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

TL;DR

This paper introduces data-driven enhancements to model reduction techniques for bifurcating solutions in fluid dynamics, combining POD, DMD, and neural networks to improve accuracy near bifurcations.

Contribution

It presents novel hybrid methods integrating data-driven models with traditional reduction techniques to better capture bifurcations in Navier-Stokes equations.

Findings

Effective recovery of solutions past Hopf bifurcations.

Accurate approximation near pitchfork bifurcations.

Numerical examples demonstrating method feasibility.

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.