Hierarchical Higher-Order Dynamic Mode Decomposition for Clustering and Feature Selection

Abstract

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 proposed 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. Two detailed kinetic mechanisms are used for the simulations, and different time horizons are considered to assess the influence of the number of considered cycles on the accuracy of the reduced model. 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, in an unsupervised fashion, chemical species whose behavior is also consistent from a kinetic point of view. In fact, radicals responsible for fast chemistry processes (such as propagation and branching reactions) are grouped together, and the same happens for nitrogen oxides (whose chemical timescales are instead order of magnitudes slower). The possibility to identify and to describe correctly the main dynamics with reduced order models for these two classes of chemical species is extremely important for practical applications in combustion. 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.