## Uncertainty Propagation

For various reasons, it is beneficial to compute the propagation and dispersion of uncertainties in the input parameters through the system. The propagation of uncertainties can provide information on the impact of uncertain model input parameters, and summary statistics such as expected value and variance of a result can be identified. Moreover, confidence intervals or probability distributions of a quantity of interest resulting from uncertain input parameters can be computed. Uncertainty in various input parameters, such as initial conditions, environmental parameters and measurement error, can influence the result of a simulation or an experiment in unexpected ways. By computing the propagation of uncertainties, it is possible to check if the system output quantities satisfy the requirements. Moreover, it is possible to estimate the probability of certain events. The knowledge of the source and extent of uncertainties in simulation and experimental results is crucial to assess if a particular design variant is suitable. The calculation of the propagation of uncertainties is therefore an important tool to provide a solid basis for high-stakes decision-making. Conventional methods for the calculation of the propagation of uncertainties such as sampling-based Monte Carlo procedures often require an exuberant amount of model evaluations to provide reliable results. Thus, they can usually not be applied in combination with complex and expensive simulation models. Aside from Monte Carlo, traditional surrogate models based on polynomials have to be mentioned. These approaches, however, cannot be applied to problems with high stochastic dimension, i.e. many uncertain input parameters. Therefore, we use innovative approaches based on state-of-the-art research for calculating the propagation of uncertainties. On the one hand, these are advanced sampling procedures, which either use particular experimental-design strategies or exploit the specific structure of the problem at hand. The latter is the case, e.g., for the calculation of failure probabilities. As an alternative, we use multi-fidelity procedures, which in addition to detailed and high-resolution models also process information from simplified models and thus require significantly less computational effort. Aside from sampling-based procedures, we also use surrogate models based on statistical emulators. Emulator-based quantification of uncertainties has become a popular solution in comparison with sampling-based methods due to the increase of speed and the reduced computational cost. Emulators are particularly well suited for problems requiring more than a “pure” propagation of uncertainties, such as sensitivity analyses. For very complex simulation models, in particular, AdCo EngineeringGW has developed multi-fidelity emulators to enable the use of information from models with varying levels of complexity efficiently. Thereby, the computational complexity is reduced as compared to standard procedures, while at the same time ensuring high-quality results.