Not yet reviewed by Pith; the record is open.

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.