Toward a certified greedy Loewner framework with minimal sampling

Abstract

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.

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Cited by in corpus (4)

• On Adaptive Frequency Sampling for Data-driven Model Order Reduction Applied to Antenna Responses
• Rational kernel-based interpolation for complex-valued frequency response functions
• Fully-Adaptive and Semi-Adaptive Frequency Sweep Algorithm Exploiting Loewner-State Model for EM Simulation of Multiport Systems
• Surrogate modeling of resonant behavior in scattering problems through adaptive rational approximation and sketching