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

Martin W. Hess; Annalisa Quaini; Gianluigi Rozza

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arXiv · 2202.09250

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

Martin W. Hess·Annalisa Quaini·Gianluigi Rozza

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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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Martin W. Hess, Annalisa Quaini, Gianluigi Rozza. 2022-02-18. Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics. https://arxiv.org/abs/2202.09250

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