Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Moreover, we propose several variants of the error estimator, and compare those variants with the existing ones both theoretically and numerically. It is shown that some of the proposed error estimators perform better than or equally well as the existing ones. All the error estimators considered can be easily extended to estimate the output error of reduced-order modeling for steady linear parametric systems.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021001
Keywords: Model order reduction, error estimation
@article{M2AN_2021__55_2_561_0,
author = {Feng, Lihong and Benner, Peter},
title = {On error estimation for reduced-order modeling of linear non-parametric and parametric systems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {561--594},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {2},
doi = {10.1051/m2an/2021001},
mrnumber = {4238778},
zbl = {1480.37086},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021001/}
}
TY - JOUR AU - Feng, Lihong AU - Benner, Peter TI - On error estimation for reduced-order modeling of linear non-parametric and parametric systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 561 EP - 594 VL - 55 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021001/ DO - 10.1051/m2an/2021001 LA - en ID - M2AN_2021__55_2_561_0 ER -
%0 Journal Article %A Feng, Lihong %A Benner, Peter %T On error estimation for reduced-order modeling of linear non-parametric and parametric systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 561-594 %V 55 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021001/ %R 10.1051/m2an/2021001 %G en %F M2AN_2021__55_2_561_0
Feng, Lihong; Benner, Peter. On error estimation for reduced-order modeling of linear non-parametric and parametric systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 2, pp. 561-594. doi: 10.1051/m2an/2021001
[1] , Approximation of Large-Scale Dynamical Systems. In: Vol. 6 of Adv. Des. Control. SIAM Publications, Philadelphia, PA (2005). | MR | Zbl
[2] and , Approximation of large-scale dynamical systems: an overview. Int. J. Appl. Math. Comput. Sci. 11 (2001) 1093–1121. | MR | Zbl
[3] , and , A survey of model reduction methods for large-scale systems. Contemp. Math. 280 (2001) 193–219. | MR | Zbl | DOI
[4] , and , Interpolatory model reduction of large-scale dynamical systems. In: Efficient Modeling and Control of Large-Scale Systems, edited by and . Springer US (2010) 3–58. | Zbl | DOI
[5] , and , Interpolatory methods for model reduction. In: Vol. 6 of Computational Science and Engineering 21. Philadelphia, PA (2020). | MR | Zbl
[6] , , and , Interpolatory projection methods for parameterized model reduction. SIAM J. Sci. Comput. 33 (2011) 2489–2518. | MR | Zbl | DOI
[7] , and , Model order reduction for linear and nonlinear systems: a system-theoretic perspective. Arch. Comput. Methods Eng. 21 (2014) 331–358. | MR | Zbl | DOI
[8] , , , , and , Comparison of methods for parametric model order reduction of time-dependent problems. In: Model Reduction and Approximation: Theory and Algorithms, edited by , , and . SIAM (2017) 377–407. | MR | DOI
[9] , and , editors. Model reduction for circuit simulation. In: Vol. 74 of Lect. Notes Electr. Eng. Springer, Dodrecht (2011). | MR | DOI
[10] , and , A survey of model reduction methods for parametric systems. SIAM Rev. 57 (2015) 483–531. | MR | Zbl | DOI
[11] , , and , editors. Model Reduction and Approximation: Theory and Algorithms. Computational Science & Engineering. SIAM Publications, Philadelphia, PA (2017). | MR | DOI
[12] , and , The Proper Generalized Decomposition for Advanced Numerical Simulations. SpringerBriefs in Applied Sciences and Technology. Springer International Publishing (2014). | MR | Zbl | DOI
[13] and , Adaptive rational Krylov subspaces for large-scale dynamical systems. Syst. Control Lett. 60 (2011) 546–560. | MR | Zbl | DOI
[14] , and , Adaptive tangential interpolation in rational Krylov subspaces for MIMO dynamical systems. SIAM J. Matrix Anal. Appl. 35 (2014) 476–498. | MR | Zbl | DOI
[15] and , A robust algorithm for parametric model order reduction based on implicit moment matching, edited by and . In: Vol. 9 of Reduced Order Methods for Modeling and Computational Reduction, Chap. 6, MS&A Series. Springer-Verlag, Berlin, Heidelberg, NY (2014) 159–186. | MR | Zbl
[16] and , A new error estimator for reduce-order modeling of linear parametric systems. IEEE Trans. Microw. Theory Techn. 67 (2019) 4848–4859. | DOI
[17] , and , Some a posteriori error bounds for reduced order modelling of (non-)parametrized linear systems. ESAIM: M2AN 51 (2017) 2127–2158. | MR | Zbl | Numdam | DOI
[18] , , and , Reliable greedy multipoint model-order reduction techniques for finite-element analysis. IEEE Trans. Antennas Propagat. 17 (2018) 821–824. | DOI
[19] , Parametric dynamical systems: Transient analysis and data driven modeling. Ph.D. thesis, Virginia Tech (2018).
[20] , , and , A hierarchical a-posteriori error estimator for the reduced basis method. Cornell University. Preprint: (2018). | arXiv | MR
[21] , and , Estimating the inf-sup constant in reduced basis methods for time-harmonic Maxwell’s equations. IEEE Trans. Microw. Theory Techn. 63 (2015) 3549–3557. | DOI
[22] , and , Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer, Cham (2016). | MR | DOI
[23] , and , An H2⊗L2-optimal model order reduction approach for parametric linear time-invariant systems. Appl. Math. Mech. 18 (2018).
[24] , , and , A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup lower bounds. C.R. Acad. Sci. Paris 345 (2007) 473–478. | MR | Zbl | DOI
[25] and , Electric field integral equation for fast frequency sweep for scattering of nonpenetrable objects via the reduced-basis method. IEEE Trans. Antennas Propagat. 68 (2020) 6232–6244. | DOI
[26] , and , Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15 (2008) 229–275. | MR | Zbl | DOI
[27] , and , Model reduction by second order Krylov subspaces: extensions, stability and proportional damping. In: IEEE Conference on Computer Aided Control Systems Design. Springer International Publishing (2006) 2997–3002.
[28] , and , Rigorous and effective a-posteriori error bounds for nonlinear problems-application to RB methods. SimTech, University of Stuttgart (2018). | MR
[29] , and , Randomized residual-based error estimators for parametrized equations. SIAM J. Sci. Comput. 41 (2019) A900–A926. | MR | Zbl | DOI
[30] , A space-time Petrov-Galerkin certified reduced basis method: application to the Boussinesq equations. SIAM J. Sci. Comput. 36 (2014) 232–266. | MR | Zbl | DOI
[31] , , and , An efficient output error estimation for model order reduction of parametrized evolution equations. SIAM J. Sci. Comput. 37 (2015) B910–B936. | MR | Zbl | DOI
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