Hokanson, Jeffrey M.; Magruder, Caleb C. \( \mathcal{H}_2\)-optimal model reduction using projected nonlinear least squares. (English) Zbl 07328659 SIAM J. Sci. Comput. 42, No. 6, A4017-A4045 (2020). MSC: 65 41A20 46E22 90C53 93A15 93C05 93C15 PDF BibTeX XML Cite \textit{J. M. Hokanson} and \textit{C. C. Magruder}, SIAM J. Sci. Comput. 42, No. 6, A4017--A4045 (2020; Zbl 07328659) Full Text: DOI
Parish, Eric J.; Wentland, Christopher R.; Duraisamy, Karthik The adjoint Petrov-Galerkin method for non-linear model reduction. (English) Zbl 1442.76069 Comput. Methods Appl. Mech. Eng. 365, Article ID 112991, 43 p. (2020). MSC: 76M10 65P99 PDF BibTeX XML Cite \textit{E. J. Parish} et al., Comput. Methods Appl. Mech. Eng. 365, Article ID 112991, 43 p. (2020; Zbl 1442.76069) Full Text: DOI
Parish, Eric J.; Carlberg, Kevin T. Time-series machine-learning error models for approximate solutions to parameterized dynamical systems. (English) Zbl 1442.65446 Comput. Methods Appl. Mech. Eng. 365, Article ID 112990, 43 p. (2020). MSC: 65P99 70-08 62M10 62H30 PDF BibTeX XML Cite \textit{E. J. Parish} and \textit{K. T. Carlberg}, Comput. Methods Appl. Mech. Eng. 365, Article ID 112990, 43 p. (2020; Zbl 1442.65446) Full Text: DOI
Etter, Philip A.; Carlberg, Kevin T. Online adaptive basis refinement and compression for reduced-order models via vector-space sieving. (English) Zbl 1442.65338 Comput. Methods Appl. Mech. Eng. 364, Article ID 112931, 54 p. (2020). MSC: 65N22 PDF BibTeX XML Cite \textit{P. A. Etter} and \textit{K. T. Carlberg}, Comput. Methods Appl. Mech. Eng. 364, Article ID 112931, 54 p. (2020; Zbl 1442.65338) Full Text: DOI
Hou, Yunsen; Liu, Cheng; Hu, Haiyan Component-level proper orthogonal decomposition for flexible multibody systems. (English) Zbl 1442.70005 Comput. Methods Appl. Mech. Eng. 361, Article ID 112690, 25 p. (2020). MSC: 70E55 65L60 70-08 PDF BibTeX XML Cite \textit{Y. Hou} et al., Comput. Methods Appl. Mech. Eng. 361, Article ID 112690, 25 p. (2020; Zbl 1442.70005) Full Text: DOI
Alawieh, Leen; Goodman, Jonathan; Bell, John B. Iterative construction of Gaussian process surrogate models for Bayesian inference. (English) Zbl 1437.62105 J. Stat. Plann. Inference 207, 55-72 (2020). MSC: 62F15 60G15 68T05 62P30 PDF BibTeX XML Cite \textit{L. Alawieh} et al., J. Stat. Plann. Inference 207, 55--72 (2020; Zbl 1437.62105) Full Text: DOI
Liao, Qifeng; Li, Jinglai An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems. (English) Zbl 1453.62587 J. Comput. Phys. 396, 364-380 (2019). MSC: 62J10 62C10 65C05 PDF BibTeX XML Cite \textit{Q. Liao} and \textit{J. Li}, J. Comput. Phys. 396, 364--380 (2019; Zbl 1453.62587) Full Text: DOI
Patel, Dhruv; Tibrewala, Raghav; Vega, Adriana; Dong, Li; Hugenberg, Nicholas; Oberai, Assad A. Circumventing the solution of inverse problems in mechanics through deep learning: application to elasticity imaging. (English) Zbl 1441.74084 Comput. Methods Appl. Mech. Eng. 353, 448-466 (2019). MSC: 74G65 PDF BibTeX XML Cite \textit{D. Patel} et al., Comput. Methods Appl. Mech. Eng. 353, 448--466 (2019; Zbl 1441.74084) Full Text: DOI
Freno, Brian A.; Carlberg, Kevin T. Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations. (English) Zbl 1440.65058 Comput. Methods Appl. Mech. Eng. 348, 250-296 (2019). MSC: 65H10 68T05 PDF BibTeX XML Cite \textit{B. A. Freno} and \textit{K. T. Carlberg}, Comput. Methods Appl. Mech. Eng. 348, 250--296 (2019; Zbl 1440.65058) Full Text: DOI
Zou, Zilong; Kouri, Drew; Aquino, Wilkins An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk. (English) Zbl 1440.65270 Comput. Methods Appl. Mech. Eng. 345, 302-322 (2019). MSC: 65N75 PDF BibTeX XML Cite \textit{Z. Zou} et al., Comput. Methods Appl. Mech. Eng. 345, 302--322 (2019; Zbl 1440.65270) Full Text: DOI
