  In this work, a new algorithm based on the application of higher-order
dynamic mode decomposition (HODMD) is proposed for feature selection and
variables clustering in reacting flow simulations. The hierarchical HODMD
(h-HODMD) performs a reduction of the model order, followed by the iterative
selection of the best reconstructed variables thus creating clusters of
features which can eventually be associated with distinct dynamical phenomena.
Firstly, h-HODMD is combined with different data pre-processing techniques to
assess their influence on the algorithm in terms of reconstruction error.
Afterwards, the algorithm is applied to analyze three different databases
obtained from numerical simulations of a non-premixed co-flow methane flame,
and its performance are compared with the standard HODMD in terms of the
achievable degree of reduction as well as in terms of reconstruction error.
Results show that h-HODMD improves the reconstruction for all the variables
when compared to the standard HODMD algorithm. This condition is achieved
thanks to the iterative variables' clustering: finding dedicated modes for a
specific group of features does in fact lead to a better reconstruction of the
dynamics with respect to the case when the same (global) modes are used to
reconstruct the entire set of variables. Finally, the clusters of variables
found by means of h-HODMD are analyzed, and it is observed that the algorithm
can group chemical species whose behavior is also consistent from a kinetic
point of view. In fact, it allows for the possibility to formulate inexpensive
reduced dynamical models for predicting flames liftoff, as well as for
identifying the formation of local extinction and blowout conditions, to
formulate accurate reduced models to describe the formation of pollutants in
aviation, and for control purposes.
