Galerkin proper orthogonal decomposition methods for parabolic problems
K Kunisch, S Volkwein - Numerische mathematik, 2001 - Springer
In this work error estimates for Galerkin proper orthogonal decomposition (POD) methods for
linear and certain non-linear parabolic systems are proved. The resulting error bounds …
linear and certain non-linear parabolic systems are proved. The resulting error bounds …
[图书][B] Model order reduction for PDE constrained optimization
The optimization and control of systems governed by partial differential equations (PDEs)
usually requires numerous evaluations of the forward problem or the optimality system …
usually requires numerous evaluations of the forward problem or the optimality system …
Enablers for robust POD models
This paper focuses on improving the stability as well as the approximation properties of
reduced order models (ROMs) based on proper orthogonal decomposition (POD). The ROM …
reduced order models (ROMs) based on proper orthogonal decomposition (POD). The ROM …
Proper orthogonal decomposition surrogate models for nonlinear dynamical systems: Error estimates and suboptimal control
M Hinze, S Volkwein - Dimension Reduction of Large-Scale Systems …, 2005 - Springer
Optimal control problems for nonlinear partial differential equations are often hard to tackle
numerically so that the need for developing novel techniques emerges. One such technique …
numerically so that the need for developing novel techniques emerges. One such technique …
Data‐driven model reduction for the Bayesian solution of inverse problems
One of the major challenges in the Bayesian solution of inverse problems governed by
partial differential equations (PDEs) is the computational cost of repeatedly evaluating …
partial differential equations (PDEs) is the computational cost of repeatedly evaluating …
Reduced-order modeling
In recent years, reduced-order modeling techniques have proven to be powerful tools for
various problems in circuit simulation. For example, today, reduction techniques are …
various problems in circuit simulation. For example, today, reduction techniques are …
Adaptive h‐refinement for reduced‐order models
K Carlberg - International Journal for Numerical Methods in …, 2015 - Wiley Online Library
This work presents a method to adaptively refine reduced‐order models a posteriori without
requiring additional full‐order‐model solves. The technique is analogous to mesh‐adaptive …
requiring additional full‐order‐model solves. The technique is analogous to mesh‐adaptive …
Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization
An adaptive approach to using reduced‐order models (ROMs) as surrogates in partial
differential equations (PDE)‐constrained optimization is introduced that breaks the …
differential equations (PDE)‐constrained optimization is introduced that breaks the …
Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models
M Bergmann, L Cordier - Journal of Computational Physics, 2008 - Elsevier
In this paper, optimal control theory is used to minimize the total mean drag for a circular
cylinder wake flow in the laminar regime (Re= 200). The control parameters are the …
cylinder wake flow in the laminar regime (Re= 200). The control parameters are the …
Recursive trust-region methods for multiscale nonlinear optimization
A class of trust-region methods is presented for solving unconstrained nonlinear and
possibly nonconvex discretized optimization problems, like those arising in systems …
possibly nonconvex discretized optimization problems, like those arising in systems …