Fetching the paper…
Reading the bibliography…
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations.
D. B. P. Huynh, D. J. Knezevic, Y. Chen, J. S. Hesthaven, A. T. Patera, A natural-norm successive constraint method for inf–sup lower bounds, Computer Methods in Applied Mechanics and Engineering 199 (2010) 1963–1975
1975
Earlier work this paper cites.
A. K. Noor, J. M. Peters, Reduced basis technique for nonlinear analysis of structures, AIAA Journal 18 (4) (1980) 455–462
1980
Earlier work this paper cites.
I. Babuška, A. Miller, The post-processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements, International Journal for Numerical Methods in Engineering 20 (6) (1984) 1085–1109
1984
Earlier work this paper cites.
D. E. Rumelhart, G. E. Hinton, R. J. Williams, Parallel distributed processing: Explorations in the microstructure of cognition, 1986, Ch. Learning Internal Representations by Error Propagation, pp. 318–362
1986
Earlier work this paper cites.
L. Sirovich, Turbulence and the dynamics of coherent structures, Quarterly of Applied Mathematics 45 (1987) 561–590
1987
Earlier work this paper cites.
R. Everson, L. Sirovich, Karhunen–Loève procedure for gappy data, Journal of the Optical Society of America A 12 (8) (1995) 1657–1664
1995
Earlier work this paper cites.
R. Becker, R. Rannacher, Weighted A Posteriori
1996
Earlier work this paper cites.
P. Holmes, J. L. Lumley, G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press, Cambridge, 1996
1996
Earlier work this paper cites.
K. Ito, S. S. Ravindran, A reduced-order method for simulation and control of fluid flows, Journal of Computational Physics 143 (2) (1998) 403–425
1998
Earlier work this paper cites.
R. Rannacher, The dual-weighted-residual method for error control and mesh adaptation in finite element methods, Mathematics of Finite Elements and Applications 99 (1999) 97–115
1999
Earlier work this paper cites.
D. Venditti, D. Darmofal, Adjoint error estimation and grid adaptation for functional outputs: Application to quasi-one-dimensional flow, Journal of Computational Physics 164 (1) (2000) 204–227
2000
Earlier work this paper cites.
N. Alexandrov, R. Lewis, C. Gumbert, L. Green, P. Newman, Approximation and model management in aerodynamic optimization with variable-fidelity models, AIAA Journal of Aircraft 38 (6) (2001) 1093–1101
2001
Earlier work this paper cites.
M. C. Kennedy, A. O’Hagan, Bayesian calibration of computer models, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (3) (2001) 425–464
2001
Earlier work this paper cites.
L. Breiman, Random forests, Machine Learning 45 (1) (2001) 5–32
2001
Earlier work this paper cites.
D. A. Venditti, D. L. Darmofal, Grid adaptation for functional outputs: application to two-dimensional inviscid flows, Journal of Computational Physics 176 (1) (2002) 40–69
2002
Earlier work this paper cites.
M. Heinkenschloss, L. Vicente, Analysis of inexact trust-region SQP algorithms, SIAM Journal on Optimization 12 (2) (2002) 283–302
2002
Earlier work this paper cites.
W. Bangerth, R. Rannacher, Adaptive finite element methods for differential equations, Springer, 2003
2003
Earlier work this paper cites.
M. Meyer, H. Matthies, Efficient model reduction in non-linear dynamics using the Karhunen–Loève expansion and dual-weighted-residual methods, Computational Mechanics 31 (1) (2003) 179–191
2003
Earlier work this paper cites.
D. Higdon, H. Lee, C. Holloman, Markov chain Monte Carlo–based approaches for inference in computationally intensive inverse problems, in: J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith, M. West (Eds.), Bayesian Statistics 7. Proceedings of the Seventh Valencia International Meeting, 2003, pp. 181–197
2003
Earlier work this paper cites.
T. Bui-Thanh, D. Murali, K. Willcox, Proper orthogonal decomposition extensions for parametric applications in compressible aerodynamics, in: 21st AIAA Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics, 2003
2003
Earlier work this paper cites.