Unger, Benjamin; Gugercin, Serkan Kolmogorov \(n\)-widths for linear dynamical systems. (English) Zbl 1439.37028 Adv. Comput. Math. 45, No. 5-6, 2273-2286 (2019). MSC: 37C79 37M21 47B35 PDF BibTeX XML Cite \textit{B. Unger} and \textit{S. Gugercin}, Adv. Comput. Math. 45, No. 5--6, 2273--2286 (2019; Zbl 1439.37028) Full Text: DOI
Dasgupta, Agnimitra; Ghosh, Debraj Failure probability estimation of linear time varying systems by progressive refinement of reduced order models. (English) Zbl 1454.60104 SIAM/ASA J. Uncertain. Quantif. 7, 1007-1028 (2019). MSC: 60H35 34F05 93E03 PDF BibTeX XML Cite \textit{A. Dasgupta} and \textit{D. Ghosh}, SIAM/ASA J. Uncertain. Quantif. 7, 1007--1028 (2019; Zbl 1454.60104) Full Text: DOI
Peherstorfer, Benjamin Multifidelity Monte Carlo estimation with adaptive low-fidelity models. (English) Zbl 1428.35570 SIAM/ASA J. Uncertain. Quantif. 7, 579-603 (2019). MSC: 35Q62 62F25 62-08 65C05 60H35 35R60 PDF BibTeX XML Cite \textit{B. Peherstorfer}, SIAM/ASA J. Uncertain. Quantif. 7, 579--603 (2019; Zbl 1428.35570) Full Text: DOI
Arridge, Simon; Maass, Peter; Öktem, Ozan; Schönlieb, Carola-Bibiane Solving inverse problems using data-driven models. (English) Zbl 1429.65116 Acta Numerica 28, 1-174 (2019). MSC: 65J20 65J22 94A08 65-02 PDF BibTeX XML Cite \textit{S. Arridge} et al., Acta Numerica 28, 1--174 (2019; Zbl 1429.65116) Full Text: DOI
Fung, Samy Wu; Ruthotto, Lars A multiscale method for model order reduction in PDE parameter estimation. (English) Zbl 07006455 J. Comput. Appl. Math. 350, 19-34 (2019). MSC: 65 92 PDF BibTeX XML Cite \textit{S. W. Fung} and \textit{L. Ruthotto}, J. Comput. Appl. Math. 350, 19--34 (2019; Zbl 07006455) Full Text: DOI
Benning, Martin; Burger, Martin Modern regularization methods for inverse problems. (English) Zbl 1431.65080 Acta Numerica 27, 1-111 (2018). MSC: 65J20 65J22 65K10 65-02 94A08 PDF BibTeX XML Cite \textit{M. Benning} and \textit{M. Burger}, Acta Numerica 27, 1--111 (2018; Zbl 1431.65080) Full Text: DOI arXiv
Carracedo Rodriguez, Andrea; Gugercin, Serkan; Borggaard, Jeff Interpolatory model reduction of parameterized bilinear dynamical systems. (English) Zbl 1406.93069 Adv. Comput. Math. 44, No. 6, 1887-1916 (2018). MSC: 93B11 93C10 93C05 41A05 93C15 PDF BibTeX XML Cite \textit{A. Carracedo Rodriguez} et al., Adv. Comput. Math. 44, No. 6, 1887--1916 (2018; Zbl 1406.93069) Full Text: DOI arXiv
Giovanis, D. G.; Shields, M. D. Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations. (English) Zbl 1392.65014 J. Comput. Phys. 364, 393-415 (2018). MSC: 65C30 PDF BibTeX XML Cite \textit{D. G. Giovanis} and \textit{M. D. Shields}, J. Comput. Phys. 364, 393--415 (2018; Zbl 1392.65014) Full Text: DOI
Hampton, Jerrad; Fairbanks, Hillary R.; Narayan, Akil; Doostan, Alireza Practical error bounds for a non-intrusive bi-fidelity approach to parametric/stochastic model reduction. (English) Zbl 1392.62352 J. Comput. Phys. 368, 315-332 (2018). MSC: 62P35 65F30 76M25 35R60 PDF BibTeX XML Cite \textit{J. Hampton} et al., J. Comput. Phys. 368, 315--332 (2018; Zbl 1392.62352) Full Text: DOI
Stuart, Andrew M.; Teckentrup, Aretha L. Posterior consistency for Gaussian process approximations of Bayesian posterior distributions. (English) Zbl 1429.60040 Math. Comput. 87, No. 310, 721-753 (2018). MSC: 60G15 62G08 65D05 65D30 65J22 PDF BibTeX XML Cite \textit{A. M. Stuart} and \textit{A. L. Teckentrup}, Math. Comput. 87, No. 310, 721--753 (2018; Zbl 1429.60040) Full Text: DOI arXiv
