Numerical N-body simulations are typically employed to map stability regions around exoplanets. This provides insights into the potential presence of satellites and ring systems. We used machine-learning (ML) techniques to generate predictive maps of stable regions surrounding a hypothetical planet. This approach can also be applied to planet-satellite systems, planetary ring systems, and other similar systems. From a set of $10^5$ numerical simulations, each incorporating nine orbital features for the planet and test particle, we created a comprehensive dataset of three-body problem outcomes (star-planet-test particle). Simulations were classified as stable or unstable based on the stability criterion that a particle must remain stable over a time span of 104 orbital periods of the planet. Various ML algorithms were compared and fine-tuned through hyperparameter optimization to identify the most effective predictive model. All tree-based algorithms demonstrated a comparable accuracy performance. The optimal model employs the extreme gradient boosting algorithm and achieved an accuracy of 98.48 , with 94 recall and precision for stable particles and 99 for unstable particles. ML algorithms significantly reduce the computational time in three-body simulations. They are approximately $10^ $ times faster than traditional numerical simulations. Based on the saved training models, predictions of entire stability maps are made in less than a second, while an equivalent numerical simulation can take up to a few days. Our ML model results will be accessible through a forthcoming public web interface, which will facilitate a broader scientific application.