Cluster membership analysis with supervised learning and $N$-body simulations

Membership analysis is an important tool for studying star clusters. There are various approaches to membership determination, including supervised and unsupervised machine learning (ML) methods. We perform membership analysis using the supervised machine learning approach. We train and test our ML models on two sets of star cluster data: snapshots from $N$-body simulations and 21 different clusters from the Gaia Data Release 3 data. We explore five different ML models: Random Forest (RF), Decision Trees, Support Vector Machines, Feed-Forward Neural Networks, and K-Nearest Neighbors. We find that all models produce similar results, with RF showing slightly better accuracy. We find that a balance of classes in datasets is optional for successful learning. The classification accuracy depends strongly on the astrometric parameters. The addition of photometric parameters does not improve performance. We do not find a strong correlation between the classification accuracy and clusters' age, mass, and half-mass radius. At the same time, models trained on clusters with a larger number of members generally produce better results.