*Article* **Mesh-Free Surrogate Models for Structural Mechanic FEM Simulation: A Comparative Study of Approaches**

**Johannes G. Hoffer 1,\*, Bernhard C. Geiger 1, Patrick Ofner <sup>1</sup> and Roman Kern 2,\***


**Abstract:** The technical world of today fundamentally relies on structural analysis in the form of design and structural mechanic simulations. A traditional and robust simulation method is the physics-based finite element method (FEM) simulation. FEM simulations in structural mechanics are known to be very accurate; however, the higher the desired resolution, the more computational effort is required. Surrogate modeling provides a robust approach to address this drawback. Nonetheless, finding the right surrogate model and its hyperparameters for a specific use case is not a straightforward process. In this paper, we discuss and compare several classes of mesh-free surrogate models based on traditional and thriving machine learning (ML) and deep learning (DL) methods. We show that relatively simple algorithms (such as *k*-nearest neighbor regression) can be competitive in applications with low geometrical complexity and extrapolation requirements. With respect to tasks exhibiting higher geometric complexity, our results show that recent DL methods at the forefront of literature (such as physics-informed neural networks) are complicated to train and to parameterize and thus, require further research before they can be put to practical use. In contrast, we show that already well-researched DL methods, such as the multi-layer perceptron, are superior with respect to interpolation use cases and can be easily trained with available tools. With our work, we thus present a basis for the selection and practical implementation of surrogate models.

**Keywords:** FEM; surrogate modeling; mesh-free; machine learning; deep learning
