## 3 Results and Discussion
Based on the DTW distance of the validation dataset, it can be seen that this was successful. This is primarily valid for FCN3. The omission of the batch normalization conversely showed a negative effect on the prediction accuracy, which should be verified for other NN architectures in the future. Generally, the comparison between MLP and CNN architectures suggests a greater potential for increasing the prediction accuracy by CNNs. This may be due to the reduction in learnable network parameters of CNNs compared to MLPs due to the sparse connections and shared weights, and the consideration of local dependencies of data points. In contrast, the BNNs based on the MLPs showed the lowest performance of the three investigated network variants. However, the reason may have been the complex and resource-intensive training process of the BNNs due to the large number of network parameters to be adjusted. Even after 20,000 epochs, the training and validation loss were still improving, which is why a continuation would probably lead to better results. Nevertheless, even for the small number of 20 to 30 hidden layer neurons, the training required several days, resulting from the high number of network parameters to be optimized. Since this number is also significantly dependent on the input point number of time series, this was reduced, whereas if the reduction is too large, as in run 35, this will lead to an SOC that is no longer representative and is therefore of limited applicability. In future investigations, further possibilities should be searched, e.g., by adapting the underlying network architecture. Due to the limitation of implementing only one subsequent stochastic layer, as described in Section 2.2.3, a larger number of neurons could be used in the first HL. This proved to be beneficial with respect to reducing the required epochs and training time and increasing the prediction accuracy; and again, a larger dataset led to better results. Varying the parameters of the normal distribution of the prior for runs 40 to 43 showed no advantage; thus, the common approach of a zero mean and a standard deviation of one is probably an appropriate starting point. Other distribution functions could be tested in future studies. As for the other network types, the use of multiple noise amounts further increased the prediction accuracy, but the training loss showed very high deviation from the corresponding validation loss. Figure 8: Learning curves of (**a**) Resnet run 25 and (**b**) Default_CNN run 19. Nevertheless, the main advantage of this network type is the distinction and quantification of the aleatoric and epistemic uncertainties. Figure 9 shows by example the effect of aleatoric uncertainties on the simulation with the predicted material parameters of run 39. This was obtained by sampling from the resulting probability density function (PDF), leading to a variety of material parameter sets, and each of these was used to simulate the ten experimental tests. Since the implementation of epistemic uncertainties leads to a divergent output for each prediction, 100 times the 500 MP sets of the PDF were sampled, and these 100 sets were then averaged. This result shows the underlying uncertainty of the data, which cannot be reduced by adding more datasets but is inherent to the data. Additionally, the experimental curve and the simulation result obtained from the point estimate which was calculated from the predicted PDF are shown. This displays that the underlying sensitivity of the MP on the simulation results has a varying impact on the different experiments. For example, the aleatoric uncertainties of the MP prediction have only a relatively small effect on the PEC of the compression test (Figure 9b) and the FDC of the bending test (Figure 9c). In contrast, they have a comparatively large impact on the FDC of the tensile test V3 (Figure 9a) and the FDC of the punch test (Figure 9d).