## 1 Introduction
[14] model the electrical discharge machining process with GPR trained from data generated with numerical FEM simulation. Using support vector regression (SVR), [PERSON] et al. [15] construct a metamodel in an optimization approach for lightweight vehicle design. Training data are generated, using design of experiment approaches with FEM simulations. To predict the stress at the implant-bone interface, [PERSON] et al. [16] utilize SVR in order to replace FEM simulation. [PERSON] and [PERSON] [17] estimate cutting coefficients in a mechanistic milling force model with SVR trained with FEM simulation data. Employing tree-based models, [PERSON] et al. [18] estimate the biomechanical behavior of breast tissue under compression, using three different tree-based models trained from FEM simulations. The models are trained with FEM data in terms of nodal coordinates and nodal tissue membership. [PERSON] et al. [19] estimate the base failure stability for braced excavations in anisotropic clay using extreme gradient boosting, random forest regression (RFR) and data obtained from FEM simulation results. [PERSON] et al. [20] utilize a decision tree regressor to predict the mechanical properties of carbon fiber reinforced plastics with data obtained from FEM simulations. Besides MLPs [PERSON] et al. [10] utilize RFRs to predict the biomechanics of livers. A recent neural network-based approach are physics informed neural networks (PINNs). PINNs are trained simultaneously on data and governing differential equations and can be used for the solution and inversion of equations governing physical systems. Utilizing PINNs, [PERSON] and [PERSON] [21] substitute a particular FEM simulation of a perforated strip under uniaxial extension. In [22], [PERSON] et al. present a surrogate modeling approach with PINNs and a specific use case. Focusing on consistency, [PERSON] [23] evaluates findings regarding PINNs with Poisson's equation and the heat equation. [PERSON] et al. [24] use PINNs to predict permeability and viscoelastic modulus from thrombus deformation data, described by the fourth-order Cahn-Hilliard and Navier-Stokes equations. In addition to the application of PINNs in structural mechanics problems, there is also a considerable number of papers, especially in computational fluid dynamics [25; 26; 27; 28; 29]. Related work shows capabilities of surrogate modeling, thus demonstrating the feasibility of supervised learning models trained with FEM simulations. From our analysis of the existing literature, we identify the following drawbacks:  
* In most cases, the surrogate model only substitutes for a subset of the considered computational domain. Thus, such an approach focuses only on a region of interest and cannot be used to evaluate the entire computational domain (notable exceptions are [12; 22]). * Surrogate models representing the complete discretized computational domain (mesh) are solely fitted and evaluated on one use case--generalization to unseen data is only achieved with respect to the discretization of the computational domain, but not with respect to other use case specific parameters (notable exception concerning material parameters [22]). * Due to differences in FEM use cases and data, the comparison of related work is useful only in some cases. * Replication of published experiments is often not achievable because important parameters are not reported, e.g., number of finite elements, type of finite elements (bilinear, biquadratic, reduced integration etc. ), method of discretization (meshing), as well as hyperparameters of the ML models, such as learning or activation functions. To address these drawbacks, we present the following contributions of our paper:  
1. We present the main DL and ML methods together with a compact description and mathematical notation to equip practitioners with a reference to surrogate FEM simulation mesh-free and assess the feasibility and maturity of the novel PINNs method. 2.