of the architectures. Due to the size of some architectures, the representation was simplified. The Vgg19-derivate uses four groups of sequential convolution layers, each followed by a ReLU (Rectified Linear Unit) layer. Compared to the original Vgg19 architecture, a block of convolutional layers was removed due to the lower resolution of the matrix input. Furthermore, the number of filters per convolutional layer was reduced so a comparable batch size could be applied for all architectures. The variant derived from ResNet is shown in a simplified manner in Figure 9 using _convUnits_, each consisting of a convolution, batch normalization, ReLU activation, convolution, and batch normalization layer. The filter size is 3 \(\times\) 3 for both convolution layers, and the values in the square brackets describe the number of filters and the stride for the layer. The two _skipConv_ blocks contain extra convolution layers and are necessary for the results to have the same format when merging. The third architecture is based on MobileNet-V2 and is illustrated schematically via _convBlock_ units in Figure 9. A _convBlock_ contains a channel-wise convolution with 6 filters, batch normalization, an ReLU layer, channel-wise convolution with one filter, batch normalization, an ReLU layer, a channel-wise convolution layer with a fixed number of filters (matching the input to the _convBlock_), and a batch normalization layer. A total of  
Figure 9: Comparison of different network architectures adapted for channel-wise input of transformed FE simulation matrices. 17 blocks are arranged one after the other with partial skip paths, modeled after the original MobileNet-V2. For the adapted Inception-V3 network, the first layers were replaced by _convUnit2_ blocks, each composed of a convolution, batch normalization, and ReLU layer, with the convolution parameters listed in the square brackets. The following _inceptBlock_ modules are carried over from the original Inception-V3 architecture and contain four threads each with different convolution, batch normalization, ReLU, and pooling layers, as shown in Figure 4. Due to the lower resolution of the input, the last two larger inception blocks were removed from the network. For all models, the last three layers depend on the classification model. In the case of binary classification, they are a fully connected layer with two neurons and a softmax and classification layer. In contrast, in the multilabel instance, a fully connected layer with three neurons and a sigmoid and cross-entropy loss layer is applied. The evaluation metric for comparison of the different approaches and models is usually classification accuracy. This metric is derived from the confusion matrix and is calculated for the three datasets: the training dataset, validation dataset, and test dataset. A confusion matrix with the associated variable names is shown in Figure 10, with the variables True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN). For a balanced dataset, classifications accuracy is often applied, which can be calculated according to [52; 53]:  
\[accuracy=\frac{TP+TN}{TP+TN+FP+FN}\]  
However, this metric is not appropriate for the evaluation of imbalanced datasets since it does not consider the uneven distribution of classes.