Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Chaotic dynamics of coherent structures
Proceedings of the eighth annual international conference of the Center for Nonlinear Studies on Advances in fluid turbulence
Reduced-order-based feedback control of the Kuramoto-Sivashinsky equation
Journal of Computational and Applied Mathematics
HIV dynamics: modeling, data analysis, and optimal treatment protocols
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Real-time deformable models of non-linear tissues by model reduction techniques
Computer Methods and Programs in Biomedicine
Computational Optimization and Applications
POD a-posteriori error estimates for linear-quadratic optimal control problems
Computational Optimization and Applications
POD-based feedback control of the burgers equation by solving the evolutionary HJB equation
Computers & Mathematics with Applications
HIV dynamics: Modeling, data analysis, and optimal treatment protocols
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Computer Methods and Programs in Biomedicine
Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition
Mathematical and Computer Modelling: An International Journal
Artificial viscosity proper orthogonal decomposition
Mathematical and Computer Modelling: An International Journal
Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
Journal of Computational and Applied Mathematics
Journal of Control Science and Engineering
A numerical investigation of velocity-pressure reduced order models for incompressible flows
Journal of Computational Physics
| Hi-index | 0.99 |
The proper orthogonal decomposition (POD) technique (or the Karhunan Loeve procedure) has been used to obtain low-dimensional dynamical models of many applications in engineering and science. In principle, the idea is to start with an ensemble of data, called snapshots, collected from an experiment or a numerical procedure of a physical system. The POD technique is then used to produce a set of basis functions which spans the snapshot collection. When these basis functions are used in a Galerkin procedure, they yield a finite-dimensional dynamical system with the smallest possible degrees of freedom. In this context, it is assumed that the physical system has a mathematical model, which may not be available for many physical and/or industrial applications. In this paper, we consider the steady-state Rayleigh-Benard convection whose mathematical model is assumed to be unknown, but numerical data are available. The aim of the paper is to show that, using the obtained ensemble of data, POD can be used to model accurately the natural convection. Furthermore, this approach is very efficient in the sense that it uses the smallest possible number of parameters, and thus, is suited for process control. Particularly, we consider two boundary control problems 1.(a) tracking problem, and 2.(b) avoiding hot spot in a certain region of the domain.