Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics

2022/02/18 by Hess, Martin W., Quaini, Annalisa, Rozza, Gianluigi · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2202.09250

Abstract

We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible Navier-Stokes equations and different types of bifurcations. To recover solutions past a Hopf bifurcation, we propose an approach that combines proper orthogonal decomposition with Hankel dynamic mode decomposition. To approximate solutions close to a pitchfork bifurcation, we combine localized reduced models with artificial neural networks. Several numerical examples are shown to demonstrate the feasibility of the presented approaches.

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