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

• URL: http://arxiv.org/abs/2305.01539v2
• Date: Sun, 23 Jun 2024 22:57:12 GMT
• Title: Jacobian-Scaled K-means Clustering for Physics-Informed Segmentation of Reacting Flows
• Authors: Shivam Barwey, Venkat Raman,
• Abstract summary: JSK-means clustering is a physics-informed clustering strategy centered on the K-means framework. The algorithm is demonstrated on a complex reacting flow simulation dataset.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work introduces Jacobian-scaled K-means (JSK-means) clustering, which is a physics-informed clustering strategy centered on the K-means framework. The method allows for the injection of underlying physical knowledge into the clustering procedure through a distance function modification: instead of leveraging conventional Euclidean distance vectors, the JSK-means procedure operates on distance vectors scaled by matrices obtained from dynamical system Jacobians evaluated at the cluster centroids. The goal of this work is to show how the JSK-means algorithm -- without modifying the input dataset -- produces clusters that capture regions of dynamical similarity, in that the clusters are redistributed towards high-sensitivity regions in phase space and are described by similarity in the source terms of samples instead of the samples themselves. The algorithm is demonstrated on a complex reacting flow simulation dataset (a channel detonation configuration), where the dynamics in the thermochemical composition space are known through the highly nonlinear and stiff Arrhenius-based chemical source terms. Interpretations of cluster partitions in both physical space and composition space reveal how JSK-means shifts clusters produced by standard K-means towards regions of high chemical sensitivity (e.g., towards regions of peak heat release rate near the detonation reaction zone). The findings presented here illustrate the benefits of utilizing Jacobian-scaled distances in clustering techniques, and the JSK-means method in particular displays promising potential for improving former partition-based modeling strategies in reacting flow (and other multi-physics) applications.

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