Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equation

TL;DR

This paper presents a reduced order modeling approach using POD and DEIM to efficiently simulate pattern formation in the FitzHugh-Nagumo equation, significantly reducing computational costs while maintaining accuracy.

Contribution

The authors develop a POD-DEIM based reduced order model for the FitzHugh-Nagumo equation that leverages the local discretization of dG to improve efficiency and accuracy.

Findings

Accurate pattern computation with few POD and DEIM modes.

Reduced computational cost due to local dG discretization.

Effective ROM for bistable nonlinearities in FHN equation.

Abstract

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, the patterns can be computed accurately. Due to the local nature of the dG discretization, the POD-DEIM requires less number of connected nodes than continuous finite element for the nonlinear terms, which leads to a significant reduction of the computational cost for dG POD-DEIM.