McQuarrie, Shane A.; Khodabakhshi, Parisa; Willcox, Karen E. Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference. (English) Zbl 1521.35022 SIAM J. Sci. Comput. 45, No. 4, A1917-A1946 (2023). MSC: 35B30 35R30 65F22 PDFBibTeX XMLCite \textit{S. A. McQuarrie} et al., SIAM J. Sci. Comput. 45, No. 4, A1917--A1946 (2023; Zbl 1521.35022) Full Text: DOI arXiv
Kramer, Boris; Willcox, Karen Balanced truncation model reduction for lifted nonlinear systems. (English) Zbl 1504.93045 Beattie, Christopher (ed.) et al., Realization and model reduction of dynamical systems. A festschrift in honor of the 70th birthday of Thanos Antoulas. Cham: Springer. 157-174 (2022). MSC: 93B11 93C10 93B17 PDFBibTeX XMLCite \textit{B. Kramer} and \textit{K. Willcox}, in: Realization and model reduction of dynamical systems. A festschrift in honor of the 70th birthday of Thanos Antoulas. Cham: Springer. 157--174 (2022; Zbl 1504.93045) Full Text: DOI arXiv
Qian, Elizabeth; Farcaş, Ionuţ-Gabriel; Willcox, Karen Reduced operator inference for nonlinear partial differential equations. (English) Zbl 1509.65101 SIAM J. Sci. Comput. 44, No. 4, A1934-A1959 (2022). Reviewer: Hussein Fakih (Nabatieh) MSC: 65M60 68T05 65Z05 62J15 62J05 62J07 35Q30 PDFBibTeX XMLCite \textit{E. Qian} et al., SIAM J. Sci. Comput. 44, No. 4, A1934--A1959 (2022; Zbl 1509.65101) Full Text: DOI arXiv
Khodabakhshi, Parisa; Willcox, Karen E. Non-intrusive data-driven model reduction for differential-algebraic equations derived from lifting transformations. (English) Zbl 1507.65135 Comput. Methods Appl. Mech. Eng. 389, Article ID 114296, 20 p. (2022). MSC: 65L80 PDFBibTeX XMLCite \textit{P. Khodabakhshi} and \textit{K. E. Willcox}, Comput. Methods Appl. Mech. Eng. 389, Article ID 114296, 20 p. (2022; Zbl 1507.65135) Full Text: DOI
Ghattas, Omar; Willcox, Karen Learning physics-based models from data: perspectives from inverse problems and model reduction. (English) Zbl 1520.65043 Acta Numerica 30, 445-554 (2021). MSC: 65K10 65L09 65M32 62F15 86A04 PDFBibTeX XMLCite \textit{O. Ghattas} and \textit{K. Willcox}, Acta Numerica 30, 445--554 (2021; Zbl 1520.65043) Full Text: DOI
Qian, Elizabeth; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen Lift & learn: physics-informed machine learning for large-scale nonlinear dynamical systems. (English) Zbl 1493.62512 Physica D 406, Article ID 132401, 10 p. (2020). MSC: 62M09 35K58 37C15 PDFBibTeX XMLCite \textit{E. Qian} et al., Physica D 406, Article ID 132401, 10 p. (2020; Zbl 1493.62512) Full Text: DOI arXiv
Benner, Peter; Goyal, Pawan; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms. (English) Zbl 1506.93015 Comput. Methods Appl. Mech. Eng. 372, Article ID 113433, 17 p. (2020). MSC: 93B11 93C05 93C20 65M99 35K58 35K67 37M10 PDFBibTeX XMLCite \textit{P. Benner} et al., Comput. Methods Appl. Mech. Eng. 372, Article ID 113433, 17 p. (2020; Zbl 1506.93015) Full Text: DOI arXiv
Swischuk, Renee; Mainini, Laura; Peherstorfer, Benjamin; Willcox, Karen Projection-based model reduction: formulations for physics-based machine learning. (English) Zbl 1411.65061 Comput. Fluids 179, 704-717 (2019). MSC: 65F15 68T05 PDFBibTeX XMLCite \textit{R. Swischuk} et al., Comput. Fluids 179, 704--717 (2019; Zbl 1411.65061) Full Text: DOI
Heinkenschloss, Matthias; Kramer, Boris; Takhtaganov, Timur; Willcox, Karen Conditional-value-at-risk estimation via reduced-order models. (English) Zbl 1405.35263 SIAM/ASA J. Uncertain. Quantif. 6, 1395-1423 (2018). MSC: 35R60 62H12 91G60 91G80 65Y20 91B30 PDFBibTeX XMLCite \textit{M. Heinkenschloss} et al., SIAM/ASA J. Uncertain. Quantif. 6, 1395--1423 (2018; Zbl 1405.35263) Full Text: DOI
Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max Survey of multifidelity methods in uncertainty propagation, inference, and optimization. (English) Zbl 1458.65003 SIAM Rev. 60, No. 3, 550-591 (2018). MSC: 65-02 62-02 49-02 PDFBibTeX XMLCite \textit{B. Peherstorfer} et al., SIAM Rev. 60, No. 3, 550--591 (2018; Zbl 1458.65003) Full Text: DOI arXiv
Qian, Elizabeth; Peherstorfer, Benjamin; O’Malley, Daniel; Vesselinov, Velimir V.; Willcox, Karen Multifidelity Monte Carlo estimation of variance and sensitivity indices. (English) Zbl 1394.62175 SIAM/ASA J. Uncertain. Quantif. 6, 683-706 (2018). MSC: 62P30 65C05 PDFBibTeX XMLCite \textit{E. Qian} et al., SIAM/ASA J. Uncertain. Quantif. 6, 683--706 (2018; Zbl 1394.62175) Full Text: DOI
