Edit Profile (opens in new tab) Willcox, Karen E. Co-Author Distance Author ID: willcox.karen-e Published as: Willcox, Karen; Willcox, K.; Willcox, Karen E.; Willcox, K. E. more...less Documents Indexed: 80 Publications since 1997, including 11 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 97 Co-Authors with 76 Joint Publications 2,658 Co-Co-Authors all top 5 Co-Authors 4 single-authored 18 Peherstorfer, Benjamin 11 Krämer, Boris 8 Ghattas, Omar N. 6 Marzouk, Youssef M. 5 Lieberman, Chad 4 Cui, Tiangang 4 Gunzburger, Max D. 4 Qian, Elizabeth 3 Allaire, Douglas 3 Benner, Peter 3 Chaudhuri, Anirban 3 Geelen, Rudy J. M. 3 Gugercin, Serkan 3 Kapteyn, Michael G. 3 Khodabakhshi, Parisa 3 Lam, Remi R. 3 Tenorio, Luis 3 Wright, Stephen J. 2 Amaral, Sergio 2 Balzano, Laura 2 Bui-Thanh, Tan 2 Farcas, Ionut-Gabriel 2 Fidkowski, Krzysztof J. 2 Garg, Vikram V. 2 Heinkenschloss, Matthias 2 Khoo, Boo Cheong 2 Marques, Alexandre Noll 2 McQuarrie, Shane A. 2 Swischuk, Renee 2 van Bloemen Waanders, Bart G. 2 Zimmermann, Ralf 1 Astrid, Patricia 1 Avron, Haim 1 Backx, Ton A. C. P. M. 1 Bashir, O. 1 Biegler, Lorenz T. 1 Biros, George 1 Buffoni, M. 1 Bungartz, Hans-Joachim 1 Butnaru, Daniel 1 Choi, Youngsoo 1 Cohen, Albert 1 Croci, Matteo 1 Degroote, Joris 1 Du, Xiaosong 1 Ehre, Max 1 Galbally, D. 1 Goyal, Pawan 1 Grepl, Martin A. 1 Gundevia, Rayomand P. 1 Guo, Mengwu 1 Hill, Judith C. 1 Horesh, Lior 1 Hormuth, David A. II 1 Huang, Cheng 1 Huynh, Dinh Bao Phuong 1 Keyes, David Elliot 1 Knezevic, David J. 1 Lassaux, Guillaume 1 Li, Harriet 1 Liao, Qifeng 1 Lim, Kian-Meng 1 Lima, Ernesto A. B. F. 1 Lorenzo, Guillermo 1 Mainini, Laura 1 Mallick, Bani K. 1 Manzoni, Andrea 1 March, Andrew 1 Mariani, Stefano 1 Martins, Joaquim R. R. A. 1 McBane, Sean 1 Megretski, Alexandre 1 Munipalli, Ramakanth 1 My-Ha, D. 1 Ng, Leo W. T. 1 Norton, Matthew D. 1 Ohlberger, Mario 1 O’Leary-Roseberry, Thomas 1 O’Malley, Daniel 1 Papaioannou, Iason 1 Pash, Graham 1 Pretorius, Jacob V. R. 1 Royset, Johannes O. 1 Spantini, Alessio 1 Straub, Daniel 1 Takhtaganov, Timur 1 Tezzele, Marco 1 Torzoni, Matteo 1 Veroy, Karen 1 Vesselinov, Velimir V. 1 Vierendeels, Jan 1 Villa, Umberto E. 1 Waanders, Bart van Bloemen 1 Weiland, Siep 1 Wu, Chengyue 1 Yankeelov, Thomas E. 1 Zahm, Olivier all top 5 Serials 16 SIAM Journal on Scientific Computing 12 Computer Methods in Applied Mechanics and Engineering 7 International Journal for Numerical Methods in Engineering 4 Computers and Fluids 4 Journal of Computational Physics 4 SIAM Review 3 SIAM/ASA Journal on Uncertainty Quantification 2 International Journal for Numerical Methods in Fluids 1 Automatica 1 IEEE Transactions on Automatic Control 1 Numerische Mathematik 1 Physica D 1 Applied Mathematics Letters 1 SIAM Journal on Matrix Analysis and Applications 1 Communications in Statistics. Theory and Methods 1 International Journal of Computational Fluid Dynamics 1 SIAM Journal on Applied Dynamical Systems 1 Structural and Multidisciplinary Optimization 1 Acta Numerica 1 Computational Science & Engineering 1 Statistics and Computing 1 International Journal for Uncertainty Quantification all top 5 Fields 46 Numerical analysis (65-XX) 28 Statistics (62-XX) 18 Systems theory; control (93-XX) 15 Partial differential equations (35-XX) 14 Fluid mechanics (76-XX) 7 Mechanics of deformable solids (74-XX) 6 Computer science (68-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Operations research, mathematical programming (90-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Probability theory and stochastic processes (60-XX) 3 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Approximations and expansions (41-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 63 