Compressed Compressor

TL;DR

This paper develops a data-driven reduced order model for viscous Moore-Greitzer PDEs using PCA, autoencoders, and sparse regression, achieving high accuracy and revealing new nonlinear behaviors near bifurcations.

Contribution

It introduces a novel combination of PCA, autoencoders, and SINDy for reduced order modeling of viscous MG systems, capturing dynamics with high fidelity and uncovering new nonlinear phenomena.

Findings

Achieves 98.9% accuracy in recovering system dynamics.

Discovers new nonlinear behavior during rotating stall instability.

Provides low-dimensional ODE models consistent with normal form structures.

Abstract

In this paper, we present a data-driven reduced order model of viscous Moore-Greitzer (MG) partial differential equation (PDE) by threading together ideas from principal component analysis (PCA) and autoencoder neural networks to sparse regression and compressed sensing. Numerical simulation of the infinite dimensional viscous MG system is reduced into low dimensional data using PCA and autoencoder neural networks based reduced order modelling (ROM) approaches. Based on the observation that MG equations close to bifurcations have a sparse representation (normal form) with respect to high-dimensional polynomial spaces, we use the Sparse Identification of Dynamical Systems (SINDy) algorithm which uses a collection of all monomials as sampling matrix and the LASSO algorithm to recover a system of sparse two ordinary differential equations (ODEs) with cubic nonlinearities. The discovered governing equations can be used to fully recover the original system dynamics up to 98.9% accuracy. When dimensional reduction is performed along the dataset's principal components, the resulting low dimensional differential equations will be consistent and have some resemblance to the normal form structure. Additionally, a new nonlinear behaviour is exhibited in viscous MG equations during rotating stall instability past the Hopf bifurcation point.