Free Access
Issue |
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
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Page(s) | 735 - 761 | |
DOI | https://doi.org/10.1051/m2an/2021010 | |
Published online | 05 May 2021 |
- A.C. Antoulas, I.V. Gosea and A.C. Ionita, Model reduction of bilinear systems in the Loewner framework. SIAM J. Sci. Comput. 38 (2016) B889–B916. [Google Scholar]
- P. Benner, S. Gugercin and K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev. 57 (2015) 483–531. [CrossRef] [Google Scholar]
- Z. Bujanović and D. Kressner, Norm and trace estimation with random rank-one vectors. 42 (2021) 202–223. [Google Scholar]
- S. Chaturantabut and D.C. Sorensen, A state space error estimate for POD-DEIM nonlinear model reduction. SIAM J. Numer. Anal. 50 (2012) 46–63. [Google Scholar]
- J.D. Dixon, Estimating extremal eigenvalues and condition numbers of matrices. SIAM J. Numer. Anal. 20 (1983) 812–814. [Google Scholar]
- Z. Drmač, S. Gugercin and C. Beattie, Vector fitting for matrix-valued rational approximation. SIAM J. Sci. Comput. 37 (2015) A2346–A2379. [Google Scholar]
- J.L. Eftang, M.A. Grepl and A.T. Patera, A posteriori error bounds for the empirical interpolation method. C.R. Math. 348 (2010) 575–579. [Google Scholar]
- L. Evans, Partial Differential Equations. American Mathematical Society (2010). [Google Scholar]
- L. Feng, A.C. Antoulas and P. Benner, Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems. ESAIM: M2AN 51 (2017) 2127–2158. [EDP Sciences] [Google Scholar]
- I.V. Gosea and A.C. Antoulas, Data-driven model order reduction of quadratic-bilinear systems. Numer. Linear Algebra App. 25 (2018). [CrossRef] [PubMed] [Google Scholar]
- M.A. Grepl and A.T. Patera, A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. ESAIM: M2AN 39 (2005) 157–181. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- S. Gugercin and A.C. Antoulas, A survey of model reduction by balanced truncation and some new results. Int. J. Control 77 (2004) 748–766. [CrossRef] [Google Scholar]
- B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Delivery 14 (1999) 1052–1061. [Google Scholar]
- B. Haasdonk and M. Ohlberger, Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: M2AN 42 (2008) 277–302. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- B. Haasdonk and M. Ohlberger, Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline/online decomposition. Math. Comput. Modell. Dyn. Syst. 17 (2011) 145–161. [Google Scholar]
- B. Haasdonk, M. Ohlberger and G. Rozza, A reduced basis method for evolution schemes with parameter-dependent explicit operators. Electron. Trans. Numer. Anal. 32 (2008) 145–161. [Google Scholar]
- J.S. Hesthaven, G. Rozza and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. Springer International Publishing (2016). [Google Scholar]
- D. Huynh, G. Rozza, S. Sen and A. Patera, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf–sup stability constants. C.R. Math. 345 (2007) 473–478. [Google Scholar]
- A.C. Ionita and A.C. Antoulas, Data-driven parametrized model reduction in the Loewner framework. SIAM J. Sci. Comput. 36 (2014) A984–A1007. [Google Scholar]
- A. Janon, M. Nodet and C. Prieur, Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values. ESAIM: M2AN 47 (2013) 317–348. [CrossRef] [EDP Sciences] [Google Scholar]
- J.-N. Juang and R.S. Pappa, An eigensystem realization algorithm for modal parameter identification and model reduction. J. Guidance Control Dyn. 8 (1985) 620–627. [Google Scholar]
- B. Kramer and A.A. Gorodetsky, System identification via CUR-factored Hankel approximation. SIAM J. Sci. Comput. 40 (2018) A848–A866. [Google Scholar]
- J.N. Kutz, S.L. Brunton, B.W. Brunton and J.L. Proctor, Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems. SIAM (2016). [Google Scholar]
