## 3 Results and Discussion
Furthermore, it can be seen in Figure 9b that regardless of the uncertainties, the BNN was not able to predict the exact MP of \(\
u_{p,press}=0.5\), which would have led to the exact simulation result. The reason is probably that the searched material parameter also lay exactly on the MP range boundary. Figure 10 shows the probability density functions of two estimated material parameters. The true MP can also lie outside the PDF, which is not necessarily due to a poor prediction. Since the MP are coupled with each other and different MP combinations can  
Figure 9: Comparison of the influence of aleatoric uncertainties on the experimental dataset simulation output for run 39: **(a)** FDC tension test V3, **(b)** PEC compression test, **(c)** FDC bending test, and **(d)** FDC punch test. lead to similar or maybe even the same simulation results, there probably exist different MP combinations that can similarly reproduce the relationship to be learned. Therefore, the plot of the simulation results based on the sampled MP shown in Figure 9 provides additional value for assessing the reliability of the subsequent numerical simulations. In the Appendix in Figure 10, the predicted MP with the true values and the aleatoric uncertainties (standard deviations) for the Runs 36 to 39 and 44 are shown. Despite the expectation of aleatoric uncertainties remaining constant for increasing dataset size, they decreased slightly (see also Table 11). Thus, the Gaussian noise amounts may not have been the main cause for the aleatoric uncertainties. Their origin lay instead in the data generation process and the occasionally unpredictable heavy oscillations, which could not be completely eliminated from the time series using the applied functions. Filter functions or other numerical effects during the simulation and the presence of many nonunique MP could also contribute to this. In contrast, the more significant reducibility of epistemic uncertainties by using larger datasets can be seen in Figure 11. Normalized standard deviations of mean MPs and STDV of MPs for the validation and the experimental dataset are shown on the graphs. These resulted because a different probability density function was obtained for each prediction based on the weights and biases sampled for each prediction. This PDF can be described by the calculated statistics mean and STDV, whereas in the present case, the STDV of these means and STDV can be calculated for the number of 100 performed predictions per BNN. For both validation and experimental datasets, a descending trend with a higher number of data can be observed for the mean and for the STDV. An exception is the MPs' STDV of the means of the second smallest dataset from the experimental dataset. This could be an indication that that model could produce a better predictions when repeating the stochastic training process with a constant number of data, and repetition could be advantageous. Based on the curve plot, it is reasonable to assume that further increasing the size of the dataset could lead to further reductions in epistemic uncertainties. However, in Table 11, when comparing the aleatoric and epistemic uncertainties, it can be seen that the latter are relatively small compared to the aleatoric uncertainties. Thus, the aleatoric uncertainties contributed more to the uncertainties of the prediction. Figure 10: Probability density function of run 39 with the virtual experiment set of (**a**) MP \(d_{t}\) and (**b**) MP \(b_{c}\).