  N-body systems characterized by inverse square attractive forces may display
a self similar collapse known as the gravo-thermal catastrophe. In star
clusters, collapse is halted by binary stars, and a large fraction of Milky Way
clusters may have already reached this phase. It has been speculated -- with
guidance from simulations -- that macroscopic variables such as central density
and velocity dispersion are governed post-collapse by an effective,
low-dimensional system of ODEs. It is still hard to distinguish chaotic, low
dimensional motion, from high dimensional stochastic noise. Here we apply three
machine learning tools to state-of-the-art dynamical simulations to constrain
the post collapse dynamics: topological data analysis (TDA) on a lag embedding
of the relevant time series, Sparse Identification of Nonlinear Dynamics
(SINDY), and Tests of Accuracy with Random Points (TARP).
