  In this work, the application of the multi-dimensional higher order dynamic
mode decomposition (HODMD) is proposed for the first time to analyse combustion
databases. In particular, HODMD has been adapted and combined with other
pre-processing techniques (generally used in machine learning), in light of the
multivariate nature of the data. A truncation step separate the main dynamics
driving the flow from less relevant non-linear dynamics. The method is applied
to analyse a database obtained from a Computational Fluid Dynamics (CFD)
simulation of an axisymmetric, time varying, non-premixed, co-flow methane
flame carried out by means of a detailed kinetic mechanism. Results show that
HODMD can reconstruct the main jet dynamics with a reduced number of relevant
modes, able to reproduce the system dynamics. These modes are found to be
representative for the main flow physics with two main advantages: (i) they
provide for the possibility to achieve a strong simplification with respect to
the high-dimensional input data, and at the same time (ii) a small
reconstruction error with respect to the original dataset is observed. In
addition, the method was also validated considering a reduced matrix obtained
using Principal Component Analysis (PCA) based feature selection and the
Varimax rotation. This validation also reveals that it is not important to have
all the variables in the dataset, just a group of them is necessary to obtain
the main dynamics of the system. This has an impact on feature selection and on
the cost these methodologies for very massive data.
