  The study of integrable systems has led to significant advancements in our
understanding of many-body physics. We design a series of numerical experiments
to analyze the integrability of a mass-imbalanced two-body system through
energy level statistics and deep learning of wavefunctions. The level spacing
distributions are fitted by a Brody distribution and the fitting parameter
$\omega$ is found to separate the integrable and non-integrable mass ratios by
a critical line $\omega=0$. The convolutional neural network built from the
probability density images could identify the transition points between
integrable and non-integrable systems with high accuracy, yet in a much shorter
computation time. A brilliant example of the network's ability is to identify a
new integrable mass ratio $1/3$ by learning from the known integrable case of
equal mass, with a remarkable network confidence of $98.78\%$. The robustness
of our neural networks is further enhanced by adversarial learning, where
samples are generated by standard and quantum perturbations mixed in the
probability density images and the wavefunctions, respectively.
