Efficient Reduced Models and A-Posteriori Error Estimation for Parametrized Dynamical Systems by Offline/Online Decomposition

Reduced basis (RB) methods are an effective approach for model reduction of parametrized partial differential equations. In the field of dynamical systems’ order reduction, these methods are not very established, but the interest in reduction of parametrized systems is increasing. In the current presentation, we show that some characteristic components of RB-methods can be transfered to model reduction of parametrized linear dynamical systems. We assume an affine parameter dependence of the system components, which allows an offline/online decomposition and is the basis for efficient reduced simulation. Additionally, error control is possible by a-posteriori error estimators for the state and output, based on residual analysis and primal-dual techniques. Experiments demonstrate the applicability of the reduced parametrized systems, the reliability of the error estimators and the runtime gain by the reduction technique. The a-posteriori error estimation technique can straightforwardly be applied to all traditional projection-based reduction techniques of non-parametric linear systems, such as modal reduction, balanced truncation, moment matching, POD, etc.