Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics

TL;DR

This paper introduces a novel sparse, interpretable reduced order modeling approach combining SINDy, deep autoencoders, and POD to efficiently capture bifurcations in CFD systems, validated on complex flow cases.

Contribution

It develops a non-intrusive, sparse identification framework integrating SINDy, autoencoders, and POD for modeling bifurcating phenomena in CFD.

Findings

Successfully reconstructs bifurcations in test cases

Accurately predicts system evolution for unseen parameters

Achieves significant computational speed-up

Abstract

This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced Order Models (ROMs) capable of capturing dynamics associated with bifurcations by identifying a minimal set of coordinates. Our methodology combines the Sparse Identification of Nonlinear Dynamics (SINDy) method with a deep learning framework based on Autoencoder (AE) architectures. To enhance dimensionality reduction, we integrate a nested Proper Orthogonal Decomposition (POD) with the SINDy-AE architecture, enabling a sparse discovery of system dynamics while maintaining efficiency of the reduced model. We demonstrate our approach via two challenging test cases defined on sudden-expansion channel geometries: a symmetry-breaking bifurcation and a Hopf bifurcation. Starting from a comprehensive analysis of their high-fidelity behavior, i.e. symmetry-breaking phenomena and the rise of unsteady periodic solutions, we validate the accuracy and computational efficiency of our ROMs. The results show successful reconstruction of the bifurcations, accurate prediction of system evolution for unseen parameter values, and significant speed-up compared to full-order methods.