Zimmermann, Ralf; Peherstorfer, Benjamin; Willcox, Karen Geometric subspace updates with applications to online adaptive nonlinear model reduction. (English) Zbl 1383.65034 SIAM J. Matrix Anal. Appl. 39, No. 1, 234-261 (2018). MSC: 65F20 65D18 PDFBibTeX XMLCite \textit{R. Zimmermann} et al., SIAM J. Matrix Anal. Appl. 39, No. 1, 234--261 (2018; Zbl 1383.65034) Full Text: DOI
Peherstorfer, Benjamin; Cui, Tiangang; Marzouk, Youssef; Willcox, Karen Multifidelity importance sampling. (English) Zbl 1426.62087 Comput. Methods Appl. Mech. Eng. 300, 490-509 (2016). MSC: 62F10 65C05 PDFBibTeX XMLCite \textit{B. Peherstorfer} et al., Comput. Methods Appl. Mech. Eng. 300, 490--509 (2016; Zbl 1426.62087) Full Text: DOI
Cui, Tiangang; Marzouk, Youssef; Willcox, Karen Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction. (English) Zbl 1349.65189 J. Comput. Phys. 315, 363-387 (2016). MSC: 65J22 65C05 62F15 PDFBibTeX XMLCite \textit{T. Cui} et al., J. Comput. Phys. 315, 363--387 (2016; Zbl 1349.65189) Full Text: DOI arXiv
Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max Optimal model management for multifidelity Monte Carlo estimation. (English) Zbl 1351.65009 SIAM J. Sci. Comput. 38, No. 5, A3163-A3194 (2016). MSC: 65C60 65C05 62F10 90B50 62P20 PDFBibTeX XMLCite \textit{B. Peherstorfer} et al., SIAM J. Sci. Comput. 38, No. 5, A3163--A3194 (2016; Zbl 1351.65009) Full Text: DOI
Zimmermann, R.; Willcox, K. An accelerated greedy missing point estimation procedure. (English) Zbl 1348.65045 SIAM J. Sci. Comput. 38, No. 5, A2827-A2850 (2016). MSC: 65C60 62F10 65H10 65F15 PDFBibTeX XMLCite \textit{R. Zimmermann} and \textit{K. Willcox}, SIAM J. Sci. Comput. 38, No. 5, A2827--A2850 (2016; Zbl 1348.65045) Full Text: DOI
Peherstorfer, Benjamin; Willcox, Karen Dynamic data-driven reduced-order models. (English) Zbl 1425.65205 Comput. Methods Appl. Mech. Eng. 291, 21-41 (2015). MSC: 65N50 PDFBibTeX XMLCite \textit{B. Peherstorfer} and \textit{K. Willcox}, Comput. Methods Appl. Mech. Eng. 291, 21--41 (2015; Zbl 1425.65205) Full Text: DOI
Cui, Tiangang; Marzouk, Youssef M.; Willcox, Karen E. Data-driven model reduction for the Bayesian solution of inverse problems. (English) Zbl 1352.65445 Int. J. Numer. Methods Eng. 102, No. 5, 966-990 (2015). MSC: 65N21 65C05 PDFBibTeX XMLCite \textit{T. Cui} et al., Int. J. Numer. Methods Eng. 102, No. 5, 966--990 (2015; Zbl 1352.65445) Full Text: DOI arXiv
Benner, Peter; Gugercin, Serkan; Willcox, Karen A survey of projection-based model reduction methods for parametric dynamical systems. (English) Zbl 1339.37089 SIAM Rev. 57, No. 4, 483-531 (2015). MSC: 37M99 35B30 41A05 65K99 93A15 93C05 PDFBibTeX XMLCite \textit{P. Benner} et al., SIAM Rev. 57, No. 4, 483--531 (2015; Zbl 1339.37089) Full Text: DOI Link
Peherstorfer, Benjamin; Willcox, Karen Online adaptive model reduction for nonlinear systems via low-rank updates. (English) Zbl 1323.65102 SIAM J. Sci. Comput. 37, No. 4, A2123-A2150 (2015). MSC: 65M22 35F50 35G50 65N22 PDFBibTeX XMLCite \textit{B. Peherstorfer} and \textit{K. Willcox}, SIAM J. Sci. Comput. 37, No. 4, A2123--A2150 (2015; Zbl 1323.65102) Full Text: DOI Link
Nguyen, V. B.; Buffoni, M.; Willcox, K.; Khoo, B. C. Model reduction for reacting flow applications. (English) Zbl 07512416 Int. J. Comput. Fluid Dyn. 28, No. 3-4, 91-105 (2014). MSC: 80-XX 76-XX PDFBibTeX XMLCite \textit{V. B. Nguyen} et al., Int. J. Comput. Fluid Dyn. 28, No. 3--4, 91--105 (2014; Zbl 07512416) Full Text: DOI
Gugercin, Serkan; Willcox, Karen Krylov projection framework for Fourier model reduction. (English) Zbl 1138.93017 Automatica 44, No. 1, 209-215 (2008). MSC: 93B11 93B20 93B28 PDFBibTeX XMLCite \textit{S. Gugercin} and \textit{K. Willcox}, Automatica 44, No. 1, 209--215 (2008; Zbl 1138.93017) Full Text: DOI
Bui-Thanh, T.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B. Goal-oriented, model-constrained optimization for reduction of large-scale systems. (English) Zbl 1123.65081 J. Comput. Phys. 224, No. 2, 880-896 (2007). MSC: 65L99 49M27 76M25 PDFBibTeX XMLCite \textit{T. Bui-Thanh} et al., J. Comput. Phys. 224, No. 2, 880--896 (2007; Zbl 1123.65081) Full Text: DOI