We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters.
Keywords: Parametric model order reduction, parametric dynamical systems, non-intrusive method, minimal rational interpolation, greedy algorithm
@article{M2AN_2021__55_5_1895_0,
author = {Nobile, Fabio and Pradovera, Davide},
title = {Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1895--1920},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021040},
mrnumber = {4313378},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021040/}
}
TY - JOUR AU - Nobile, Fabio AU - Pradovera, Davide TI - Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 1895 EP - 1920 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021040/ DO - 10.1051/m2an/2021040 LA - en ID - M2AN_2021__55_5_1895_0 ER -
%0 Journal Article %A Nobile, Fabio %A Pradovera, Davide %T Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 1895-1920 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021040/ %R 10.1051/m2an/2021040 %G en %F M2AN_2021__55_5_1895_0
Nobile, Fabio; Pradovera, Davide. Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 1895-1920. doi: 10.1051/m2an/2021040
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