Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1547704
- Grant/Contract Number:
- CBET-1508713; ACI-1550593; W911NF-15-2-0121; SC0009286; SC0010518
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Name: Journal of Computational Physics Journal Volume: 385 Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
Citation Formats
Chen, Peng, Villa, Umberto, and Ghattas, Omar. Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.01.047.
Chen, Peng, Villa, Umberto, & Ghattas, Omar. Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty. United States. https://doi.org/10.1016/j.jcp.2019.01.047
Chen, Peng, Villa, Umberto, and Ghattas, Omar. Wed .
"Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty". United States. https://doi.org/10.1016/j.jcp.2019.01.047.
@article{osti_1547704,
title = {Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty},
author = {Chen, Peng and Villa, Umberto and Ghattas, Omar},
abstractNote = {},
doi = {10.1016/j.jcp.2019.01.047},
journal = {Journal of Computational Physics},
number = C,
volume = 385,
place = {United States},
year = {Wed May 01 00:00:00 EDT 2019},
month = {Wed May 01 00:00:00 EDT 2019}
}
Free Publicly Available Full Text
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https://doi.org/10.1016/j.jcp.2019.01.047
https://doi.org/10.1016/j.jcp.2019.01.047
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Cited by: 19 works
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Works referenced in this record:
Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
journal, January 2012
- Tiesler, Hanne; Kirby, Robert M.; Xiu, Dongbin
- SIAM Journal on Control and Optimization, Vol. 50, Issue 5
Progressive construction of a parametric reduced-order model for PDE-constrained optimization: PDE-CONSTRAINED OPTIMIZATION USING A PROGRESSIVELY CONSTRUCTED ROM
journal, December 2014
- Zahr, Matthew J.; Farhat, Charbel
- International Journal for Numerical Methods in Engineering, Vol. 102, Issue 5
Weighted Reduced Basis Method for Stochastic Optimal Control Problems with Elliptic PDE Constraint
journal, January 2014
- Chen, Peng; Quarteroni, Alfio
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 2, Issue 1
A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized $\ell_0$-Sparsification
journal, January 2014
- Alexanderian, Alen; Petra, Noemi; Stadler, Georg
- SIAM Journal on Scientific Computing, Vol. 36, Issue 5
Goal-oriented, model-constrained optimization for reduction of large-scale systems
journal, June 2007
- Bui-Thanh, T.; Willcox, K.; Ghattas, O.
- Journal of Computational Physics, Vol. 224, Issue 2
Analysis of the Hessian for inverse scattering problems. Part III: Inverse medium scattering of electromagnetic waves in three dimensions
journal, January 2013
- Bui-Thanh, Tan; Ghattas, Omar
- Inverse Problems & Imaging, Vol. 7, Issue 4
Sparse, adaptive Smolyak quadratures for Bayesian inverse problems
journal, May 2013
- Schillings, Claudia; Schwab, Christoph
- Inverse Problems, Vol. 29, Issue 6
A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors
journal, January 2015
- Bui-Thanh, Tan; Ghattas, Omar
- Inverse Problems & Imaging, Vol. 9, Issue 1
Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
journal, April 2011
- Avron, Haim; Toledo, Sivan
- Journal of the ACM, Vol. 58, Issue 2
Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs
journal, December 2011
- Hou, L. S.; Lee, J.; Manouzi, H.
- Journal of Mathematical Analysis and Applications, Vol. 384, Issue 1
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
journal, January 2012
- Martin, James; Wilcox, Lucas C.; Burstedde, Carsten
- SIAM Journal on Scientific Computing, Vol. 34, Issue 3
Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk
journal, January 2016
- Kouri, D. P.; Surowiec, T. M.
- SIAM Journal on Optimization, Vol. 26, Issue 1
A-optimal encoding weights for nonlinear inverse problems, with application to the Helmholtz inverse problem
journal, June 2017
- Crestel, Benjamin; Alexanderian, Alen; Stadler, Georg
- Inverse Problems, Vol. 33, Issue 7
Optimal Control of Two- and Three-Dimensional Incompressible Navier–Stokes Flows
journal, September 1997
- Ghattas, Omar; Bark, Jai-Hyeong
- Journal of Computational Physics, Vol. 136, Issue 2
Error Estimates of Stochastic Optimal Neumann Boundary Control Problems
journal, January 2011
- Gunzburger, Max D.; Lee, Hyung-Chun; Lee, Jangwoon
- SIAM Journal on Numerical Analysis, Vol. 49, Issue 4
Block-Diagonal Preconditioning for Optimal Control Problems Constrained by PDEs with Uncertain Inputs
journal, January 2016
- Benner, Peter; Onwunta, Akwum; Stoll, Martin
- SIAM Journal on Matrix Analysis and Applications, Vol. 37, Issue 2
Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen-Loève expansion: RANDOMIZED ALGORITHMS FOR GHEP
journal, November 2015
- Saibaba, Arvind K.; Lee, Jonghyun; Kitanidis, Peter K.
- Numerical Linear Algebra with Applications, Vol. 23, Issue 2
Optimal control with stochastic PDE constraints and uncertain controls
journal, March 2012
- Rosseel, Eveline; Wells, Garth N.
- Computer Methods in Applied Mechanics and Engineering, Vol. 213-216
Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs
journal, January 2013
- Kunoth, Angela; Schwab, Christoph
- SIAM Journal on Control and Optimization, Vol. 51, Issue 3
Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations
journal, January 2013
- Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi
- SIAM Journal on Numerical Analysis, Vol. 51, Issue 5
Efficient shape optimization for certain and uncertain aerodynamic design
journal, July 2011
- Schillings, Claudia; Schmidt, Stephan; Schulz, Volker
- Computers & Fluids, Vol. 46, Issue 1
Theory and Applications of Robust Optimization
journal, January 2011
- Bertsimas, Dimitris; Brown, David B.; Caramanis, Constantine
- SIAM Review, Vol. 53, Issue 3
Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations
journal, February 2015
- Negri, Federico; Manzoni, Andrea; Rozza, Gianluigi
- Computers & Mathematics with Applications, Vol. 69, Issue 4
Hessian-based model reduction for large-scale systems with initial-condition inputs
journal, February 2008
- Bashir, O.; Willcox, K.; Ghattas, O.
- International Journal for Numerical Methods in Engineering, Vol. 73, Issue 6
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach: Link between Gaussian Fields and Gaussian Markov Random Fields
journal, August 2011
- Lindgren, Finn; Rue, Håvard; Lindström, Johan
- Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 73, Issue 4
Multifidelity approaches for optimization under uncertainty: MULTIFIDELITY APPROACHES FOR OPTIMIZATION UNDER UNCERTAINTY
journal, September 2014
- Ng, Leo W. T.; Willcox, Karen E.
- International Journal for Numerical Methods in Engineering, Vol. 100, Issue 10
High-dimensional integration: The quasi-Monte Carlo way
journal, April 2013
- Dick, Josef; Kuo, Frances Y.; Sloan, Ian H.
- Acta Numerica, Vol. 22
A Posteriori Error Estimation for Reduced Order Solutions of Parametrized Parabolic Optimal Control Problems
journal, September 2014
- Kärcher, Mark; Grepl, Martin A.
- ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 48, Issue 6
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
journal, January 2015
- Benner, Peter; Gugercin, Serkan; Willcox, Karen
- SIAM Review, Vol. 57, Issue 4
Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems
journal, December 2017
- Chen, Peng; Villa, Umberto; Ghattas, Omar
- Computer Methods in Applied Mechanics and Engineering, Vol. 327
Sparse Adaptive Tensor Galerkin Approximations of Stochastic PDE-Constrained Control Problems
journal, January 2016
- Kunoth, Angela; Schwab, Christoph
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 4, Issue 1
Sparse quadrature for high-dimensional integration with Gaussian measure
journal, March 2018
- Chen, Peng
- ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 52, Issue 2
Reduced Basis Methods for Uncertainty Quantification
journal, January 2017
- Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 5, Issue 1
Improved Bounds on Sample Size for Implicit Matrix Trace Estimators
journal, September 2014
- Roosta-Khorasani, Farbod; Ascher, Uri
- Foundations of Computational Mathematics, Vol. 15, Issue 5
Hessian-Based Sampling for High-Dimensional Model Reduction
journal, January 2019
- Chen, Peng; Ghattas, Omar
- International Journal for Uncertainty Quantification, Vol. 9, Issue 2
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
journal, January 2011
- Halko, N.; Martinsson, P. G.; Tropp, J. A.
