Optimization & Uncertainty Quantification

The numerical simulation of real physical processes is characterized by a complex interplay of factors such as model accuracy, physical understanding, and valid data. These challenges become particularly evident in the context of the complexity of multiscale and multiphysical modeling, as required in fields such as biology or environmental engineering. Uncertainty quantification (UQ) provides a means to analyze and assess the effects of uncertainties on the predictive accuracy of such models. It contributes to a better understanding of the reliability and significance of simulation results. These uncertainties can be addressed through an analysis that encompasses both aleatoric and epistemic uncertainties, i.e. polymorphic uncertainty quantification (PUQ), thereby accounting for variations in model input parameters as well as the challenges arising from model inaccuracies or unmeasurable elements due to incomplete knowledge. To achieve this, we employ approaches such as Bayesian and fuzzy techniques. Furthermore, the combination of optimization and uncertainty quantification offers an opportunity not only to enhance the models themselves but also to optimize the underlying assumptions and data foundations. This enables a holistic approach to complex systems and supports the development of more robust and precise models.

In both PUQ and Structural Optimization, sensitivity analysis plays a pivotal role. It aids in comprehensively assessing the influence of input parameters on a model and can also increase the efficiency of models themselves. For instance, sensitivities can be applied to create more efficient metamodels in the framework of PUQ, e.g. Gardient enhanced Kriging Model. Moreover, the integration of sensitivity analysis can lead to efficiency improvements in optimization algorithms.