## 4 Discussion  
All classes of surrogate models that we considered in this work share several key characteristics: (1) they are mesh-free and thus, can deliver results with infinite resolution; (2) the computation time required to obtain the target values at predefined positions is orders of magnitude lower than for FEM simulations; (3) since for each simulation setup,  
Figure 10: Compression of a block, Simulation 13 (extrapolation): absolute errors of different surrogate models (**a–f**) and ground truth Abaqus FEM simulation (**g**) of \(\sigma_{xy}\). Figure 9: Compression of a block, Simulation 7 (interpolation): absolute errors of different surrogate models (**a–f**) and ground truth Abaqus FEM simulation (**g**) of \(\epsilon_{xx}^{p}\). where the geometry changes, a different mesh is created during FEM simulations, our results indicate that all classes of surrogate models generalize (interpolate) reasonably well across training data positions; (4) furthermore, all surrogate model classes generalize at least to some extent across use case parameters, such as changes in geometry or material parameters. Finally, all surrogate model classes must be used with care, as they do not extrapolate well to data positions and/or use case parameters unseen during training. Our findings show this in the extrapolation result of the beam use case, Simulation 9: due to the greater yield stress, almost no plastic deformation occurs; thus, the surrogate models are not able to learn such material behavior. Similar findings can be seen from the extrapolation results of the block use case, Simulation 1, 2, 12 and 13: approaches utilizing PINNs and SVRs are not able to predict acceptable strain components, leading to overall worse averaged R2-scores. In general, it can be stated that the surrogate models used show similar behavior with respect to inter- and extrapolation, but differ with respect to individual components, i.e., some models are better at predicting individual components (e.g., strains) for unknown generalization variables (e.g., yield strength) than others. Another example would be the symmetric nature of the use case, making it redundant to evaluate, e.g., stresses at negative x-positions, the proposed surrogate models will certainly respond with such stress values, which consequently, cannot be considered meaningful. Similarly, while the surrogate models may well be evaluated at physically meaningless use case parameters, e.g., negative radii, the thus obtained results must be considered meaningless as well. Therefore, all surrogate models must be treated with this in mind, which is a fundamental difference to FEM simulations that do not offer such modes of failure. With these considerations in mind, we now turn to discuss specific characteristics of each surrogate model class. Our KNN approach, which can be considered simple compared to the other algorithms, gave competitive results; moreover, this approach showed the best results regarding extrapolation (i.e., Simulations 1, 2, 12 and 13) in the block use case. Algorithms we constructed with MultiOutputRegressor (SVR and GBDTR) could give better results if the hyperparameters are tuned to each target separately. However, we did not do this for fairness reasons since our other algorithms are also fitted to the overall use case and not to each target individually. We intend to monitor this in the future. In our setting, the GPR algorithm did not deliver good results. Tuning the kernel function could deliver better results; however, we do not believe that it would be practical to modify for each new simulation use case. Thus, we not intend to head in this direction. However, we plan to investigate whether other Bayesian methods (e.g., Bayesian neural network [30] or neural processes [31]) could be beneficial. Our MLPs approaches delivered the overall best results in our comparison, especially regarding interpolation (i.e., in the plate and beam use cases Simulations 4 and 6 and in the block use case, Simulation 7).