## 1 Introduction  
Assessing the properties of mechanical structures with real physical experiments is expensive, as it costs both time and resources. To reduce these costs of knowledge enrichment in the field of structural analysis, computer simulations of structural mechanics have become crucial. An essential simulation method is the finite element method (FEM) in which the simulation domain space is represented by a finite number of connected elements. Space- and time-dependent behavior between connected elements and within the elements themselves is governed by physical equations. Observation of real physical experiments provides the coefficients for these governing equations. Since most geometries and use cases cannot be solved analytically, an approximation of the proposed physical equations is obtained by numerical methods [1]. However, solving complex problems with FEM is time-consuming and computationally expensive. In order to reduce the computational effort, surrogate modeling offers a promising solution [2]. Surrogate models are trained in a supervised manner and are designed to learn the function mapping between inputs and outputs from a given FEM simulation use case. With a sufficient amount of training data with respect to the use case, an according model is able to substitute for the FEM simulation use case up to a certain accuracy. There is already a considerable number of related work concerning surrogate modeling of structural mechanics simulations with machine learning (ML) or deep learning (DL)approaches. In the following, we want to present the most important works for this paper. Artificial neural networks (ANN) are used in the work of [PERSON] et al. [3] to predict damage development in forged brake discs reinforced with Al-SiC particles, using damage maps. The ANN is a multilayer perceptron (MLP), and training data are obtained from FEM simulations using the commercial DEFORM simulation software. For rapid estimation of forming and cutting forces for given process parameters, [PERSON] et al. [4] investigate a method using MLP models. The researchers focus on two processes: hot upsetting and extrusion. Each process, represented by a MLP, is trained with FEM simulation results from the FORGE2 commercial FEM simulation software. [PERSON] et al. [5] predict the projectile response after impact with steel armor using a MLP; their surrogate model studied is trained with data from FEM simulations of the use case. [PERSON] et al. [6] explore generalizable surrogate models for 3D trusses, using MLP and FEM training data. [PERSON] et al. [7] estimate the performance of hot-forged product designs, using a MLP trained on FEM results obtained with the commercial software DEFORM. [PERSON] and [PERSON] [8] use single-layer feedforward ANNs instead of FEM as a metamodel in a sequential approximate optimization (SAO) algorithm. In a case study on hot forging of a steel disk, they compare their results with an ANN trained on FEM simulation results and the FEM simulation software QForm3D. [PERSON] and [PERSON] [9] predict the velocity field and location of neutral point of cold flat rolling with a MLP trained with rigid-plastic FEM simulation results. [PERSON] et al. [10] predict the mechanical behavior of different livers with MLPs trained from FEM simulations. [PERSON] et al. [11] estimate the mechanical properties of a two-dimensional checkerboard composite using a convolutional neural network (CNN) trained with FEM results. Regarding mesh-based approaches, [PERSON] et al. [12] present a framework to train graph neural networks (GNN) on mesh-based simulations and show the applicability in aerodynamics, structural mechanics, and fabric. Surrogate models were also obtained using classical, i.e., non-neural ML, approaches. For example, the authors of [3] apply Gaussian process regression (GPR) besides ANN in their approach. [PERSON] and [PERSON] [13] predict the stress intensity factors, using GPR trained with FEM results of a classical bolt-nut assembly. [PERSON] et al.