Shah, A. A.; Xing, W. W.; Triantafyllidis, V. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models. (English) Zbl 1404.65212 Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2200, Article ID 20160809, 21 p. (2017). MSC: 65M99 35K15 PDF BibTeX XML Cite \textit{A. A. Shah} et al., Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2200, Article ID 20160809, 21 p. (2017; Zbl 1404.65212) Full Text: DOI
Hintermüller, Michael; Rautenberg, Carlos N.; Wu, Tao; Langer, Andreas Optimal selection of the regularization function in a weighted total variation model. II: Algorithm, its analysis and numerical tests. (English) Zbl 1382.94016 J. Math. Imaging Vis. 59, No. 3, 515-533 (2017). MSC: 94A08 68U10 49K20 49K30 49K40 49M37 65K15 PDF BibTeX XML Cite \textit{M. Hintermüller} et al., J. Math. Imaging Vis. 59, No. 3, 515--533 (2017; Zbl 1382.94016) Full Text: DOI
De los Reyes, J. C.; Schönlieb, C.-B.; Valkonen, T. Bilevel parameter learning for higher-order total variation regularisation models. (English) Zbl 1425.94010 J. Math. Imaging Vis. 57, No. 1, 1-25 (2017). MSC: 94A08 68U10 PDF BibTeX XML Cite \textit{J. C. De los Reyes} et al., J. Math. Imaging Vis. 57, No. 1, 1--25 (2017; Zbl 1425.94010) Full Text: DOI arXiv
Carlberg, Kevin; Barone, Matthew; Antil, Harbir Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction. (English) Zbl 1378.65145 J. Comput. Phys. 330, 693-734 (2017). MSC: 65L05 65L60 76M25 PDF BibTeX XML Cite \textit{K. Carlberg} et al., J. Comput. Phys. 330, 693--734 (2017; Zbl 1378.65145) Full Text: DOI arXiv
Ali, Mazen; Steih, Kristina; Urban, Karsten Reduced basis methods with adaptive snapshot computations. (English) Zbl 1379.65087 Adv. Comput. Math. 43, No. 2, 257-294 (2017). Reviewer: Petr Sváček (Praha) MSC: 65N30 35B10 65Y20 65N15 65N12 PDF BibTeX XML Cite \textit{M. Ali} et al., Adv. Comput. Math. 43, No. 2, 257--294 (2017; Zbl 1379.65087) Full Text: DOI
Billaud-Friess, Marie; Nouy, Anthony Dynamical model reduction method for solving parameter-dependent dynamical systems. (English) Zbl 1373.65091 SIAM J. Sci. Comput. 39, No. 4, A1766-A1792 (2017). MSC: 65P99 37M05 65M15 PDF BibTeX XML Cite \textit{M. Billaud-Friess} and \textit{A. Nouy}, SIAM J. Sci. Comput. 39, No. 4, A1766--A1792 (2017; Zbl 1373.65091) Full Text: DOI arXiv
O’Connell, Meghan; Kilmer, Misha E.; de Sturler, Eric; Gugercin, Serkan Computing reduced order models via inner-outer Krylov recycling in diffuse optical tomography. (English) Zbl 1365.65242 SIAM J. Sci. Comput. 39, No. 2, B272-B297 (2017). MSC: 65N21 35R30 65D18 PDF BibTeX XML Cite \textit{M. O'Connell} et al., SIAM J. Sci. Comput. 39, No. 2, B272--B297 (2017; Zbl 1365.65242) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{B. Peherstorfer} et al., Comput. Methods Appl. Mech. Eng. 300, 490--509 (2016; Zbl 1426.62087) Full Text: DOI
Xing, W. W.; Triantafyllidis, V.; Shah, A. A.; Nair, P. B.; Zabaras, N. Manifold learning for the emulation of spatial fields from computational models. (English) Zbl 1373.68340 J. Comput. Phys. 326, 666-690 (2016). MSC: 68T05 35B30 60G15 62H25 68U20 PDF BibTeX XML Cite \textit{W. W. Xing} et al., J. Comput. Phys. 326, 666--690 (2016; Zbl 1373.68340) Full Text: DOI
Oberai, Assad A.; Jagalur-Mohan, Jayanth Approximate optimal projection for reduced-order models. (English) Zbl 1360.65267 Int. J. Numer. Methods Eng. 105, No. 1, 63-80 (2016). MSC: 65N22 65N30 PDF BibTeX XML Cite \textit{A. A. Oberai} and \textit{J. Jagalur-Mohan}, Int. J. Numer. Methods Eng. 105, No. 1, 63--80 (2016; Zbl 1360.65267) Full Text: DOI
Liao, Qifeng; Lin, Guang Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs. (English) Zbl 1349.65684 J. Comput. Phys. 317, 148-164 (2016). MSC: 65N75 62J10 65C50 PDF BibTeX XML Cite \textit{Q. Liao} and \textit{G. Lin}, J. Comput. Phys. 317, 148--164 (2016; Zbl 1349.65684) Full Text: DOI
