  Chaotic systems such as the gravitational N-body problem are ubiquitous in
astronomy. Machine learning (ML) is increasingly deployed to predict the
evolution of such systems, e.g. with the goal of speeding up simulations.
Strategies such as active Learning (AL) are a natural choice to optimize ML
training. Here we showcase an AL failure when predicting the stability of the
Sitnikov three-body problem, the simplest case of N-body problem displaying
chaotic behavior. We link this failure to the fractal nature of our
classification problem's decision boundary. This is a potential pitfall in
optimizing large sets of N-body simulations via AL in the context of star
cluster physics, galactic dynamics, or cosmology.