Publications have been cited 2,268 times in 1,237 Documents Cited by ▼ Year ▼ A survey of projection-based model reduction methods for parametric dynamical systems. Zbl 1339.37089 Benner, Peter; Gugercin, Serkan; Willcox, Karen 393 2015 Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Zbl 1458.65003 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 146 2018 Missing point estimation in models described by proper orthogonal decomposition. Zbl 1367.93110 Astrid, Patricia; Weiland, Siep; Willcox, Karen; Backx, Ton 142 2008 Model reduction and approximation. Theory and algorithms. Zbl 1378.65010 126 2017 Model reduction for large-scale systems with high-dimensional parametric input space. Zbl 1196.37127 Bui-Thanh, T.; Willcox, K.; Ghattas, O. 120 2008 Data-driven operator inference for nonintrusive projection-based model reduction. Zbl 1436.93062 Peherstorfer, Benjamin; Willcox, Karen 90 2016 Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition. Zbl 1160.76394 Willcox, K. 83 2006 Online adaptive model reduction for nonlinear systems via low-rank updates. Zbl 1323.65102 Peherstorfer, Benjamin; Willcox, Karen 75 2015 Localized discrete empirical interpolation method. Zbl 1290.65080 Peherstorfer, Benjamin; Butnaru, Daniel; Willcox, Karen; Bungartz, Hans-Joachim 75 2014 Parameter and state model reduction for large-scale statistical inverse problems. Zbl 1217.65123 Lieberman, Chad; Willcox, Karen; Ghattas, Omar 75 2010 Nonlinear model reduction for uncertainty quantification in large-scale inverse problems. Zbl 1183.76837 Galbally, D.; Fidkowski, K.; Willcox, K.; Ghattas, O. 69 2010 Goal-oriented, model-constrained optimization for reduction of large-scale systems. Zbl 1123.65081 Bui-Thanh, T.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B. 67 2007 Data-driven model reduction for the Bayesian solution of inverse problems. Zbl 1352.65445 Cui, Tiangang; Marzouk, Youssef M.; Willcox, Karen E. 61 2015 Dynamic data-driven reduced-order models. Zbl 1425.65205 Peherstorfer, Benjamin; Willcox, Karen 52 2015 Optimal model management for multifidelity Monte Carlo estimation. Zbl 1351.65009 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 50 2016 Projection-based model reduction: formulations for physics-based machine learning. Zbl 1411.65061 Swischuk, Renee; Mainini, Laura; Peherstorfer, Benjamin; Willcox, Karen 46 2019 Lift & learn: physics-informed machine learning for large-scale nonlinear dynamical systems. Zbl 1493.62512 Qian, Elizabeth; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen 43 2020 Multifidelity approaches for optimization under uncertainty. Zbl 1352.74230 Ng, Leo W. T.; Willcox, Karen E. 41 2014 Multifidelity importance sampling. Zbl 1426.62087 Peherstorfer, Benjamin; Cui, Tiangang; Marzouk, Youssef; Willcox, Karen 36 2016 Interpolation among reduced-order matrices to obtain parameterized models for design, optimization and probabilistic analysis. Zbl 1188.65110 Degroote, Joris; Vierendeels, Jan; Willcox, Karen 36 2010 Hessian-based model reduction for large-scale systems with initial-condition inputs. Zbl 1195.76311 Bashir, O.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B.; Hill, J. 34 2008 Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction. Zbl 1349.65189 Cui, Tiangang; Marzouk, Youssef; Willcox, Karen 27 2016 Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms. Zbl 1506.93015 Benner, Peter; Goyal, Pawan; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen 27 2020 Large-scale inverse problems and quantification of uncertainty. Zbl 1203.62002 27 2011 Geometric subspace updates with applications to online adaptive nonlinear model reduction. Zbl 1383.65034 Zimmermann, Ralf; Peherstorfer, Benjamin; Willcox, Karen 26 2018 Data-driven reduced model construction with time-domain Loewner models. Zbl 1448.65087 Peherstorfer, Benjamin; Gugercin, Serkan; Willcox, Karen 25 2017 Learning physics-based models from data: perspectives from inverse problems and model reduction. Zbl 1520.65043 Ghattas, Omar; Willcox, Karen 20 2021 An accelerated greedy missing point estimation procedure. Zbl 1348.65045 Zimmermann, R.; Willcox, K. 18 2016 A certified trust region reduced basis approach to PDE-constrained optimization. Zbl 1377.35078 Qian, Elizabeth; Grepl, Martin; Veroy, Karen; Willcox, Karen 17 2017 Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation. Zbl 1394.35493 Peherstorfer, Benjamin; Kramer, Boris; Willcox, Karen 16 2018 Multifidelity Monte Carlo estimation of variance and sensitivity indices. Zbl 1394.62175 Qian, Elizabeth; Peherstorfer, Benjamin; O’Malley, Daniel; Vesselinov, Velimir V.; Willcox, Karen 14 2018 Fourier series for accurate, stable, reduced-order models in large-scale linear applications. Zbl 1088.37050 Willcox, K.; Megretski, A. 13 2005 Convergence analysis of multifidelity Monte Carlo estimation. Zbl 1394.35492 Peherstorfer, Benjamin; Gunzburger, Max; Willcox, Karen 11 2018 Goal-oriented optimal approximations of Bayesian linear inverse problems. Zbl 1373.15027 Spantini, Alessio; Cui, Tiangang; Willcox, Karen; Tenorio, Luis; Marzouk, Youssef 11 2017 An Arnoldi approach for generation of reduced-order models for turbomachinery. Zbl 1059.76057 Willcox, K.; Peraire, J.; White, J. 10 2002 Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models. Zbl 1376.93020 Peherstorfer, Benjamin; Kramer, Boris; Willcox, Karen 10 2017 A domain decomposition approach for uncertainty analysis. Zbl 1327.35464 Liao, Qifeng; Willcox, Karen 9 2015 A decomposition-based approach to uncertainty analysis of feed-forward multicomponent systems. Zbl 1352.93016 Amaral, Sergio; Allaire, Douglas; Willcox, Karen 9 2014 Multifidelity dimension reduction via active subspaces. Zbl 07194366 Lam, Remi R.; Zahm, Olivier; Marzouk, Youssef M.; Willcox, Karen E. 9 2020 Conditional-value-at-risk estimation via reduced-order models. Zbl 1405.35263 Heinkenschloss, Matthias; Kramer, Boris; Takhtaganov, Timur; Willcox, Karen 8 2018 Goal-oriented inference: approach, linear theory, and application to advection diffusion. Zbl 1273.35303 Lieberman, Chad; Willcox, Karen 7 2013 Constrained multifidelity optimization using model calibration. Zbl 1274.74286 March, Andrew; Willcox, Karen 7 2012 Operator inference for non-intrusive model reduction with quadratic manifolds. Zbl 07644207 Geelen, Rudy; Wright, Stephen; Willcox, Karen 7 2023 Model reduction of an actively controlled supersonic diffuser. Zbl 1129.76352 Willcox, Karen; Lassaux, Guillaume 6 2005 Real-time optimization using proper orthogonal decomposition: free surface shape prediction due to underwater bubble dynamics. Zbl 1177.76069 My-Ha, D.; Lim, K. M.; Khoo, B. C.; Willcox, K. 6 2007 Non-intrusive data-driven model reduction for differential-algebraic equations derived from lifting transformations. Zbl 1507.65135 Khodabakhshi, Parisa; Willcox, Karen E. 6 2022 Multifidelity probability estimation via fusion of estimators. Zbl 1453.62513 Kramer, Boris; Marques, Alexandre Noll; Peherstorfer, Benjamin; Villa, Umberto; Willcox, Karen 6 2019 Goal-oriented inference: approach, linear theory, and application to advection diffusion. Zbl 1250.62058 Lieberman, Chad; Willcox, Karen 5 2012 Bayesian operator inference for data-driven reduced-order modeling. Zbl 1507.65105 Guo, Mengwu; McQuarrie, Shane A.; Willcox, Karen E. 5 2022 Hessian-based model reduction: large-scale inversion and prediction. Zbl 1431.65155 Lieberman, C.; Fidkowski, K.; Willcox, K.; Waanders, B. van