Hesthaven, Jan S.; Zhang, Shun On the use of ANOVA expansions in reduced basis methods for parametric partial differential equations. (English) Zbl 1352.65508 J. Sci. Comput. 69, No. 1, 292-313 (2016). MSC: 65N30 35J25 35J05 PDF BibTeX XML Cite \textit{J. S. Hesthaven} and \textit{S. Zhang}, J. Sci. Comput. 69, No. 1, 292--313 (2016; Zbl 1352.65508) Full Text: DOI
Goury, Olivier; Amsallem, David; Bordas, Stéphane Pierre Alain; Liu, Wing Kam; Kerfriden, Pierre Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization. (English) Zbl 1398.74053 Comput. Mech. 58, No. 2, 213-234 (2016). MSC: 74E30 74S05 74Q15 74S30 74Q05 PDF BibTeX XML Cite \textit{O. Goury} et al., Comput. Mech. 58, No. 2, 213--234 (2016; Zbl 1398.74053) Full Text: DOI
Ballani, Jonas; Kressner, Daniel Reduced basis methods: from low-rank matrices to low-rank tensors. (English) Zbl 1382.15036 SIAM J. Sci. Comput. 38, No. 4, A2045-A2067 (2016). MSC: 15A69 65F99 PDF BibTeX XML Cite \textit{J. Ballani} and \textit{D. Kressner}, SIAM J. Sci. Comput. 38, No. 4, A2045--A2067 (2016; Zbl 1382.15036) Full Text: DOI
De Los Reyes, J. C.; Schönlieb, C.-B.; Valkonen, T. The structure of optimal parameters for image restoration problems. (English) Zbl 1327.49063 J. Math. Anal. Appl. 434, No. 1, 464-500 (2016). MSC: 49N45 49J45 94A08 PDF BibTeX XML Cite \textit{J. C. De Los Reyes} et al., J. Math. Anal. Appl. 434, No. 1, 464--500 (2016; Zbl 1327.49063) Full Text: DOI
Baiges, Joan; Codina, Ramon; Idelsohn, Sergio Reduced-order subscales for POD models. (English) Zbl 1423.76206 Comput. Methods Appl. Mech. Eng. 291, 173-196 (2015). MSC: 76M10 65M60 76D05 PDF BibTeX XML Cite \textit{J. Baiges} et al., Comput. Methods Appl. Mech. Eng. 291, 173--196 (2015; Zbl 1423.76206) 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 PDF BibTeX XML Cite \textit{B. Peherstorfer} and \textit{K. Willcox}, Comput. Methods Appl. Mech. Eng. 291, 21--41 (2015; Zbl 1425.65205) Full Text: DOI
Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting. (English) Zbl 1425.65073 Comput. Methods Appl. Mech. Eng. 289, 79-103 (2015). MSC: 65L05 PDF BibTeX XML Cite \textit{K. Carlberg} et al., Comput. Methods Appl. Mech. Eng. 289, 79--103 (2015; Zbl 1425.65073) Full Text: DOI arXiv
Cyr, E. C.; Shadid, J. N.; Wildey, T. Towards efficient backward-in-time adjoint computations using data compression techniques. (English) Zbl 1423.76222 Comput. Methods Appl. Mech. Eng. 288, 24-44 (2015). MSC: 76M10 65M60 35Q30 35Q35 65M15 76D05 PDF BibTeX XML Cite \textit{E. C. Cyr} et al., Comput. Methods Appl. Mech. Eng. 288, 24--44 (2015; Zbl 1423.76222) Full Text: DOI
Naets, F.; Croes, J.; Desmet, W. An online coupled state/input/parameter estimation approach for structural dynamics. (English) Zbl 1423.93380 Comput. Methods Appl. Mech. Eng. 283, 1167-1188 (2015). MSC: 93E10 93E11 PDF BibTeX XML Cite \textit{F. Naets} et al., Comput. Methods Appl. Mech. Eng. 283, 1167--1188 (2015; Zbl 1423.93380) Full Text: DOI
Zhang, Yongjin; Feng, Lihong; Li, Suzhou; Benner, Peter Accelerating PDE constrained optimization by the reduced basis method: application to batch chromatography. (English) Zbl 1352.49026 Int. J. Numer. Methods Eng. 104, No. 11, 983-1007 (2015). MSC: 49M15 49J10 65K05 PDF BibTeX XML Cite \textit{Y. Zhang} et al., Int. J. Numer. Methods Eng. 104, No. 11, 983--1007 (2015; Zbl 1352.49026) Full Text: DOI
He, Jiajun; Durlofsky, L. J. Constraint reduction procedures for reduced-order subsurface flow models based on POD-TPWL. (English) Zbl 1352.76112 Int. J. Numer. Methods Eng. 103, No. 1, 1-30 (2015). MSC: 76S05 PDF BibTeX XML Cite \textit{J. He} and \textit{L. J. Durlofsky}, Int. J. Numer. Methods Eng. 103, No. 1, 1--30 (2015; Zbl 1352.76112) Full Text: DOI
