Journal ArticleDOI
Galerkin proper orthogonal decomposition methods for parabolic problems
Karl Kunisch,Stefan Volkwein +1 more
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In this article, error bounds for Galerkin proper orthogonal decomposition (POD) methods for linear and certain non-linear parabolic systems are proved and the resulting error bounds depend on the number of POD basis functions and on the time discretization.Abstract:
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 depend on the number of POD basis functions and on the time discretization. Numerical examples are included.read more
Citations
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Journal ArticleDOI
Development and application of reduced‐order neural network model based on proper orthogonal decomposition for BOD5 monitoring: Active and online prediction
TL;DR: In this paper, a reduced-order neural network model (RONNM) based on proper orthogonal decomposition (POD) was proposed for online prediction of the 5 days biochemical oxygen demand (BOD5).
Dissertation
Reduced order modeling and parameter identification for coupled nonlinear PDE systems
TL;DR: In this paper, a parameter identification problem is formulated as a nonlinear least squares problem and a sensitivity analysis is carried out to investigate the parameter depending behavior of the nonlinear system output.
Journal ArticleDOI
Projection-based reduced order models for flow problems: A variational multiscale approach
Ricardo Reyes,Ramon Codina +1 more
TL;DR: A Variational Multi-Scale stabilized formulation for a general projection-based Reduced Order Model is presented and a mesh based hyper-Reduced Order Model technique and a Petrov–Galerkin projection technique are described.
Journal ArticleDOI
Efficient Space–Time Reduced Order Model for Linear Dynamical Systems in Python Using Less than 120 Lines of Code
TL;DR: This work presents for the first time the derivation of the space-time Petrov-Galerkin projection for linear dynamical systems and its corresponding block structures and derives an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.
References
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Book
Infinite-Dimensional Dynamical Systems in Mechanics and Physics
TL;DR: In this article, the authors give bounds on the number of degrees of freedom and the dimension of attractors of some physical systems, including inertial manifolds and slow manifolds.
Book
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
Book
Galerkin Finite Element Methods for Parabolic Problems
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
Journal ArticleDOI
Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
Karl Kunisch,Stefan Volkwein +1 more
TL;DR: POD is utilized to solve open-loop and closed-loop optimal control problems for the Burgers equation to comparison of POD-based algorithms with numerical results obtained from finite-element discretization of the optimality system.
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Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
Karl Kunisch,Stefan Volkwein +1 more