Free Access
Issue
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
Page(s) 735 - 761
DOI https://doi.org/10.1051/m2an/2021010
Published online 05 May 2021
  1. 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]
  2. 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. [Google Scholar]
  3. Z. Bujanović and D. Kressner, Norm and trace estimation with random rank-one vectors. 42 (2021) 202–223. [Google Scholar]
  4. 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]
  5. J.D. Dixon, Estimating extremal eigenvalues and condition numbers of matrices. SIAM J. Numer. Anal. 20 (1983) 812–814. [Google Scholar]
  6. Z. Drmač, S. Gugercin and C. Beattie, Vector fitting for matrix-valued rational approximation. SIAM J. Sci. Comput. 37 (2015) A2346–A2379. [Google Scholar]
  7. 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]
  8. L. Evans, Partial Differential Equations. American Mathematical Society (2010). [Google Scholar]
  9. 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]
  10. I.V. Gosea and A.C. Antoulas, Data-driven model order reduction of quadratic-bilinear systems. Numer. Linear Algebra App. 25 (2018). [Google Scholar]
  11. 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]
  12. 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. [Google Scholar]
  13. B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting. IEEE Trans. Power Delivery 14 (1999) 1052–1061. [Google Scholar]
  14. 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]
  15. 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]
  16. 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]
  17. J.S. Hesthaven, G. Rozza and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. Springer International Publishing (2016). [Google Scholar]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. B. Kramer and A.A. Gorodetsky, System identification via CUR-factored Hankel approximation. SIAM J. Sci. Comput. 40 (2018) A848–A866. [Google Scholar]
  23. 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]
  24. L. Ljung, System identification: theory for the user, 2nd edition. Prentice Hall Information and System Sciences Series. Prentice Hall PTR (1999). [Google Scholar]
  25. M. Mohri, A. Rostamizadeh and A. Talwalkar, Foundations of Machine Learning. MIT Press (2012). [Google Scholar]
  26. 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]
  27. 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]
  28. B. Peherstorfer and K. Willcox, Dynamic data-driven reduced-order models. Comput. Methods Appl. Mech. Eng. 291 (2015) 21–41. [Google Scholar]
  29. 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]
  30. 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]
  31. 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]
  32. 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]
  33. 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]
  34. 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]
  35. P. Schmid, Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656 (2010) 5–28. [Google Scholar]
  36. 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]
  37. 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]
  38. 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]
  39. V. Thomee, Galerkin Finite Element Methods for Parabolic Problems. Springer, Berlin Heidelberg (2006). [Google Scholar]
  40. 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]
  41. 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]
  42. 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]
  43. 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]
  44. 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]
  45. 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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you