Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics
Numerical Analysis
2022-07-19 v3 Numerical Analysis
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.
Cite
@article{arxiv.2202.09250,
title = {Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics},
author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza},
journal= {arXiv preprint arXiv:2202.09250},
year = {2022}
}