Bloemen 5 2013 Data-driven physics-based digital twins via a library of component-based reduced-order models. Zbl 07767894 Kapteyn, M. G.; Knezevic, D. J.; Huynh, D. B. P.; Tran, M.; Willcox, K. E. 5 2022 A mathematical and computational framework for multifidelity design and analysis with computer models. Zbl 07612593 Allaire, Douglas; Willcox, Karen 4 2014 Learning high-dimensional parametric maps via reduced basis adaptive residual networks. Zbl 1507.68273 O’Leary-Roseberry, Thomas; Du, Xiaosong; Chaudhuri, Anirban; Martins, Joaquim R. R. A.; Willcox, Karen; Ghattas, Omar 4 2022 Reduced operator inference for nonlinear partial differential equations. Zbl 1509.65101 Qian, Elizabeth; Farcaş, Ionuţ-Gabriel; Willcox, Karen 4 2022 Optimal \(L_2\)-norm empirical importance weights for the change of probability measure. Zbl 1505.62028 Amaral, Sergio; Allaire, Douglas; Willcox, Karen 3 2017 Feedback control for systems with uncertain parameters using online-adaptive reduced models. Zbl 1369.93212 Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen 3 2017 Nonlinear goal-oriented Bayesian inference: application to carbon capture and storage. Zbl 1429.62711 Lieberman, Chad; Willcox, Karen 3 2014 Balanced truncation model reduction for lifted nonlinear systems. Zbl 1504.93045 Kramer, Boris; Willcox, Karen 3 2022 A multifidelity method for a nonlocal diffusion model. Zbl 1524.35206 Khodabakhshi, Parisa; Willcox, Karen E.; Gunzburger, Max 3 2021 Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models. Zbl 1507.74323 McBane, Sean; Choi, Youngsoo; Willcox, Karen 3 2022 Krylov projection framework for Fourier model reduction. Zbl 1138.93017 Gugercin, Serkan; Willcox, Karen 3 2008 Model adaptivity for goal-oriented inference using adjoints. Zbl 1439.74502 Li, Harriet; Garg, Vikram V.; Willcox, Karen 2 2018 Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference. Zbl 1521.35022 McQuarrie, Shane A.; Khodabakhshi, Parisa; Willcox, Karen E. 1 2023 Operator inference for non-intrusive model reduction with quadratic manifolds. Zbl 07644207 Geelen, Rudy; Wright, Stephen; Willcox, Karen 7 2023 Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference. Zbl 1521.35022 McQuarrie, Shane A.; Khodabakhshi, Parisa; Willcox, Karen E. 1 2023 Non-intrusive data-driven model reduction for differential-algebraic equations derived from lifting transformations. Zbl 1507.65135 Khodabakhshi, Parisa; Willcox, Karen E. 6 2022 Bayesian operator inference for data-driven reduced-order modeling. Zbl 1507.65105 Guo, Mengwu; McQuarrie, Shane A.; Willcox, Karen E. 5 2022 Data-driven physics-based digital twins via a library of component-based reduced-order models. Zbl 07767894 Kapteyn, M. G.; Knezevic, D. J.; Huynh, D. B. P.; Tran, M.; Willcox, K. E. 5 2022 Learning high-dimensional parametric maps via reduced basis adaptive residual networks. Zbl 1507.68273 O’Leary-Roseberry, Thomas; Du, Xiaosong; Chaudhuri, Anirban; Martins, Joaquim R. R. A.; Willcox, Karen; Ghattas, Omar 4 2022 Reduced operator inference for nonlinear partial differential equations. Zbl 1509.65101 Qian, Elizabeth; Farcaş, Ionuţ-Gabriel; Willcox, Karen 4 2022 Balanced truncation model reduction for lifted nonlinear systems. Zbl 1504.93045 Kramer, Boris; Willcox, Karen 3 2022 Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models. Zbl 1507.74323 McBane, Sean; Choi, Youngsoo; Willcox, Karen 3 2022 Learning physics-based models from data: perspectives from inverse problems and model reduction. Zbl 1520.65043 Ghattas, Omar; Willcox, Karen 20 2021 A multifidelity method for a nonlocal diffusion model. Zbl 1524.35206 Khodabakhshi, Parisa; Willcox, Karen E.; Gunzburger, Max 3 2021 Lift & learn: physics-informed