Paul-Dubois-Taine, A.; Amsallem, D. An adaptive and efficient greedy procedure for the optimal training of parametric reduced-order models. (English) Zbl 1352.65217 Int. J. Numer. Methods Eng. 102, No. 5, 1262-1292 (2015). MSC: 65L99 PDF BibTeX XML Cite \textit{A. Paul-Dubois-Taine} and \textit{D. Amsallem}, Int. J. Numer. Methods Eng. 102, No. 5, 1262--1292 (2015; Zbl 1352.65217) Full Text: DOI
Zahr, Matthew J.; Farhat, Charbel Progressive construction of a parametric reduced-order model for PDE-constrained optimization. (English) Zbl 1352.49029 Int. J. Numer. Methods Eng. 102, No. 5, 1111-1135 (2015). MSC: 49M25 65N30 PDF BibTeX XML Cite \textit{M. J. Zahr} and \textit{C. Farhat}, Int. J. Numer. Methods Eng. 102, No. 5, 1111--1135 (2015; Zbl 1352.49029) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \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 PDF BibTeX XML Cite \textit{P. Benner} et al., SIAM Rev. 57, No. 4, 483--531 (2015; Zbl 1339.37089) Full Text: DOI
Peherstorfer, Benjamin; Gómez, Pablo; Bungartz, Hans-Joachim Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation. (English) Zbl 1336.91086 Adv. Comput. Math. 41, No. 5, 1365-1389 (2015). MSC: 91G60 65M60 65M22 35Q91 PDF BibTeX XML Cite \textit{B. Peherstorfer} et al., Adv. Comput. Math. 41, No. 5, 1365--1389 (2015; Zbl 1336.91086) Full Text: DOI
Himpe, Christian; Ohlberger, Mario Data-driven combined state and parameter reduction for inverse problems. (English) Zbl 1327.37025 Adv. Comput. Math. 41, No. 5, 1343-1364 (2015). MSC: 37M05 37N40 93A15 PDF BibTeX XML Cite \textit{C. Himpe} and \textit{M. Ohlberger}, Adv. Comput. Math. 41, No. 5, 1343--1364 (2015; Zbl 1327.37025) Full Text: DOI arXiv
Son, Nguyen Thanh; Stykel, Tatjana Model order reduction of parameterized circuit equations based on interpolation. (English) Zbl 1336.93037 Adv. Comput. Math. 41, No. 5, 1321-1342 (2015). MSC: 93B11 65D05 65L80 93C05 65F30 PDF BibTeX XML Cite \textit{N. T. Son} and \textit{T. Stykel}, Adv. Comput. Math. 41, No. 5, 1321--1342 (2015; Zbl 1336.93037) Full Text: DOI
San, Omer; Iliescu, Traian A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation. (English) Zbl 1327.37028 Adv. Comput. Math. 41, No. 5, 1289-1319 (2015). MSC: 37N10 76M25 76F20 76D99 PDF BibTeX XML Cite \textit{O. San} and \textit{T. Iliescu}, Adv. Comput. Math. 41, No. 5, 1289--1319 (2015; Zbl 1327.37028) Full Text: DOI
Hintermüller, Michael; Valkonen, Tuomo; Wu, Tao Limiting aspects of nonconvex \({TV}^{\phi}\) models. (English) Zbl 1328.65064 SIAM J. Imaging Sci. 8, No. 4, 2581-2621 (2015). MSC: 65D18 94A08 PDF BibTeX XML Cite \textit{M. Hintermüller} et al., SIAM J. Imaging Sci. 8, No. 4, 2581--2621 (2015; Zbl 1328.65064) Full Text: DOI arXiv
Elman, Howard C.; Forstall, Virginia Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations. (English) Zbl 06502310 SIAM J. Sci. Comput. 37, No. 5, S177-S194 (2015). MSC: 65N22 65F08 65F10 PDF BibTeX XML Cite \textit{H. C. Elman} and \textit{V. Forstall}, SIAM J. Sci. Comput. 37, No. 5, S177--S194 (2015; Zbl 06502310) Full Text: DOI
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 PDF BibTeX XML Cite \textit{B. Peherstorfer} and \textit{K. Willcox}, SIAM J. Sci. Comput. 37, No. 4, A2123--A2150 (2015; Zbl 1323.65102) Full Text: DOI
de Sturler, Eric; Gugercin, Serkan; Kilmer, Misha E.; Chaturantabut, Saifon; Beattie, Christopher; O’Connell, Meghan Nonlinear parametric inversion using interpolatory model reduction. (English) Zbl 1433.65194 SIAM J. Sci. Comput. 37, No. 3, B495-B517 (2015). MSC: 65M32 65F10 65K10 92C55 PDF BibTeX XML Cite \textit{E. de Sturler} et al., SIAM J. Sci. Comput. 37, No. 3, B495--B517 (2015; Zbl 1433.65194) Full Text: DOI arXiv
