N-Body Simulation and Machine Learning-Based Stability Prediction for Multi-Planet Exoplanetary Systems

Abstract

We present a reproducible pipeline that combines a fast batched symplectic N-body integrator, a renormalized two-particle MEGNO chaos indicator, and supervised machine learning to predict the 10^4-orbit stability of compact multi-planet systems from only the first 10^2-10^3 orbits. Using 3200 coplanar three-planet systems sampled across mutual-Hill spacings Δ∈[3,13] and initial eccentricities e∈[0,0.1], we first map how instability fraction rises sharply as Δ decreases. We then show that a histogram-gradient-boosting classifier using twelve physics-inspired features achieves ROC-AUC 0.976 ± 0.002 and balanced accuracy 0.909 from a 10^3-orbit window, outperforming the MEGNO-threshold (AUC 0.671) and a spacing-threshold baseline (AUC 0.904). A label-leakage control that excludes all systems destabilizing inside the feature window still yields AUC 0.952 from 100 orbits, an ablation study finds that 100 orbits already contain most predictive information (AUC 0.971), and transfer to an independent 1600-system four-planet sample retains AUC 0.972 with a well-calibrated Brier score of 0.077. An error analysis shows that the residual failures concentrate within about one mutual Hill radius of the stability transition and are dominated by late, diffusion-driven instabilities. These results suggest that short-run machine-learning surrogates can substantially accelerate stability surveys of exoplanetary systems.