M. A. Park, Adjoint-based, three-dimensional error prediction and grid adaptation, AIAA Journal 42 (9) (2004) 1854–1862
2004
Earlier work this paper cites.
M. S. Eldred, A. A. Giunta, S. S. Collis, N. A. Alexandrov, R. M. Lewis, Second-order corrections for surrogate-based optimization with model hierarchies, in: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, American Institute of Aeronautics and Astronautics, 2004
2004
Earlier work this paper cites.
D. Higdon, M. Kennedy, J. C. Cavendish, J. A. Cafeo, R. D. Ryne, Combining field data and computer simulations for calibration and prediction, SIAM Journal on Scientific Computing 26 (2) (2004) 448–466
2004
Earlier work this paper cites.
M. Barrault, Y. Maday, N. C. Nguyen, A. T. Patera, An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathématique Académie des Sciences 339 (9) (2004) 667–672
2004
Cited alongside, same era.
D. A. Knoll, D. E. Keyes, Jacobian-free Newton–Krylov methods: a survey of approaches and applications, Journal of Computational Physics 193 (2) (2004) 357–397
2004
Cited alongside, same era.
D. Venturi, G. E. Karniadakis, Gappy data and reconstruction procedures for flow past a cylinder, Journal of Fluid Mechanics 519 (2004) 315–336
2004
Cited alongside, same era.
T. Bui-Thanh, M. Damodaran, K. Willcox, Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition, AIAA Journal 42 (8) (2004) 1505–1516
2004
Cited alongside, same era.
M. Hinze, M. Kunkel, Residual based sampling in POD model order reduction of drift–diffusion equations in parametrized electrical networks, ZAMM-Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 92 (2) (2012) 91–104
2012
Later among the works it cites.
A. March, K. Willcox, Provably convergent multifidelity optimization algorithm not requiring high-fidelity derivatives, AIAA Journal 50 (5) (2012) 1079–1089
2012
Later among the works it cites.
L. W.-T. Ng, M. Eldred, Multifidelity uncertainty quantification using non-intrusive polynomial chaos and stochastic collocation, in: 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, American Institute of Aeronautics and Astronautics, 2012
2012
Later among the works it cites.
K. Carlberg, C. Farhat, J. Cortial, D. Amsallem, The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows, Journal of Computational Physics 242 (2013) 623–647
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
R. Bos, X. Bombois, P. Van den Hof, Accelerating large-scale non-linear models for monitoring and control using spatial and temporal correlations, Proceedings of the American Control Conference 4 (2004) 3705–3710
2004
Cited alongside, same era.
A. J. Smola, B. Schölkopf, A tutorial on support vector regression, Statistics and Computing 14 (2004) 199–222
2004
Cited alongside, same era.
J. C.-C. Lu, An a posteriori
2005
Cited alongside, same era.
M. Grepl, A. Patera, A posteriori
2005
Cited alongside, same era.
S. E. Gano, J. E. Renaud, B. Sanders, Hybrid variable fidelity optimization by using a kriging-based scaling function, AIAA Journal 43 (11) (2005) 2422–2433
2005
Cited alongside, same era.
D. Huang, T. T. Allen, W. I. Notz, R. A. Miller, Sequential kriging optimization using multiple-fidelity evaluations, Structural and Multidisciplinary Optimization 32 (5) (2006) 369–382
2006
Cited alongside, same era.
C. Rasmussen, C. Williams, Gaussian Processes for Machine Learning, Adaptive computation and machine learning series, University Press Group Limited, 2006
2006
Cited alongside, same era.
P. A. LeGresley, Application of proper orthogonal decomposition (POD) to design decomposition methods, Ph.D. thesis, Stanford University (2006)
2006
Cited alongside, same era.
2013
Later among the works it cites.
L. Buitinck, G. Louppe, M. Blondel, F. Pedregosa, A. Mueller, O. Grisel, V. Niculae, P. Prettenhofer, A. Gramfort, J. Grobler, R. Layton, J. VanderPlas, A. Joly, B. Holt, G. Varoquaux, API design for machine learning software: experiences from the scikit-learn project, in: ECML PKDD Workshop: Languages for Data Mining and Machine Learning, 2013, pp. 108–122
2013
Later among the works it cites.
D. Wirtz, D. C. Sorensen, B. Haasdonk, A-posteriori
2014
Later among the works it cites.
B. A. Freno, P. G. A. Cizmas, A proper orthogonal decomposition method for nonlinear flows with deforming meshes, International Journal of Heat and Fluid Flow 50 (2014) 145–159
2014
Later among the works it cites.
D. Amsallem, M. Zahr, Y. Choi, C. Farhat, Design optimization using hyper-reduced-order models, Structural and Multidisciplinary Optimization 51 (4) (2015) 919–940
2015
Later among the works it cites.
Y. Wu, U. Hetmaniuk, Adaptive training of local reduced bases for unsteady incompressible Navier–Stokes flows, International Journal for Numerical Methods in Engineering 103 (3) (2015) 183–204
2015
Later among the works it cites.
M. J. Zahr, C. Farhat, Progressive construction of a parametric reduced-order model for PDE-constrained optimization, International Journal for Numerical Methods in Engineering 102 (5) (2015) 1111–1135
2015
Later among the works it cites.
K. Carlberg, Adaptive h h -refinement for reduced-order models, International Journal for Numerical Methods in Engineering 102 (5) (2015) 1192–1210
2015
Later among the works it cites.
M. Drohmann, K. Carlberg, The ROMES method for statistical modeling of reduced-order-model error, SIAM/ASA Journal on Uncertainty Quantification 3 (1) (2015) 116–145
2015
Later among the works it cites.
K. Carlberg, J. Ray, B. van Bloemen Waanders, Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting, Computer Methods in Applied Mechanics and Engineering 289 (2015) 79–103
2015
Later among the works it cites.
M. Zahr, Adaptive model reduction to accelerate optimization problems governed by partial differential equations, Ph.D. thesis, Stanford University (2016)
2016
Later among the works it cites.
A. Manzoni, S. Pagani, T. Lassila, Accurate solution of Bayesian inverse uncertainty quantification problems using model and error reduction methods, SIAM/ASA Journal on Uncertainty Quantification 4 (1) (2016) 380–412
2016
Later among the works it cites.
B. Peherstorfer, K. Willcox, Dynamic data-driven model reduction: adapting reduced models from incomplete data, Advanced Modeling and Simulation in Engineering Sciences 3 (1) (2016) 11
2016
Later among the works it cites.
Z. Drmac, S. Gugercin, A new selection operator for the discrete empirical interpolation method—improved a priori
2016
Later among the works it cites.
A. G. Salinger, R. A. Bartlett, A. M. Bradley, Q. Chen, I. P. Demeshko, X. Gao, G. A. Hansen, A. Mota, R. P. Muller, E. Nielsen, J. T. Ostien, R. P. Pawlowski, M. Perego, E. T. Phipps, W. Sun, I. K. Tezaur, Albany: Using component-based design to develop a flexible, generic multiphysics analysis code, International Journal for Multiscale Computational Engineering 14 (4) (2016) 415–438
2016
Later among the works it cites.
S. Pagani, A. Manzoni, A. Quarteroni, Efficient state/parameter estimation in nonlinear unsteady PDEs by a reduced basis ensemble Kalman filter, SIAM/ASA Journal on Uncertainty Quantification 5 (1) (2017) 890–921
2017
Later among the works it cites.
S. Trehan, K. Carlberg, L. J. Durlofsky, Error modeling for surrogates of dynamical systems using machine learning, International Journal for Numerical Methods in Engineering 112 (12) (2017) 1801–1827
2017
Later among the works it cites.
K. Carlberg, M. Barone, H. Antil, Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction, Journal of Computational Physics 330 (2017) 693–734
2017
Later among the works it cites.
A. Moosavi, R. Ştefănescu, A. Sandu, Multivariate predictions of local reduced-order-model errors and dimensions, International Journal for Numerical Methods in Engineering 113 (3) (2018) 512–533
2018
Closest in time.
R. Stefanescu, A. Moosavi, A. Sandu, Parametric domain decomposition for accurate reduced order models: Applications of MP-LROM methodology, Journal of Computational and Applied Mathematics 340 (2018) 629–644
2018
Closest in time.