Dihlmann, Markus A.; Haasdonk, Bernard Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems. (English) Zbl 1319.49046 Comput. Optim. Appl. 60, No. 3, 753-787 (2015). MSC: 49M30 49M25 49J20 49K20 PDF BibTeX XML Cite \textit{M. A. Dihlmann} and \textit{B. Haasdonk}, Comput. Optim. Appl. 60, No. 3, 753--787 (2015; Zbl 1319.49046) Full Text: DOI
Bui-Thanh, Tan; Ghattas, Omar A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors. (English) Zbl 1347.49045 Inverse Probl. Imaging 9, No. 1, 27-53 (2015). MSC: 49M15 49N45 62F15 49K45 49K20 49K21 90C51 42C40 PDF BibTeX XML Cite \textit{T. Bui-Thanh} and \textit{O. Ghattas}, Inverse Probl. Imaging 9, No. 1, 27--53 (2015; Zbl 1347.49045) Full Text: DOI
Hernández, J. A.; Oliver, J.; Huespe, A. E.; Caicedo, M. A.; Cante, J. C. High-performance model reduction techniques in computational multiscale homogenization. (English) Zbl 1423.74785 Comput. Methods Appl. Mech. Eng. 276, 149-189 (2014). MSC: 74Q05 65N30 74S05 PDF BibTeX XML Cite \textit{J. A. Hernández} et al., Comput. Methods Appl. Mech. Eng. 276, 149--189 (2014; Zbl 1423.74785) Full Text: DOI
Tamarozzi, T.; Heirman, G. H. K.; Desmet, W. An on-line time dependent parametric model order reduction scheme with focus on dynamic stress recovery. (English) Zbl 1295.70001 Comput. Methods Appl. Mech. Eng. 268, 336-358 (2014). MSC: 70-04 70E55 PDF BibTeX XML Cite \textit{T. Tamarozzi} et al., Comput. Methods Appl. Mech. Eng. 268, 336--358 (2014; Zbl 1295.70001) Full Text: DOI
Roderick, Oleg; Anitescu, Mihai; Peet, Yulia Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models. (English) Zbl 1353.65013 Int. J. Comput. Math. 91, No. 4, 748-769 (2014). MSC: 65C60 60G15 62P30 76D05 76M25 62D05 PDF BibTeX XML Cite \textit{O. Roderick} et al., Int. J. Comput. Math. 91, No. 4, 748--769 (2014; Zbl 1353.65013) Full Text: DOI
Carlberg, Kevin; Farhat, Charbel; Cortial, Julien; Amsallem, David The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows. (English) Zbl 1299.76180 J. Comput. Phys. 242, 623-647 (2013). MSC: 76M25 76M10 PDF BibTeX XML Cite \textit{K. Carlberg} et al., J. Comput. Phys. 242, 623--647 (2013; Zbl 1299.76180) Full Text: DOI arXiv
Baiges, Joan; Codina, Ramon; Idelsohn, Sergio A domain decomposition strategy for reduced order models. Application to the incompressible Navier-Stokes equations. (English) Zbl 1286.76028 Comput. Methods Appl. Mech. Eng. 267, 23-42 (2013). MSC: 76D05 65N30 35Q30 PDF BibTeX XML Cite \textit{J. Baiges} et al., Comput. Methods Appl. Mech. Eng. 267, 23--42 (2013; Zbl 1286.76028) Full Text: DOI
Audouze, Christophe; De Vuyst, Florian; Nair, Prasanth B. Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations. (English) Zbl 1274.65270 Numer. Methods Partial Differ. Equations 29, No. 5, 1587-1628 (2013). MSC: 65M60 PDF BibTeX XML Cite \textit{C. Audouze} et al., Numer. Methods Partial Differ. Equations 29, No. 5, 1587--1628 (2013; Zbl 1274.65270) Full Text: DOI
Bui-Thanh, Tan; Demkowicz, Leszek; Ghattas, Omar Constructively well-posed approximation methods with unity inf-sup and continuity constants for partial differential equations. (English) Zbl 1281.65129 Math. Comput. 82, No. 284, 1923-1952 (2013). Reviewer: Roland Pulch (Greifswald) MSC: 65M60 65M12 65M15 35L02 PDF BibTeX XML Cite \textit{T. Bui-Thanh} et al., Math. Comput. 82, No. 284, 1923--1952 (2013; Zbl 1281.65129) Full Text: DOI
Franke, Thomas; Hoppe, Ronald H. W.; Linsenmann, Christopher; Wixforth, Achim Projection based model reduction for optimal design of the time-dependent Stokes system. (English) Zbl 1356.65156 Leugering, Günter (ed.) et al., Constrained optimization and optimal control for partial differential equations. Basel: Birkhäuser (ISBN 978-3-0348-0132-4/hbk; 978-3-0348-0133-1/ebook). ISNM. International Series of Numerical Mathematics 160, 75-98 (2012). MSC: 65K10 49M05 49M15 93A15 65M55 65M60 76Z99 90C06 PDF BibTeX XML Cite \textit{T. Franke} et al., ISNM, Int. Ser. Numer. Math. 160, 75--98 (2012; Zbl 1356.65156) Full Text: DOI
Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi Computational reduction for parametrized PDEs: strategies and applications. (English) Zbl 1432.65171 Milan J. Math. 80, No. 2, 283-309 (2012). MSC: 65N30 35J25 76M10 76D55 76G25 49J20 PDF BibTeX XML Cite \textit{A. Manzoni} et al., Milan J. Math. 80, No. 2, 283--309 (2012; Zbl 1432.65171) Full Text: DOI
Dedè, Luca Reduced basis method and error estimation for parametrized optimal control problems with control constraints. (English) Zbl 1244.65094 J. Sci. Comput. 50, No. 2, 287-305 (2012). Reviewer: Jan Lovíšek (Bratislava) MSC: 65K10 49J20 49N10 49M25 PDF BibTeX XML Cite \textit{L. Dedè}, J. Sci. Comput. 50, No. 2, 287--305 (2012; Zbl 1244.65094) Full Text: DOI
Hinze, M.; Kunkel, M. Residual based sampling in POD model order reduction of drift-diffusion equations in parametrized electrical networks. (English) Zbl 1237.78038 ZAMM, Z. Angew. Math. Mech. 92, No. 2, 91-104 (2012). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M10 82D37 65L60 37N20 78M34 PDF BibTeX XML Cite \textit{M. Hinze} and \textit{M. Kunkel}, ZAMM, Z. Angew. Math. Mech. 92, No. 2, 91--104 (2012; Zbl 1237.78038) Full Text: DOI
Chaturantabut, Saifon; Sorensen, Danny C. Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media. (English) Zbl 1302.76127 Math. Comput. Model. Dyn. Syst. 17, No. 4, 337-353 (2011). MSC: 76M20 76M25 76S05 65M06 76D27 PDF BibTeX XML Cite \textit{S. Chaturantabut} and \textit{D. C. Sorensen}, Math. Comput. Model. Dyn. Syst. 17, No. 4, 337--353 (2011; Zbl 1302.76127) Full Text: DOI
Braconnier, T.; Ferrier, M.; Jouhaud, J.-C.; Montagnac, M.; Sagaut, P. Towards an adaptive POD/SVD surrogate model for aeronautic design. (English) Zbl 1245.76063 Comput. Fluids 40, No. 1, 195-209 (2011). MSC: 76M12 76F50 76N25 PDF BibTeX XML Cite \textit{T. Braconnier} et al., Comput. Fluids 40, No. 1, 195--209 (2011; Zbl 1245.76063) Full Text: DOI
Druskin, V.; Simoncini, V. Adaptive rational Krylov subspaces for large-scale dynamical systems. (English) Zbl 1236.93035 Syst. Control Lett. 60, No. 8, 546-560 (2011). MSC: 93B11 93C05 PDF BibTeX XML Cite \textit{V. Druskin} and \textit{V. Simoncini}, Syst. Control Lett. 60, No. 8, 546--560 (2011; Zbl 1236.93035) Full Text: DOI
Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel Efficient non linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations. (English) Zbl 1235.74351 Int. J. Numer. Methods Eng. 86, No. 2, 155-181 (2011). MSC: 74S30 65N22 PDF BibTeX XML Cite \textit{K. Carlberg} et al., Int. J. Numer. Methods Eng. 86, No. 2, 155--181 (2011; Zbl 1235.74351) Full Text: DOI
Leblond, C.; Allery, C.; Inard, C. An optimal projection method for the reduced-order modeling of incompressible flows. (English) Zbl 1230.76041 Comput. Methods Appl. Mech. Eng. 200, No. 33-36, 2507-2527 (2011). MSC: 76M25 76D05 PDF BibTeX XML Cite \textit{C. Leblond} et al., Comput. Methods Appl. Mech. Eng. 200, No. 33--36, 2507--2527 (2011; Zbl 1230.76041) Full Text: DOI
Tayeb, Shaul; Givoli, Dan Optimal modal reduction of dynamic subsystems: extensions and improvements. (English) Zbl 1217.70017 Int. J. Numer. Methods Eng. 85, No. 1, 1-30 (2011). MSC: 70J10 70-08 PDF BibTeX XML Cite \textit{S. Tayeb} and \textit{D. Givoli}, Int. J. Numer. Methods Eng. 85, No. 1, 1--30 (2011; Zbl 1217.70017) Full Text: DOI
