Reduced Order Optimal Control Using Proper Orthogonal Decomposition Sensitivities

In general, reduced-order model (ROM) solutions obtained using proper orthogonal decomposition (POD) at a single parameter cannot approximate the solutions at other parameter values accurately. In this paper, parameter sensitivity analysis is performed for POD reduced order optimal control problems (OCPs) governed by linear diffusion-convection-reaction equations. The OCP is discretized in space and time by discontinuous Galerkin (dG) finite elements. We apply two techniques, extrapolating and expanding the POD basis, to assess the accuracy of the reduced solutions for a range of parameters. Numerical results are presented to demonstrate the performance of these techniques to analyze the sensitivity of the OCP with respect to the ratio of the convection to the diffusion terms.


Reduced order optimal control of the convective FitzHugh-Nagumo equations
Karasözen, Bülent; KÜÇÜKSEYHAN, TUĞBA (2020-02-15)
In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective FitzHugh-Nagumo (FHN) equations. The convective FHN equations consist of the semi-linear activator and the linear inhibitor equations, modeling blood coagulation in moving excitable media. The semilinear activator equation leads to a non-convex optimal control problem (OCP). The ...
Model order reduction for nonlinear Schrodinger equation
Karasözen, Bülent; Uzunca, Murat (2015-05-01)
We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reprodu...
Reduced order modelling of nonlinear cross-diffusion systems
Karasözen, Bülent; Uzunca, Murat; Yıldız, Süleyman (2021-07-15)
In this work, we present reduced-order models (ROMs) for a nonlinear cross-diffusion problem from population dynamics, the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The formation of the patterns of the SKT equation consists of a fast transient phase and a long stationary phase. Reduced order solutions are computed by separating the time into two time-intervals. In numerical experiments, we show for one- and two-dimensional SKT equations with pattern formation, the reduced-orde...
Structure preserving model order reduction of shallow water equations
Karasözen, Bülent; UZUNCA, MURAT (2020-07-01)
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Decoupled Modular Regularized VMS-POD for Darcy-Brinkman Equations
Güler Eroğlu, Fatma; Kaya Merdan, Songül; Rebholz, Leo G (2019-05-01)
We extend the post-processing implementation of a projection based variational multiscale (VMS) method with proper orthogonal decomposition (POD) to flows governed by double diffusive convection. In the method, the stabilization terms are added to momentum equation, heat and mass transfer equations as a completely decoupled separate steps. The theoretical analyses are presented. The results are verified with numerical tests on a benchmark problem.
Citation Formats
B. Karasözen, “Reduced Order Optimal Control Using Proper Orthogonal Decomposition Sensitivities,” 2015, vol. 103, Accessed: 00, 2020. [Online]. Available: