BATEIA-1: An Approach for determining the structural parameters of open star clusters via machine and deep learning

Galactic open stellar clusters (OCs) are groups of gravitationally bound stars originating from the same molecular cloud. Given their diversity in age, metallic content, morphology and Galactic location, these objects are useful tools to understand stellar evolution and the Galactic structure. Current approaches to determine their structural parameters often rely on fitting analytical profiles to empirical stellar radial density profiles using trial-and-error methods, such as Markov Chain Monte Carlo (MCMC) and Maximum-Likelihood Poisson Regression, which require significant parameter space exploration. However, depending on convergence criteria, these methods can become trapped in local minima, leading to suboptimal solutions. This article aims to determine the structural parameters of OCs via artificial intelligence, offering a more efficient and scalable solution. The Balanced ArTificial-intelligence Method for EstImating parameters of stAr clusters (BATEIA-1) is a machine learning (ML) and deep learning strategy. It integrates the analytical King profile with ML techniques trained on astrometric and photometric data from the Gaia DR3 catalog. BATEIA-1 derives parameters such as central density, core and tidal radii and background density, contributing to the automation of cluster structure characterization. Based on nine Deep Neural Network (DNN) models to extract features from celestial maps and two traditional ML techniques (Multilayer Perceptron Regressor and Support Vector Regression), our results show that the BATEIA-1 approach performed effectively in predicting OC structural parameters. Comparisons with literature benchmarks for M67, NGC 188, and NGC 6811 indicate divergences ranging from 0.7% to 12.8% for the tidal radius. Regarding core radius and central density, discrepancies fall within 1.1%–5.5% and 1.1%–8.7%, respectively. Finally, Explainable AI (XAI) techniques, specifically Score-CAM and Ablation-CAM, were used to elucidate the decision-making behavior of the DNN models.