Benchmarking Machine Learning for Chaotic Three-Body Dynamics in Astrophysics

Sheng Wan, Pavan Vynatheya, Duo Xu, Li Kevin Wenliang, Ye Zhu

Machine learning (ML) and generative AI have recently made impressive progress in understanding physics. We explore a hierarchy of prediction problems stemming from chaotic three-body systems and benchmark existing ML approaches, including general-purpose prediction algorithms and those that build on top of foundational physics models. We first simulate the trajectories of triple systems near the critical boundary of stable/unstable initial conditions. We then design a hierarchy of learning tasks, focusing mainly on two broad problems: stability prediction and trajectory prediction. The former classifies whether a given triple system has diverged or not up to a specific horizon, while the latter predicts the exact trajectory, both given suitable input features. We benchmark a range of ML approaches, from simple regression methods to state-of-the-art foundational physics models, across these tasks, and compare them against astrophysical methods such as the Mardling-Aarseth stability criterion. Our experiments reveal a clear order of task difficulties in chaotic three-body dynamics: early dynamics enable strong stability prediction, while precise long-horizon trajectory forecasting…