# Reduced Order Optimal Control of the Convective FitzHugh-Nagumo Equation

## TL;DR

This paper compares three model order reduction methods—POD, DEIM, and DMD—for optimal control of the convective FitzHugh-Nagumo equations, focusing on accuracy and computational efficiency in blood coagulation modeling.

## Contribution

It introduces a comparative analysis of POD, DEIM, and DMD methods for reduced order optimal control of convective FHN equations, highlighting their accuracy and speed.

## Key findings

- POD provides the highest accuracy.
- POD-DMD offers the fastest computation.
- All methods are compared against full order solutions.

## Abstract

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 consists 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.