An adaptive local reduced basis method for solving PDEs with uncertain inputs and evaluating risk

DOI10.1016/j.cma.2018.10.028zbMath1440.65270OpenAlexW2898353227WikidataQ114196946 ScholiaQ114196946MaRDI QIDQ1986786

Zilong Zou, Wilkins Aquino, Drew P. Kouri

Publication date: 9 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://www.osti.gov/biblio/1485450

zbMATH Keywords

stochastic partial differential equationa posteriori error estimationadaptive samplingconditional value-at-riskcoherent risk measurereduced basis

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75)

Related Items

A Locally Adapted Reduced-Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems, Reduced Order Model Hessian Approximations in Newton Methods for Optimal Control, Reduced order modeling for elliptic problems with high contrast diffusion coefficients, Conditional-Value-at-Risk Estimation via Reduced-Order Models, Adaptive Reduced-Order Model Construction for Conditional Value-at-Risk Estimation, An Interior-Point Approach for Solving Risk-Averse PDE-Constrained Optimization Problems with Coherent Risk Measures, Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold, Nonlinear methods for model reduction, Nonlinear approximation spaces for inverse problems

Cites Work

• Unnamed Item
• Unnamed Item
• Reduced basis techniques for stochastic problems
• Comparison between reduced basis and stochastic collocation methods for elliptic problems
• A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient
• An adaptive Monte Carlo algorithm for computing mixed logit estimators
• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations
• An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations
• Dimension-adaptive tensor-product quadrature
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• Sparse grid collocation schemes for stochastic natural convection problems
• Certified reduced basis approximation for parametrized partial differential equations and applications
• A method for solving stochastic equations by reduced order models and local approximations
• Accurate and efficient evaluation of failure probability for partial different equations with random input data
• Error-bounds for finite element method
• Sparse-grid, reduced-basis Bayesian inversion
• Coherent Measures of Risk
• The complexity of the matrix eigenproblem
• A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
• A Review of Unified A Posteriori Finite Element Error Control
• Response Statistics for Random Heterogeneous Microstructures
• The ROMES Method for Statistical Modeling of Reduced-Order-Model Error
• Data-driven model reduction for the Bayesian solution of inverse problems
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
• Reduced Basis Methods for Uncertainty Quantification
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Inexact Objective Function Evaluations in a Trust-Region Algorithm for PDE-Constrained Optimization under Uncertainty
• An Overview of the Discontinuous Petrov Galerkin Method
• A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data
• High-Order Collocation Methods for Differential Equations with Random Inputs
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Solution of stochastic partial differential equations using Galerkin finite element techniques