- SIAM Review, Vol. 53, Issue 2
Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
journal, January 2018
- Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max
- SIAM Review, Vol. 60, Issue 3
Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations
journal, January 2017
- Alexanderian, Alen; Petra, Noemi; Stadler, Georg
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 5, Issue 1
Investigation of the influence of the Reynolds number on a plane jet using direct numerical simulation
journal, December 2003
- Klein, M.; Sadiki, A.; Janicka, J.
- International Journal of Heat and Fluid Flow, Vol. 24, Issue 6
A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
journal, January 2013
- Bui-Thanh, Tan; Ghattas, Omar; Martin, James
- SIAM Journal on Scientific Computing, Vol. 35, Issue 6
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations: Application to Transport and Continuum Mechanics
journal, May 2008
- Rozza, G.; Huynh, D. B. P.; Patera, A. T.
- Archives of Computational Methods in Engineering, Vol. 15, Issue 3
A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems, Part II: Stochastic Newton MCMC with Application to Ice Sheet Flow Inverse Problems
journal, January 2014
- Petra, Noemi; Martin, James; Stadler, Georg
- SIAM Journal on Scientific Computing, Vol. 36, Issue 4
Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations
journal, January 2011
- Flath, H. P.; Wilcox, L. C.; Akçelik, V.
- SIAM Journal on Scientific Computing, Vol. 33, Issue 1
On the treatment of distributed uncertainties in PDE-constrained optimization
journal, October 2010
- Borzì, A.; Schulz, V.; Schillings, C.
- GAMM-Mitteilungen, Vol. 33, Issue 2
Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations
journal, July 2015
- Chen, Peng; Quarteroni, Alfio; Rozza, Gianluigi
- Numerische Mathematik, Vol. 133, Issue 1
Inexact Objective Function Evaluations in a Trust-Region Algorithm for PDE-Constrained Optimization under Uncertainty
journal, January 2014
- Kouri, D. P.; Heinkenschloss, M.; Ridzal, D.
- SIAM Journal on Scientific Computing, Vol. 36, Issue 6
Certified Reduced Basis Methods for Parametrized Distributed Elliptic Optimal Control Problems with Control Constraints
journal, January 2016
- Bader, Eduard; Kärcher, Mark; Grepl, Martin A.
- SIAM Journal on Scientific Computing, Vol. 38, Issue 6
Weak imposition of Dirichlet boundary conditions in fluid mechanics
journal, January 2007
- Bazilevs, Y.; Hughes, T. J. R.
- Computers & Fluids, Vol. 36, Issue 1
A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
journal, January 2013
- Kouri, D. P.; Heinkenschloss, M.; Ridzal, D.
- SIAM Journal on Scientific Computing, Vol. 35, Issue 4
Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet
journal, September 2015
- Isaac, Tobin; Petra, Noemi; Stadler, Georg
- Journal of Computational Physics, Vol. 296
Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
journal, June 2013
- Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio
- ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 47, Issue 4
Higher Order Quasi--Monte Carlo Integration for Holomorphic, Parametric Operator Equations
journal, January 2016
- Dick, Josef; Le Gia, Quoc T.; Schwab, Christoph
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 4, Issue 1
Reduced Basis Method for Parametrized Elliptic Optimal Control Problems
journal, January 2013
- Negri, Federico; Rozza, Gianluigi; Manzoni, Andrea
- SIAM Journal on Scientific Computing, Vol. 35, Issue 5
Multilevel Monte Carlo Analysis for Optimal Control of Elliptic PDEs with Random Coefficients
journal, January 2017
- Ali, Ahmad Ahmad; Ullmann, Elisabeth; Hinze, Michael
- SIAM/ASA Journal on Uncertainty Quantification, Vol. 5, Issue 1
A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems
journal, January 2016
- Alexanderian, Alen; Petra, Noemi; Stadler, Georg
- SIAM Journal on Scientific Computing, Vol. 38, Issue 1