  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.

Dynamical Systems;Analysis of PDEs;Optimization and Control