Predicting the final states of binary-single scattering with machine learning
Context. Binary-single encounters are particularly frequent in dense stellar environments, where they play a central role in shaping the dynamical evolution of their host systems. However, predicting their final outcomes remains an open question due to the intrinsic chaotic nature of the three-body problem. This challenge motivates the adoption of data-driven machine learning (ML) methods. Aims. We investigate whether ML can predict the final outcomes of binary-single encounters from initial conditions alone. Methods. We generated 5.8 million binary-single scattering simulations using the REBOUND N-body package with the IAS15 integrator. A cascaded binary classification strategy, comprising four sequential XGBoost classifiers, and a single multi-class model were trained on the synthetic dataset and compared. Results. The cascaded strategy outperforms the single multi-class model across all metrics. F1-scores for the cascaded models exceed 0.92, with precision-recall area under the curve (PR-AUC) values reaching 0.99, compared to 0.95 for the multi-class model. Feature importance analysis identifies encounter timescale, binary hardness, and mass ratio as key predictors. Misclassification analysis shows that prediction failures concentrate near chaotic boundaries where the outcome is sensitive to small perturbations. Speed benchmarks demonstrate that the cascaded models are up to 300 times faster than direct N-body integrations. However, all models fail to generalize to new datasets, highlighting a key limitation. Conclusions. This study demonstrates that, for any specific environment and data distribution, the proposed cascaded ML strategy provides a robust and rapid framework for predicting binary-single scattering outcomes.