Toward a certified greedy Loewner framework with minimal sampling

We propose a strategy for greedy sampling in the context of non-intrusive interpolation-based surrogate modeling for frequency-domain problems. We rely on a non-intrusive and cheap error indicator to drive the adaptive selection of the high-fidelity samples on which the surrogate is based. We develop a theoretical framework to support our proposed indicator. We also present several practical approaches for the termination criterion that is used to end the greedy sampling iterations. To showcase our greedy strategy, we numerically test it in combination with the well-known Loewner framework. To this effect, we consider several benchmarks, highlighting the effectiveness of our adaptive approach in approximating the transfer function of complex systems from few samples.