## 2 Materials and Methods
### Direct, Inverse Neural Network-Based Material Parameter Identification Process
For comparability purposes, the FDC and PEC were evaluated by default with an equidistant discretization of 200 points and at the same abscissa locations. Consequently, twelve SOC 2400 input values were opposed to the corresponding 18 material parameters as output. Since the output of the simulations was noise-free and clean, and typically data from experimental measurements are not, Gaussian noise with zero mean and standard deviation of 0.001 was applied to the force and 0.0005 to the PPR data, taking this into account. As mentioned initially, time series data augmentation (AUG) and manipulation are beneficial for increasing the prediction accuracy of the NN and its generalization ability by reducing overfitting [22,43]. The basic idea of data augmentation is the generation of additional datasets by adding slightly modified variations of already existing data or newly created synthetic data from existing sets while maintaining correct labels [44]. This  
Figure 3: Applied direct inverse material parameter identification method. Own figure based on [7]. is especially relevant for real-world data such as experimental results and can contribute to counteracting problems due to insufficient or expensive generated input datasets. While data AUG is a popular method in image recognition with NNs, it is not a well-established approach for time series regression tasks, and many techniques are borrowed from the former [43]. Many different methods exist, which according to [PERSON] et al. [24] can be categorized into random transformation, pattern mixing, using generative models (such as NNs), and decomposition. However, not all techniques are beneficial for each time series dataset due to their different features and may also cause prediction-accuracy-degrading effects. In the domain of direct inverse MPI, random transformation in the form of applying Gaussian noise to the time series datasets to account for random measurement errors and deviations has already been successfully applied [7, 8, 26]. Previously, a noise amount adapted to the noise ratio of the experimental data was used, while the initial dataset size was unchanged. In this work, several noise amounts also were used in some runs to artificially increase the dataset size and to investigate whether an increase in the prediction accuracy can be achieved. A fundamentally different kind of data augmentation methods are decomposition methods, which decompose time series by extracting features or underlying patterns [24]. Empirical mode decomposition (EMD) is a technique to decompose nonlinear and non-stationary signals. The decomposed oscillatoriy components are typically named an intrinsic mode function (IMF). These, however, differ in nuances depending on the chosen settings of the EMD. In this work, it was applied to the virtual dataset using the Python library PyEMD, which is based on the algorithm by [PERSON] et al. [45]. The input dataset consisting of the simulation results thus was artificially extended by the IMFs resulting from the EMD. As is usual for data augmentation techniques, only the training dataset was increased in size, and for validation, the original data remained unchanged. The chosen settings are explained in Section 2.3. For more detailed information on data augmentation methods, please refer to [23, 24, 43]. Model-related effects in the numerical simulations, such as oscillations after abrupt failure, complicate the NN training process. Hence, automated data preparation techniques are often required--e.g., truncating the force-displacement curves after failure in the present case. Additionally, filtering functions such as moving averages are applied in this step, which also have to be executed for the prediction based on unknown data. To avoid indirect weighting and problems during the training of the NN, the input and output data were normalized separately. Different ML algorithms can be used as surrogate models, whereas three different NN types were implemented and compared in this work.