machine learning for large-scale nonlinear dynamical systems. Zbl 1493.62512 Qian, Elizabeth; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen 43 2020 Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms. Zbl 1506.93015 Benner, Peter; Goyal, Pawan; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen 27 2020 Multifidelity dimension reduction via active subspaces. Zbl 07194366 Lam, Remi R.; Zahm, Olivier; Marzouk, Youssef M.; Willcox, Karen E. 9 2020 Projection-based model reduction: formulations for physics-based machine learning. Zbl 1411.65061 Swischuk, Renee; Mainini, Laura; Peherstorfer, Benjamin; Willcox, Karen 46 2019 Multifidelity probability estimation via fusion of estimators. Zbl 1453.62513 Kramer, Boris; Marques, Alexandre Noll; Peherstorfer, Benjamin; Villa, Umberto; Willcox, Karen 6 2019 Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Zbl 1458.65003 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 146 2018 Geometric subspace updates with applications to online adaptive nonlinear model reduction. Zbl 1383.65034 Zimmermann, Ralf; Peherstorfer, Benjamin; Willcox, Karen 26 2018 Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation. Zbl 1394.35493 Peherstorfer, Benjamin; Kramer, Boris; Willcox, Karen 16 2018 Multifidelity Monte Carlo estimation of variance and sensitivity indices. Zbl 1394.62175 Qian, Elizabeth; Peherstorfer, Benjamin; O’Malley, Daniel; Vesselinov, Velimir V.; Willcox, Karen 14 2018 Convergence analysis of multifidelity Monte Carlo estimation. Zbl 1394.35492 Peherstorfer, Benjamin; Gunzburger, Max; Willcox, Karen 11 2018 Conditional-value-at-risk estimation via reduced-order models. Zbl 1405.35263 Heinkenschloss, Matthias; Kramer, Boris; Takhtaganov, Timur; Willcox, Karen 8 2018 Model adaptivity for goal-oriented inference using adjoints. Zbl 1439.74502 Li, Harriet; Garg, Vikram V.; Willcox, Karen 2 2018 Model reduction and approximation. Theory and algorithms. Zbl 1378.65010 126 2017 Data-driven reduced model construction with time-domain Loewner models. Zbl 1448.65087 Peherstorfer, Benjamin; Gugercin, Serkan; Willcox, Karen 25 2017 A certified trust region reduced basis approach to PDE-constrained optimization. Zbl 1377.35078 Qian, Elizabeth; Grepl, Martin; Veroy, Karen; Willcox, Karen 17 2017 Goal-oriented optimal approximations of Bayesian linear inverse problems. Zbl 1373.15027 Spantini, Alessio; Cui, Tiangang; Willcox, Karen; Tenorio, Luis; Marzouk, Youssef 11 2017 Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models. Zbl 1376.93020 Peherstorfer, Benjamin; Kramer, Boris; Willcox, Karen 10 2017 Optimal \(L_2\)-norm empirical importance weights for the change of probability measure. Zbl 1505.62028 Amaral, Sergio; Allaire, Douglas; Willcox, Karen 3 2017 Feedback control for systems with uncertain parameters using online-adaptive reduced models. Zbl 1369.93212 Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen 3 2017 Data-driven operator inference for nonintrusive projection-based model reduction. Zbl 1436.93062 Peherstorfer, Benjamin; Willcox, Karen 90 2016 Optimal model management for multifidelity Monte Carlo estimation. Zbl 1351.65009 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 50 2016 Multifidelity importance sampling. Zbl 1426.62087 Peherstorfer, Benjamin; Cui, Tiangang; Marzouk, Youssef; Willcox, Karen 36 2016 Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction. Zbl 1349.65189 Cui, Tiangang; Marzouk, Youssef; Willcox, Karen 27 2016 An accelerated greedy missing point estimation procedure. Zbl 1348.65045 Zimmermann, R.; Willcox, K. 18 2016 A survey of projection-based model reduction methods for parametric dynamical systems. Zbl 1339.37089 Benner, Peter; Gugercin, Serkan; Willcox, Karen 