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

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.