Kalashnikova, I.; Barone, M. F. On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment. (English) Zbl 1202.74123 Int. J. Numer. Methods Eng. 83, No. 10, 1345-1375 (2010). MSC: 74M25 74N15 PDF BibTeX XML Cite \textit{I. Kalashnikova} and \textit{M. F. Barone}, Int. J. Numer. Methods Eng. 83, No. 10, 1345--1375 (2010; Zbl 1202.74123) Full Text: DOI
An, Yu’e; Gu, Chuanqing Model reduction for large-scale dynamical systems via equality constrained least squares. (English) Zbl 1201.65108 J. Comput. Appl. Math. 234, No. 8, 2420-2431 (2010). Reviewer: Nicholas Karampetakis (Thessaloniki) MSC: 65K10 93A15 93E24 93B20 93C80 65F10 PDF BibTeX XML Cite \textit{Y. An} and \textit{C. Gu}, J. Comput. Appl. Math. 234, No. 8, 2420--2431 (2010; Zbl 1201.65108) Full Text: DOI
Weller, J.; Lombardi, E.; Bergmann, M.; Iollo, A. Numerical methods for low-order modeling of fluid flows based on POD. (English) Zbl 1423.76356 Int. J. Numer. Methods Fluids 63, No. 2, 249-268 (2010). MSC: 76M25 35Q30 PDF BibTeX XML Cite \textit{J. Weller} et al., Int. J. Numer. Methods Fluids 63, No. 2, 249--268 (2010; Zbl 1423.76356) Full Text: DOI
Degroote, Joris; Vierendeels, Jan; Willcox, Karen Interpolation among reduced-order matrices to obtain parameterized models for design, optimization and probabilistic analysis. (English) Zbl 1188.65110 Int. J. Numer. Methods Fluids 63, No. 2, 207-230 (2010). MSC: 65L80 35K20 34A09 65D05 65M20 65C05 PDF BibTeX XML Cite \textit{J. Degroote} et al., Int. J. Numer. Methods Fluids 63, No. 2, 207--230 (2010; Zbl 1188.65110) Full Text: DOI
Galbally, D.; Fidkowski, K.; Willcox, K.; Ghattas, O. Nonlinear model reduction for uncertainty quantification in large-scale inverse problems. (English) Zbl 1183.76837 Int. J. Numer. Methods Eng. 81, No. 12, 1581-1608 (2010). MSC: 76M25 76R99 76V05 76M35 PDF BibTeX XML Cite \textit{D. Galbally} et al., Int. J. Numer. Methods Eng. 81, No. 12, 1581--1608 (2010; Zbl 1183.76837) Full Text: DOI
Audouze, C.; De Vuyst, F.; Nair, P. B. Reduced-order modeling of parameterized PDEs using time-space-parameter principal component analysis. (English) Zbl 1176.76059 Int. J. Numer. Methods Eng. 80, No. 8, 1025-1057 (2009). MSC: 76M10 76M12 76R99 PDF BibTeX XML Cite \textit{C. Audouze} et al., Int. J. Numer. Methods Eng. 80, No. 8, 1025--1057 (2009; Zbl 1176.76059) Full Text: DOI
Chen, Yanlai; Hesthaven, Jan S.; Maday, Yvon; Rodríguez, Jerónimo Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell’s problem. (English) Zbl 1181.78019 ESAIM, Math. Model. Numer. Anal. 43, No. 6, 1099-1116 (2009). Reviewer: Teodora-Liliana Rădulescu (Craiova) MSC: 78M25 65N15 65N30 78A25 35Q61 PDF BibTeX XML Cite \textit{Y. Chen} et al., ESAIM, Math. Model. Numer. Anal. 43, No. 6, 1099--1116 (2009; Zbl 1181.78019) Full Text: DOI EuDML
Nguyen, Ngoc-Cuong; Rozza, Gianluigi; Patera, Anthony T. Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation. (English) Zbl 1178.65109 Calcolo 46, No. 3, 157-185 (2009). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65M15 65M60 35Q53 PDF BibTeX XML Cite \textit{N.-C. Nguyen} et al., Calcolo 46, No. 3, 157--185 (2009; Zbl 1178.65109) Full Text: DOI
Weller, J.; Lombardi, E.; Iollo, A. Robust model identification of actuated vortex wakes. (English) Zbl 1157.93012 Physica D 238, No. 4, 416-427 (2009). MSC: 93B30 76D05 65M32 35R30 PDF BibTeX XML Cite \textit{J. Weller} et al., Physica D 238, No. 4, 416--427 (2009; Zbl 1157.93012) Full Text: DOI
Rozza, G.; Huynh, D. B. P.; Patera, A. T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics. (English) Zbl 1304.65251 Arch. Comput. Methods Eng. 15, No. 3, 229-275 (2008). MSC: 65N30 74S05 65N15 76M10 PDF BibTeX XML Cite \textit{G. Rozza} et al., Arch. Comput. Methods Eng. 15, No. 3, 229--275 (2008; Zbl 1304.65251) Full Text: DOI