Reduced order optimal control of the convective FitzHugh-Nagumo equations

Karasözen, Bülent
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 most commonly used method in reduced optimal control is POD. We use DEIM and DMD to approximate efficiently the nonlinear terms in reduced order models. We compare the accuracy and computational times of three reduced-order optimal control solutions with the full order discontinuous Galerkin finite element solution of the convection dominated FHN equations with terminal controls. Numerical results show that POD is the most accurate whereas POD-DMD is the fastest.


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Karasözen, Bülent (2015-06-02)
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...
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Karasözen, Bülent; Küçükseyhan, Tuğba; Mülayim, Gülden (null; 2017-09-22)
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Energy preserving model order reduction of the nonlinear Schrodinger equation
Karasözen, Bülent (2018-12-01)
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Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equations
Karasözen, Bülent; Kucukseyhan, Tugba (2015-09-18)
We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the discontinuous Galerkin (dG) method and in time by the backward Euler method. Applying POD-DEIM (discrete empirical interpolation method) to the full order model (FOM) for different values of the parameter in the bistable nonlinearity, we show that using few POD and DEIM modes...
Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation
UZUNCA, MURAT; Karasözen, Bülent; Sariaydin-Filibelioglu, Ayse (2015-09-18)
We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization for the advective Allen-Cahn equation with nondivergence-free velocity fields. Numerical simulations for convection dominated problems demonstrate the accuracy and efficiency of the adaptive algorithm for resolving the sharp layers occurring in interface problems with small surface tension.
Citation Formats
B. Karasözen and T. KÜÇÜKSEYHAN, “Reduced order optimal control of the convective FitzHugh-Nagumo equations,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 982–995, 2020, Accessed: 00, 2020. [Online]. Available: