Convergence analysis of two-level response and parameter mapping-based methods

Abstract

Space mapping-based methodologies for optimization and inverse problems in low- and high- frequency electromagnetic applications are well-established. This methodology uses one or multiple low-fidelity models and a high-fidelity model. The objective is to shift the optimization or inverse problem that is carried out within the high-fidelity forward model to a space mapped coarse model, which acts as surrogate model. Convergence problems however may occur since convergence rates depend on the fidelity of the coarse model(s) compared to the fine model. The recently proposed two-level response and parameter mapping (RPM) method, which employs input and output mapping, shows some improved convergence properties. This article proposes a mathematical framework for determining the robustness of this RPM methodology. We express accuracy and speed up of the RPM-based procedures through the use of four different quality measures.