  The relative motion of three impenetrable particles on a ring, in our case
two identical fermions and one impurity, is isomorphic to a triangular quantum
billiard. Depending on the ratio $\kappa$ of the impurity and fermion masses,
the billiards can be integrable or non-integrable (also referred to in the main
text as chaotic). To set the stage, we first investigate the energy level
distributions of the billiards as a function of $1/\kappa\in [0,1]$ and find no
evidence of integrable cases beyond the limiting values $1/\kappa=1$ and
$1/\kappa=0$. Then, we use machine learning tools to analyze properties of
probability distributions of individual quantum states. We find that
convolutional neural networks can correctly classify integrable and
non-integrable states. The decisive features of the wave functions are the
normalization and a large number of zero elements, corresponding to the
existence of a nodal line. The network achieves typical accuracies of
97\%,suggesting that machine learning tools can be used to analyze and classify
the morphology of probability densities obtained in theory and experiment.
