## 3 Results and Discussion
Due to the widely varying characteristics of the individual time series (see Figure 11), they would have to be decomposed into different numbers of IMFs. This quantity of the resulting IMFs is furthermore dependent on the chosen stopping criteria of the used algorithm, which can be selected separately for different time series. For the present study, a limitation was defined by a maximum number of five resulting IMFs. Without this limitation, certain complex SOCs with sophisticated characteristics, such as the FDC of the tensile test V4, would have to be decomposed into additional curves. Other time series, such as the PEC of the compression and punch test, resulted in a smaller number of IMFs. However, the current implementation in the direct inverse MPI required an equal number of IMFs for the different tests, and therefore, the dataset was replenished with the available IMFs. This resulted in implicit weighting, which may influence the training process. Furthermore, different settings of the EMD algorithm may also affect it, which is why the suitability of data decomposition methods and EMD in particular for increasing the prediction accuracy for complex direct inverse MPIs cannot be conclusively evaluated. This should be further investigated in future studies. Figure 6 compares the distance measures of the five best runs of each network type with an additional 95% confidence interval, revealing the performance advantage of the CNN runs for both validation and experimental datasets. In Figure 11, the simulation results of run 19 are compared with those of the virtual experiment, whereby a good match can be observed. Except for run 21, which showed outlying high deviation in all error measures, the performances of all CNN runs are compared in Figure 7.  
The higher performance regarding the prediction accuracy of the Default_CNN, compared to the remaining CNN types, is assumed to result from the relative simplicity of the network architecture (see Section 2.2.2). Unlike the other CNNs, this has no third convolutional block and no GAP or subsequent MLP layer, and possesses the smallest number of parameters due to the use of sparse connections and shared weights. Here, the CNN architecture seems to be of higher importance compared to the hyperparameters, since run 30 with HPO and the same architecture yielded comparable results. Partially, the other CNN types, such as CNN_Rautela, Resnet, and Encoder, achieved lower loss values for the training dataset compared to the Default_CNN, which suggests a too-high level of complexity of these CNN architectures regarding the present dataset. Thereby, the differences between the loss values for the training and the validation dataset are very large, which indicates overlearning. This can also be detected by observing the learning curves, whereas in Figure 8 the differences between training and validation loss of (a) Resnet and (b) Default_CNN are compared. The implemented early stopping prevented a further separation of the training and validation losses. Figure 6: Distance measure comparison for the five best runs of each network: (**a**) the validation dataset, and (**b**) the corresponding experimental dataset. Figure 7: Distance measure comparison for CNN runs on (**a**) the validation dataset and (**b**) the corresponding experimental dataset. The worst performance in terms of DTW distance for validation and experimental dataset was obtained by run 21 with CNN_[PERSON] and run 22 with CNN_[PERSON], these being networks using dropout, which could have a negative impact on the present dataset. The second-best performance of the CNNs from the literature regarding DTW distances was achieved by the encoder architecture. To counteract overlearning and adapt the capacity of the networks to the fundamental time series regression problem, the number of parameters to be learned was reduced in FCN2 and FCN3 compared to FCN. This was done by significantly decreasing the number of filters in all three convolutional blocks. FCN2 omitted batch normalization.