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

arXiv: https://arxiv.org/abs/2305.01539 · HTML: https://mlsanity.com/paper/2305.01539/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 58 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 7 of 7)

- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Deep k-Means: Jointly clustering with k-Means and learning representations](https://mlsanity.com/paper/1806.10069/) (2018)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)

## Built on by (most cited first, 1 of 1)

- [Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2311.07548/) (2023)

## Abstract (arXiv)

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.