## 2 Materials and Methods
### Dataset  
The nodal data from our Abaqus FEM simulations constitute the datasets. For each use case, the nodal data are split into training and test dataset, respectively. The training dataset \(D=\{X_{1},\ldots,X_{n}\}\) with number of training instances \(n\) and the test dataset \(T=\{X_{n+1},\ldots,X_{n+m}\}\) with number of test instances \(m\) are generated from several FEM simulations; see Tables 2 and 6, where bold marked simulations belong to \(T\) and the remaining to \(D\). Thus, we split our data due to different generalization variables and not randomly. We denote each instance with index \(i\), \(i\in\{1,2,\ldots,n+m\}\). An instance \(X_{i}=(x_{i},y_{i})\) is generated of an input vector \(x_{i}\in\mathbb{R}^{p}\) and output vector \(y_{i}\in\mathbb{R}^{q}\). Each input vector \(x_{i}\) is composed of the initial \(x\)- and \(y\)-coordinates of a FEM node and the respective generalization variable (i.e., perforated plate: _Diameter_, beam: _Yield Stress_, block with four perforations: \(Width\) and _Yield Stress_) of the FEM simulation; see Table 4. Thus, we have \(p=3\) in the plate and beam use case, and \(p=4\) in the block use case.  
In our setting, each output vector \(y_{i}\) contains 13 (\(q=13\)) output variables obtained from FEM simulation with input \(x_{i}\), namely the \(\varepsilon_{xx}^{t}\), \(\varepsilon_{xy}^{t}\) and \(\varepsilon_{yy}^{t}\) total strain components, the \(\varepsilon_{xx}^{p}\), \(\varepsilon_{xy}^{p}\), \(\varepsilon_{yy}^{p}\) and \(\varepsilon_{zz}^{p}\) plastic strain components, the \(\sigma_{xx}\), \(\sigma_{xy}\), \(\sigma_{yy}\) and \(\sigma_{zz}\) principal and shear stress components and the displacement in x- and y-directions \(u\) and \(v\) of each node; see Table 5 and Figure 4. We split the data in a training and test dataset (see Table 6) and standardized the data by removing the mean and scaling to unit variance.  
In Figure 4, we present graphical results with visible mesh obtained from Abaqus FEM simulation of the output variables used for a block use case.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Plate** & **Beam** & **Block** \\ \hline Training dataset \(D\) & 4447 & 2720 & 6722 \\ Test dataset \(T\) & 3534 & 2176 & 4107 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Dataset splits: number of training instances \(n\) and test instances \(m\) due to the data generation from Table 2.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Simulation** & **Plate** & **Beam** & **Block** \\ \hline \multirow{4}{*}{Input variables} & x-coordinate & x-coordinate & x-coordinate \\  & y-coordinate & y-coordinate & y-coordinate \\  & Diameter & Yield Stress & Yield Stress \\  & & & Width \\ \hline \hline \end{tabular}
\end{table}
Table 4: Surrogate model input variables. Data obtained from FEM simulations are transformed so that each FEM node (represented by its x- and y-coordinates) with the respective generalization variable is an instance.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & \multicolumn{3}{c}{**Output Variables**} \\ \hline \(\varepsilon_{xx}^{t}\) & \(\varepsilon_{xx}^{p}\) & \(\sigma_{xx}\) & \(u\) \\ \(\varepsilon_{yy}^{t}\) & \(\varepsilon_{yy}^{p}\) & \(\sigma_{xy}\) & \(v\) \\ \(\varepsilon_{yy}^{t}\) & \(\varepsilon_{yy}^{p}\) & \(\sigma_{yy}\) & \\  & \(\varepsilon_{zz}^{p}\) & \(\sigma_{zz}\) & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Surrogate model output variables. For each input FEM node, a surrogate model predicts its respective strains, stresses and displacements.