Appendix 1 Methods details

Two-body system initialization The trajectories are initialized in a near-circular way. Three-body system initialization For the chaotic three-body systems, we also apply initial condition regularization such that the initial trajectories of the system is also near-circular. Examples of the two-body systems and three-body systems we generated. We show a few examples of the two-body systems and three-body systems in Figure.A1. Similar as in Section.4.1, we show the latent space obtained from The recordings are collected from surgically implanted electrode arrays and are thresholded and spike sorted when collected.