An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids

DOI10.1137/18M1220996zbMath1448.65057arXiv1811.00177MaRDI QIDQ5237179

Drew P. Kouri, Matthew J. Zahr, Kevin T. Carlberg

Publication date: 17 October 2019

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.00177

zbMATH Keywords

model order reductionstochastic collocationtrust region methodsadaptive sparse gridsoptimization under uncertaintyincompressible Navier-Stokesgreedy sampling

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Numerical optimization and variational techniques (65K10) Stochastic programming (90C15) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Numerical approximation of high-dimensional functions; sparse grids (65D40)

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Cites Work

• Unnamed Item
• Unnamed Item
• Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations
• Approximation of parametric derivatives by the empirical interpolation method
• Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations
• A method for numerical integration on an automatic computer
• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• Dimension-adaptive tensor-product quadrature
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modeling
• A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods
• Sparse-grid, reduced-basis Bayesian inversion: nonaffine-parametric nonlinear equations
• Sparse-grid, reduced-basis Bayesian inversion
• Non-intrusive reduced order modelling of the Navier-Stokes equations
• Coherent Measures of Risk
• Analysis of Inexact Trust-Region SQP Algorithms
• A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
• Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
• Weighted Reduced Basis Method for Stochastic Optimal Control Problems with Elliptic PDE Constraint
• Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization
• The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
• Trust Region Methods
• Conditional-Value-at-Risk Estimation via Reduced-Order Models
• Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs
• Inexact Objective Function Evaluations in a Trust-Region Algorithm for PDE-Constrained Optimization under Uncertainty
• POD-Galerkin Modeling and Sparse-Grid Collocation for a Natural Convection Problem with Stochastic Boundary Conditions
• A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data
• A Locally Adapted Reduced-Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems