Page 367 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 367
TIONAL APPROXIMATION FOR DATA-DRIVEN MODELING AND COMPLEXITY
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction
of Parametric Systems in Electromagnetics
Sridhar Chellappa, chellappa@mpi-magdeburg.mpg.de
Max Planck Institute for Dynamics of Complex Technical Systems, Germany
Coauthors: Lihong Feng, Valentin de la Rubia, Peter Benner
In this talk, we discuss efficient, sharp a posteriori state error estimation for reduced-order mod-
els of general linear parametric systems. Standard a posteriori state error estimation for model
order reduction relies on the inf-sup constant. The a posteriori error estimation for systems with
very small or vanishing inf-sup constant poses a challenge, since it is inversely proportional to
the inf-sup constant, resulting in overly pessimistic error estimators. Such systems appear in
electromagnetics since the inf-sup constant values are zero or close to zero, at or near resonant
frequencies. We propose a novel a posteriori state error estimator which avoids the calculation
of the inf-sup constant. The proposed state error estimator is compared with the standard er-
ror estimator and a recently proposed one in the literature. It is shown that our proposed error
estimator outperforms both existing estimators. Furthermore, our new estimator is integrated
within an adaptive greedy algorithm that iteratively builds the reduced-order model. Numerical
experiments are performed on real-life microwave devices such as narrowband and wideband
antennas, as well as a dual-mode waveguide filter. These examples show the capabilities and
efficiency of the proposed methodology.
References
[1] S. Chellappa, L. Feng, V. de la Rubia, and P. Benner, “Inf-Sup-Constant-Free State Error
Estimator for Model Order Reduction of Parametric Systems in Electromagnetics," arXiv
preprint, 2021. https://arxiv.org/abs/2104.12802
On improving the data collection step for data driven modeling methods
Karim Cherifi, cherifi@math.tu-berlin.de
TU Berlin, Germany
Coauthors: Pawan Goyal, Peter Benner
Data-driven modeling methods have gained in popularity in recent years. However, to obtain
good reliable models, one generally needs to process a huge amount of data. In this work,
we present a heuristic algorithm to improve the data collection step such that the data used is
only the data that holds the most information about the system that we are trying to model.
This algorithm is applied on the Loewner framework where interpolation points are chosen
adaptively in order to obtain a reliable low order realization of the system at hand. It is designed
for frequency domain data then extended to time domain data. The operation of the algorithm
is illustrated by applications and well known benchmarks.
365
REDUCTION OF LINEAR AND NONLINEAR DYNAMICAL SYSTEMS (MS-69)
Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction
of Parametric Systems in Electromagnetics
Sridhar Chellappa, chellappa@mpi-magdeburg.mpg.de
Max Planck Institute for Dynamics of Complex Technical Systems, Germany
Coauthors: Lihong Feng, Valentin de la Rubia, Peter Benner
In this talk, we discuss efficient, sharp a posteriori state error estimation for reduced-order mod-
els of general linear parametric systems. Standard a posteriori state error estimation for model
order reduction relies on the inf-sup constant. The a posteriori error estimation for systems with
very small or vanishing inf-sup constant poses a challenge, since it is inversely proportional to
the inf-sup constant, resulting in overly pessimistic error estimators. Such systems appear in
electromagnetics since the inf-sup constant values are zero or close to zero, at or near resonant
frequencies. We propose a novel a posteriori state error estimator which avoids the calculation
of the inf-sup constant. The proposed state error estimator is compared with the standard er-
ror estimator and a recently proposed one in the literature. It is shown that our proposed error
estimator outperforms both existing estimators. Furthermore, our new estimator is integrated
within an adaptive greedy algorithm that iteratively builds the reduced-order model. Numerical
experiments are performed on real-life microwave devices such as narrowband and wideband
antennas, as well as a dual-mode waveguide filter. These examples show the capabilities and
efficiency of the proposed methodology.
References
[1] S. Chellappa, L. Feng, V. de la Rubia, and P. Benner, “Inf-Sup-Constant-Free State Error
Estimator for Model Order Reduction of Parametric Systems in Electromagnetics," arXiv
preprint, 2021. https://arxiv.org/abs/2104.12802
On improving the data collection step for data driven modeling methods
Karim Cherifi, cherifi@math.tu-berlin.de
TU Berlin, Germany
Coauthors: Pawan Goyal, Peter Benner
Data-driven modeling methods have gained in popularity in recent years. However, to obtain
good reliable models, one generally needs to process a huge amount of data. In this work,
we present a heuristic algorithm to improve the data collection step such that the data used is
only the data that holds the most information about the system that we are trying to model.
This algorithm is applied on the Loewner framework where interpolation points are chosen
adaptively in order to obtain a reliable low order realization of the system at hand. It is designed
for frequency domain data then extended to time domain data. The operation of the algorithm
is illustrated by applications and well known benchmarks.
365