393 2015 Online adaptive model reduction for nonlinear systems via low-rank updates. Zbl 1323.65102 Peherstorfer, Benjamin; Willcox, Karen 75 2015 Data-driven model reduction for the Bayesian solution of inverse problems. Zbl 1352.65445 Cui, Tiangang; Marzouk, Youssef M.; Willcox, Karen E. 61 2015 Dynamic data-driven reduced-order models. Zbl 1425.65205 Peherstorfer, Benjamin; Willcox, Karen 52 2015 A domain decomposition approach for uncertainty analysis. Zbl 1327.35464 Liao, Qifeng; Willcox, Karen 9 2015 Localized discrete empirical interpolation method. Zbl 1290.65080 Peherstorfer, Benjamin; Butnaru, Daniel; Willcox, Karen; Bungartz, Hans-Joachim 75 2014 Multifidelity approaches for optimization under uncertainty. Zbl 1352.74230 Ng, Leo W. T.; Willcox, Karen E. 41 2014 A decomposition-based approach to uncertainty analysis of feed-forward multicomponent systems. Zbl 1352.93016 Amaral, Sergio; Allaire, Douglas; Willcox, Karen 9 2014 A mathematical and computational framework for multifidelity design and analysis with computer models. Zbl 07612593 Allaire, Douglas; Willcox, Karen 4 2014 Nonlinear goal-oriented Bayesian inference: application to carbon capture and storage. Zbl 1429.62711 Lieberman, Chad; Willcox, Karen 3 2014 Goal-oriented inference: approach, linear theory, and application to advection diffusion. Zbl 1273.35303 Lieberman, Chad; Willcox, Karen 7 2013 Hessian-based model reduction: large-scale inversion and prediction. Zbl 1431.65155 Lieberman, C.; Fidkowski, K.; Willcox, K.; Waanders, B. van Bloemen 5 2013 Constrained multifidelity optimization using model calibration. Zbl 1274.74286 March, Andrew; Willcox, Karen 7 2012 Goal-oriented inference: approach, linear theory, and application to advection diffusion. Zbl 1250.62058 Lieberman, Chad; Willcox, Karen 5 2012 Large-scale inverse problems and quantification of uncertainty. Zbl 1203.62002 27 2011 Parameter and state model reduction for large-scale statistical inverse problems. Zbl 1217.65123 Lieberman, Chad; Willcox, Karen; Ghattas, Omar 75 2010 Nonlinear model reduction for uncertainty quantification in large-scale inverse problems. Zbl 1183.76837 Galbally, D.; Fidkowski, K.; Willcox, K.; Ghattas, O. 69 2010 Interpolation among reduced-order matrices to obtain parameterized models for design, optimization and probabilistic analysis. Zbl 1188.65110 Degroote, Joris; Vierendeels, Jan; Willcox, Karen 36 2010 Missing point estimation in models described by proper orthogonal decomposition. Zbl 1367.93110 Astrid, Patricia; Weiland, Siep; Willcox, Karen; Backx, Ton 142 2008 Model reduction for large-scale systems with high-dimensional parametric input space. Zbl 1196.37127 Bui-Thanh, T.; Willcox, K.; Ghattas, O. 120 2008 Hessian-based model reduction for large-scale systems with initial-condition inputs. Zbl 1195.76311 Bashir, O.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B.; Hill, J. 34 2008 Krylov projection framework for Fourier model reduction. Zbl 1138.93017 Gugercin, Serkan; Willcox, Karen 3 2008 Goal-oriented, model-constrained optimization for reduction of large-scale systems. Zbl 1123.65081 Bui-Thanh, T.; Willcox, K.; Ghattas, O.; van Bloemen Waanders, B. 67 2007 Real-time optimization using proper orthogonal decomposition: free surface shape prediction due to underwater bubble dynamics. Zbl 1177.76069 My-Ha, D.; Lim, K. M.; Khoo, B. C.; Willcox, K. 6 2007 Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition. Zbl 1160.76394 Willcox, K. 83 2006 Fourier series for accurate, stable, reduced-order models in large-scale linear applications. Zbl 1088.37050 Willcox, K.; Megretski, A. 13 2005 Model reduction of an actively controlled supersonic diffuser. Zbl 1129.76352 