Abstract

In many engineering applications, mathematical models and simulation tools are available to determine relevant objective values for given input variables. For example, in structural mechanics, the given input variables are the geometry and material parameters of a structure, as well as the acting loads. Typical target variables are the deformation of the structure and the maximum occurring stresses, from which the component failure results. In reality, the input variables are not known exactly, but are subject to a stochastic scatter. Accordingly, the objective values are also subject to scatter, which can be determined using probabilistic methods (a.k.a. Uncertainty Quantification).
A widely used probabilistic method is the Monte Carlo method. This very robust method is easy to implement, but also very computationally intensive. The basic idea is that the values of the input variables are generated according to their stochastic distribution and inserted into the simulation model. This is done until the distribution of the objective function is determined with sufficient accuracy (e.g., until the mean and standard deviation of the objective function converge). This means that the simulation model must be evaluated very often (order of magnitude 10^3 to 10^6), which becomes a problem with complex, very computationally intensive simulation models. Here, machine learning methods are used to generate efficient surrogate models (a.k.a. meta models). These surrogate models (e.g. neural networks) are first trained and then evaluated much faster instead of the actual simulation model. In the workshop, structural mechanics examples will be used to show how the scatter of a target variable can be determined by means of Monte Carlo simulation using surrogate models.