Weisfeiler-Lehman Graph Kernel Method: A New Approach to Weak Chemical Tagging

TL;DR

This paper introduces a novel application of the Weisfeiler-Lehman graph kernel to analyze stellar chemical signatures, demonstrating its superior interpretability and efficiency in identifying patterns in elemental abundance data compared to neural network methods.

Contribution

The study presents a new approach using the Weisfeiler-Lehman graph kernel for analyzing stellar chemical signatures, significantly reducing the need for extensive simulations.

Findings

WL algorithm outperforms deep sets and GCNs in interpretability and robustness

Effective pattern recognition with only about 10 simulations

Demonstrates potential for analyzing chemical distributions in astrophysics

Abstract

Stars' chemical signatures provide invaluable insights into stellar cluster formation. This study utilized the Weisfeiler-Lehman (WL) Graph Kernel to examine a 15-dimensional elemental abundance space. Through simulating chemical distributions using normalizing flows, the effectiveness of our algorithm was affirmed. The results highlight the capability of the WL algorithm, coupled with Gaussian Process Regression, to identify patterns within elemental abundance point clouds correlated with various cluster mass functions. Notably, the WL algorithm exhibits superior interpretability, efficacy and robustness compared to deep sets and graph convolutional neural networks and enables optimal training with significantly fewer simulations (O(10)), a reduction of at least two orders of magnitude relative to graph neural networks.