We apply two standard machine learning classifiers -- k-nearest neighbours (k-NN) and Random Forest -- to the problem of orbit family identification in the gravitational three-body problem, using the Kelvin-simplex descriptor framework introduced in companion works 1, 2 as the feature representation. A dataset of 300 numerically integrated trajectories spanning six canonical orbit families (figure-eight, Lagrange equilateral, hierarchical, Pythagorean, chaotic, and near-collinear) is constructed by applying family-specific initial-condition perturbations to reference configurations. Each trajectory is characterised by a six-dimensional descriptor vector comprising mean entropy, entropy standard deviation, centroid distance, corner proximity, simplex path length, and spectral concentration. Both classifiers achieve 100% accuracy on an 80/20 stratified hold-out test set, with cross-validation accuracies of 98.0% (plus or minus 1.2%) for k-NN and 98.0% (plus or minus 0.8%) for Random Forest. Feature importance analysis identifies simplex path length as the most discriminative single descriptor (29.5% of Random Forest impurity reduction), with the remaining five descriptors contributing in a relatively balanced manner (11--16% each). The results confirm that the Kelvin-simplex descriptor set provides a compact, physically interpretable feature space in which three-body orbit families are linearly and non-linearly separable by simple, interpretable algorithms. No hand-crafted decision rules are required: the geometry of the simplex encodes the dynamical distinctions automatically.
Lee Michael John Rich (Thu,) studied this question.