Comparison of A‐Posteriori Error Estimators in the Context of Parametric Model Order Reduction by Matrix Interpolation

ABSTRACT The use of parametric model order reduction (pMOR) by matrix interpolation enables efficient simulation of large‐scale finite element (FE) models in multi‐query applications such as optimization and uncertainty quantification. In this method, high‐fidelity systems are sampled, individually reduced by projection‐based model order reduction, and finally, the reduced operators are interpolated, which allows to predict reduced systems for queried parameter points quickly. In order to use these approaches in a multi‐query application, an accurate error estimation for the parametric reduced‐order models (pROMs) is of great importance. This work investigates and compares the use of three a‐posteriori error estimators in the context of pMOR by matrix interpolation. A specific challenge in this pMOR method is that neither the full operators nor the reduced basis are directly available at a queried parameter point. Therefore, two strategies for obtaining each of these quantities are evaluated. Results show that accurate and reliable results are only achieved if the full operators are assembled; interpolating them with the same interpolation method used for the reduced operators can accumulate the errors strongly. Regarding the reduced basis, selecting the basis from the closest sample provides accurate results not only at the sample points but also away from them. The most effective configuration turned out to be applicable both for sharp error estimation and to differentiate which pROM provides the best prediction if multiple local pROMs are available.