  In the framework of reduced basis methods, we recently introduced a new
certified hierarchical and adaptive surrogate model, which can be used for
efficient approximation of input-output maps that are governed by parametrized
partial differential equations. This adaptive approach combines a full order
model, a reduced order model and a machine-learning model. In this
contribution, we extend the approach by leveraging novel kernel models for the
machine learning part, especially structured deep kernel networks as well as
two layered kernel models. We demonstrate the usability of those enhanced
kernel models for the RB-ML-ROM surrogate modeling chain and highlight their
benefits in numerical experiments.
