Ahmad Farhani Asl
Three-body encounters are frequent events in stellar systems. They are intrinsically chaotic and computationally costly to model with direct N-body integration. Predicting whether such encounters lead to binary formation is therefore challenging, particularly in large-scale simulations. We aim to develop an accurate and physically interpretable machine-learning model that predicts binary formation from the initial conditions of three-body encounters, assess its reliability, and identify the physical parameters that most strongly determine the outcome. We trained an XGBoost binary classifier on a balanced dataset of over 162,000 three-body scattering experiments computed with the REBOUND code and the IAS15 integrator. The input to the model consists of 30 physically motivated features describing the masses, energies, and kinematics of the initial configuration. Our classifier achieves excellent performance, with accuracy, precision, recall, and F1-score all above 0.94 and ROC-AUC (the receiver operating characteristic area under the curve) and PR-AUC (the precision-recall area under the curve) values both reaching nearly 0.99. Feature-importance analysis shows that the outcome is governed primarily by the mass hierarchy and hardness ratio of the encounter, followed by velocity fraction and mass entropy. The predicted probabilities are well calibrated, with an expected calibration error of 0.02. Inference is approximately 400 times faster than direct N-body integration. The model also generalizes well across encounter radii, although its performance decreases in the weak-interaction regime where binary formation becomes intrinsically rare. These results show that machine learning can provide fast, accurate, and physically interpretable predictions of binary formation in three-body encounters. Such models offer a practical complement to direct N-body simulations and may enable efficient probability estimates in large-scale simulations of stellar systems.