Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms

In this work, the empirical-Gramian-based model reduction methods: Empirical poor man’s truncated balanced realization, empirical approximate balancing, empirical dominant subspaces, empirical balanced truncation, and empirical balanced gains are compared in a non-parametric and two parametric variants, via ten error measures: Approximate Lebesgue $L_0$, $L_1$, $L_2$, $L_{\mathrm{\infty }}$, Hardy $H_2$, $H_{\mathrm{\infty }}$, Hankel, Hilbert-Schmidt-Hankel, modified induced primal, and modified induced dual norms, for variants of the thermal block model reduction benchmark. This comparison is conducted via a new meta-measure for model reducibility called MORscore.