- L. Ljung, System identification: theory for the user, 2nd edition. Prentice Hall Information and System Sciences Series. Prentice Hall PTR (1999). [Google Scholar]
- M. Mohri, A. Rostamizadeh and A. Talwalkar, Foundations of Machine Learning. MIT Press (2012). [Google Scholar]
- N.-C. Nguyen, G. Rozza and A.T. Patera, Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation. Calcolo 46 (2009) 157–185. [Google Scholar]
- B. Peherstorfer, Sampling low-dimensional markovian dynamics for preasymptotically recovering reduced models from data with operator inference. SIAM J. Sci. Comput. 42 (2020) A3489–A3515. [Google Scholar]
- B. Peherstorfer and K. Willcox, Dynamic data-driven reduced-order models. Comput. Methods Appl. Mech. Eng. 291 (2015) 21–41. [Google Scholar]
- B. Peherstorfer and K. Willcox, Data-driven operator inference for nonintrusive projection-based model reduction. Comput. Methods Appl. Mech. Eng. 306 (2016) 196–215. [Google Scholar]
- C. Prud’homme, D.V. Rovas, K. Veroy, L. Machiels, Y. Maday, A.T. Patera and G. Turinici, Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods. J. Fluids Eng. 124 (2001) 70–80. [Google Scholar]
- E. Qian, B. Kramer, B. Peherstorfer and K. Willcox, Lift & learn: Physics-informed machine learning for large-scale nonlinear dynamical systems. Phys. D: Nonlinear Phenomena 406 (2020) 132401. [Google Scholar]
- A. Quarteroni, G. Rozza and A. Manzoni, Certified reduced basis approximation for parametrized partial differential equations and applications. J. Math. Ind. 1 (2011) 3. [Google Scholar]
- C. Rowley, I. Mezić, S. Bagheri, P. Schlatter and D. Henningson, Spectral analysis of nonlinear flows. J. Fluid Mech. 641 (2009) 115–127. [Google Scholar]
- G. Rozza, D. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15 (2008) 1–47. [Google Scholar]
- P. Schmid, Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656 (2010) 5–28. [Google Scholar]
- P. Schmid and J. Sesterhenn, Dynamic mode decomposition of numerical and experimental data. In: Bull. Amer. Phys. Soc., 61st APS Meeting. American Physical Society (2008) 208. [Google Scholar]
- A. Schmidt and B. Haasdonk, Reduced basis approximation of large scale parametric algebraic Riccati equations. ESAIM: COCV 24 (2018) 129–151. [EDP Sciences] [Google Scholar]
- K. Smetana, O. Zahm and A.T. Patera, Randomized residual-based error estimators for parametrized equations. SIAM J. Sci. Comput. 41 (2019) A900–A926. [Google Scholar]
- V. Thomee, Galerkin Finite Element Methods for Parabolic Problems. Springer, Berlin Heidelberg (2006). [Google Scholar]
- J.H. Tu, C.W. Rowley, D.M. Luchtenburg, S.L. Brunton and J.N. Kutz, On dynamic mode decomposition: theory and applications. J. Comput. Dyn. 1 (2014) 391–421. [Google Scholar]
- K. Veroy and A.T. Patera, Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Int. J. Numer. Methods Fluids 47 (2005) 773–788. [Google Scholar]
- K. Veroy, C. Prudhomme, D. Rovas and A.T. Patera, A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations. In: 16th AIAA Computational Fluid Dynamics Conference, Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics (2003). [Google Scholar]
- K. Veroy, D.V. Rovas and A.T. Patera, A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations: “convex inverse” bound conditioners. ESAIM: COCV 8 (2002) 1007–1028. [CrossRef] [EDP Sciences] [Google Scholar]
- D. Wirtz, D.C. Sorensen and B. Haasdonk, A posteriori error estimation for DEIM reduced nonlinear dynamical systems. SIAM J. Sci. Comput. 36 (2014) A311–A338. [Google Scholar]
- Y. Zhang, L. Feng, S. Li and P. Benner, An efficient output error estimation for model order reduction of parametrized evolution equations. SIAM J. Sci. Comput. 37 (2015) B910–B936. [Google Scholar]
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