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This work introduces Jacobian-scaled K-means (JSK-means) clustering, which isa physics-informed clustering strategy centered on the K-means framework. Themethod allows for the injection of underlying physical knowledge into theclustering procedure through a distance function modification: instead ofleveraging conventional Euclidean distance vectors, the JSK-means procedureoperates on distance vectors scaled by matrices obtained from dynamical systemJacobians evaluated at the cluster centroids. The goal of this work is to showhow the JSK-means algorithm -- without modifying the input dataset -- producesclusters that capture regions of dynamical similarity, in that the clusters areredistributed towards high-sensitivity regions in phase space and are describedby similarity in the source terms of samples instead of the samples themselves.The algorithm is demonstrated on a complex reacting flow simulation dataset (achannel detonation configuration), where the dynamics in the thermochemicalcomposition space are known through the highly nonlinear and stiffArrhenius-based chemical source terms. Interpretations of cluster partitions inboth physical space and composition space reveal how JSK-means shifts clustersproduced by standard K-means towards regions of high chemical sensitivity(e.g., towards regions of peak heat release rate near the detonation reactionzone). The findings presented here illustrate the benefits of utilizingJacobian-scaled distances in clustering techniques, and the JSK-means method inparticular displays promising potential for improving former partition-basedmodeling strategies in reacting flow (and other multi-physics) applications.

Jacobian-Scaled K-means Clustering for Physics-Informed Segmentation of Reacting Flows