Willcox, Karen; Lassaux, Guillaume 6 2005 An Arnoldi approach for generation of reduced-order models for turbomachinery. Zbl 1059.76057 Willcox, K.; Peraire, J.; White, J. 10 2002 all cited Publications top 5 cited Publications all top 5 Cited by 2,086 Authors 46 Benner, Peter 43 Willcox, Karen E. 36 Peherstorfer, Benjamin 29 Rozza, Gianluigi 26 Gugercin, Serkan 22 Carlberg, Kevin T. 20 Ghattas, Omar N. 20 Marzouk, Youssef M. 19 Chen, Peng 19 Hesthaven, Jan S. 19 Manzoni, Andrea 18 Kutz, J. Nathan 17 Brunton, Steven L. 17 Feng, Lihong 17 Iliescu, Traian 16 Farhat, Charbel H. 16 Krämer, Boris 14 Haasdonk, Bernard 13 Cui, Tiangang 13 Jiang, Yaolin 13 Navon, Ionel Michael 13 Quarteroni, Alfio M. 13 San, Omer 11 Choi, Youngsoo 11 Gosea, Ion Victor 11 Narayan, Akil C. 11 Stabile, Giovanni 11 Wang, Zhu 10 Beattie, Christopher A. 10 Goyal, Pawan 10 Lin, Guang 9 Amsallem, David 9 Chinesta, Francisco 9 Nouy, Anthony 9 Soize, Christian 8 Alla, Alessandro 8 Antoulas, Athanasios C. 8 Cueto, Elias 8 Kirby, Robert M. II 8 Ohlberger, Mario 8 Yano, Masayuki 8 Zahr, Matthew J. 8 Zimmermann, Ralf 7 Barone, Matthew F. 7 Doostan, Alireza 7 Drmač, Zlatko 7 Fang, Fangxin 7 Gunzburger, Max D. 7 Karasözen, Bülent 7 Karniadakis, George Em 7 Nguyen, Ngoc Cuong 7 Pulch, Roland 7 Sun, Xiang 7 Zhang, Zhiwen 6 Babaee, Hessam 6 Bui-Thanh, Tan 6 Bungartz, Hans-Joachim 6 Chaturantabut, Saifon 6 Eberhard, Peter 6 Fresca, Stefania 6 Girolami, Mark A. 6 Guo, Mengwu 6 Heinkenschloss, Matthias 6 Iollo, Angelo 6 Jakeman, John Davis 6 Kalashnikova, Irina 6 Koutsourelakis, Phaedon-Stelios 6 Papaioannou, Iason 6 Parish, Eric J. 6 Patera, Anthony T. 6 Saibaba, Arvind Krishna 6 Taddei, Tommaso 6 Ullmann, Elisabeth 6 Uzunca, Murat 6 Vega, José Manuel 6 Veroy, Karen 6 Volkwein, Stefan 5 Abisset-Chavanne, Emmanuelle 5 Aguado, Jose Vicente 5 Ballarin, Francesco 5 Bordas, Stéphane Pierre Alain 5 Borggaard, Jeff T. 5 de Sturler, Eric 5 Dolgov, Sergey V. 5 Duraisamy, Karthik 5 Farcas, Ionut-Gabriel 5 Geraci, Gianluca 5 Ghanem, Roger G. 5 Gorodetsky, Alex Arkady 5 Hess, Martin Wilfried 5 Huerta, Antonio 5 Lanteri, Stéphane 5 Li, Jinglai 5 Li, Kun 5 Li, Liang 5 Luo, Zhendong 5 Maday, Yvon 5 Mamonov, Alexander V. 5 Mou, Changhong 5 Mula, Olga ...and 1,986 more Authors all top 5 Cited in 159 Serials 184 Computer Methods in Applied Mechanics and Engineering 179 Journal of Computational Physics 111 SIAM Journal on Scientific Computing 48 International Journal for Numerical Methods in Engineering 45 Advances in Computational Mathematics 45 SIAM/ASA Journal on Uncertainty Quantification 38 Journal of Scientific Computing 32 Computational Mechanics 26 Computers and Fluids 18 Applied Mathematical Modelling 17 Journal of Computational and Applied Mathematics 15 Inverse Problems 15 Journal of Fluid Mechanics 14 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 13 Applied Mathematics and Computation 13 Multiscale Modeling & Simulation 12 Computers & Mathematics with Applications 12 SIAM Journal on Applied Dynamical Systems 10 Automatica 10 Physica D 10 SIAM Journal on Matrix Analysis and Applications 8 Applied Numerical Mathematics 8 Communications in Computational Physics 7 International Journal for Numerical Methods in Fluids 7 Numerical Methods for Partial Differential Equations 7 International Journal of Computational Fluid Dynamics 7 Computational Geosciences 7 Acta Numerica 7 GAMM-Mitteilungen 6 Journal of the Franklin Institute 6 Mathematics of Computation 6 Mathematics and Computers in Simulation 6 Mathematical and Computer Modelling of Dynamical Systems 6 Optimization and Engineering 6 Archives of Computational Methods in Engineering 6 Inverse Problems and Imaging 6 SIAM Journal on Imaging Sciences 6 Statistics