Modern discretization techniques for differential equations yield high dimensional simulation models, which require high computational effort for determining approximate solutions. This even gets more problematic, if many of such simulations are required, e.g. for parametrized problems. Such settings can be parameter studies, interactive simulations, parameter identification problems, statistical investigations, etc.
For such problems, efficient techniques for dimensionality reduction are desirable. In addition to fast algorithms, also error quantification is crucial. Methods for this can be found and are developed in the fields of Reduced Basis (RB) techniques for parametrized partial differential equations and Model Order Reduction (MOR) for parametrized dynamical systems. On the present website, we present our collaborative work on these questions.