This study introduces the Extended Cluster-based Network Modeling (eCNM),
an innovative approach designed to enhance the understanding of coherent structures in turbulent flows. The eCNM focuses on characterizing the dynamics within specific subspaces or
subsets of variables, providing valuable insights into complex flow phenomena. In the context of
Proper Orthogonal Decomposition, several extended approaches have been proposed to tackle
these challenges, such as Extended POD (EPOD) and Extended SPOD (ESPOD). One powerful
method for data-driven modeling of complex nonlinear dynamics is the standard Cluster-based
Network Modeling (CNM), consisting in an unsupervised machine learning procedure to reduce
a dataset of snapshots to a few representative flow states. However, the presence of variable
heterogeneity and measurement noise, both in time and space, can complicate interpretations
and model training. The Extended Clustering approach offers enhanced control over the clustering process, can lead to significant computational savings, enables the extraction of dynamical
features correlated with a specific subdomain or subset of variables, and facilitates the clustering
of heterogeneous variables that are challenging to incorporate in a spatial norm. To demonstrate
the effectiveness of the eCNM, it has been employed for the analysis of a swirl flame in unforced
conditions, characterized by a precessing vortex core (PVC).
