Hierarchical higher-order dynamic mode decomposition for clustering and feature selection

This article introduces a novel, fully data -driven method for forming reduced order models (ROMs) in complex flow databases that consist of a large number of variables. The algorithm utilizes higher order dynamic mode decomposition (HODMD), a modal decomposition method, to identify the main frequencies and associated patterns that govern the flow dynamics. By incorporating various normalization techniques into an iterative process, clusters of variables with similar dynamics are identified, allowing the classification of different instabilities and patterns present in the flow. This method, known as hierarchical HODMD (h-HODMD), has been thoroughly tested in the development of ROMs using three different databases obtained from numerical simulations of a nonpremixed coflow methane flame. The effectiveness of h-HODMD has been demonstrated as it consistently outperforms HODMD in terms of modeling and reconstructing flow dynamics using a reduced number of modes. Additionally, the clusters of variables identified by h-HODMD reveal the algorithm's ability to group chemical species whose behavior is consistent from a kinetic perspective. h-HODMD allows for the construction of inexpensive reduced dynamical models that can predict flame liftoff, identify the occurrence of local extinction and blowout conditions, and facilitate control purposes.