and Computing 5 Systems & Control Letters 5 International Journal of Computer Mathematics 4 Journal of Mathematical Analysis and Applications 4 SIAM Journal on Numerical Analysis 4 SIAM Review 4 SIAM Journal on Optimization 4 ETNA. Electronic Transactions on Numerical Analysis 4 Chaos 4 International Journal of Computational Methods 4 Inverse Problems in Science and Engineering 4 International Journal of Systems Science. Principles and Applications of Systems and Integration 3 Numerische Mathematik 3 Journal of Mathematical Imaging and Vision 3 Discrete and Continuous Dynamical Systems 3 Vietnam Journal of Mathematics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Communications in Nonlinear Science and Numerical Simulation 3 Journal of Machine Learning Research (JMLR) 3 Oberwolfach Reports 3 Journal of Mathematics in Industry 3 Journal of Computational Dynamics 3 Electronic Research Archive 2 Computer Physics Communications 2 International Journal of Control 2 Wave Motion 2 SIAM Journal on Control and Optimization 2 Applied Mathematics Letters 2 European Journal of Applied Mathematics 2 Numerical Algorithms 2 Journal of Nonlinear Science 2 Complexity 2 European Journal of Control 2 Multibody System Dynamics 2 Nonlinear Dynamics 2 SIAM Journal on Financial Mathematics 2 GEM - International Journal on Geomathematics 2 Numerical Algebra, Control and Optimization 2 S\(\vec{\text{e}}\)MA Journal 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Mathematics in Engineering 2 SMAI Journal of Computational Mathematics 1 Acta Mechanica 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Transport Theory and Statistical Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Calcolo 1 Journal of the American Statistical Association 1 Journal of Optimization Theory and Applications 1 Journal of Statistical Planning and Inference 1 Meccanica 1 Proceedings of the American Mathematical Society 1 Zeitschrift für Analysis und ihre Anwendungen 1 Circuits, Systems, and Signal Processing 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Journal of Computational Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Machine Learning ...and 59 more Serials all top 5 Cited in 40 Fields 778 Numerical analysis (65-XX) 282 Fluid mechanics (76-XX) 238 Partial differential equations (35-XX) 230 Statistics (62-XX) 190 Systems theory; control (93-XX) 168 Computer science (68-XX) 137 Mechanics of deformable solids (74-XX) 83 Probability theory and stochastic processes (60-XX) 80 Dynamical systems and ergodic theory (37-XX) 70 Calculus of variations and optimal control; optimization (49-XX) 66 Operations research, mathematical programming (90-XX) 60 Biology and other natural sciences (92-XX) 49 Optics, electromagnetic theory (78-XX) 46 Linear and multilinear algebra; matrix theory (15-XX) 34 Approximations and expansions (41-XX) 31 Ordinary differential equations (34-XX) 29 Geophysics (86-XX) 23 Classical thermodynamics, heat transfer (80-XX) 22 Information and communication theory, circuits (94-XX) 18 Statistical mechanics, structure of matter (82-XX) 17 Mechanics of particles and systems (70-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Functional analysis (46-XX) 10 Operator theory (47-XX) 8 General and overarching topics; collections (00-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Differential geometry (53-XX) 5 Special functions (33-XX) 4 Combinatorics (05-XX) 4 Real functions (26-XX) 4 Integral equations (45-XX) 3 Quantum theory (81-XX) 2 Functions of a complex variable (30-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Mathematical logic and foundations (03-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Mathematics education (97-XX) Citations by Year