  Quantum material phases such as the Anderson insulator, diffusive metal, and
Weyl/Dirac semimetal as well as topological insulators show specific wave
functions both in real and Fourier spaces. These features are well captured by
convolutional neural networks, and the phase diagrams have been obtained, where
standard methods are not applicable. One of these examples is the cases of
random lattices such as quantum percolation. Here, we study the topological
insulators with random vacancies, namely, the quantum percolation in
topological insulators, by analyzing the wave functions via a convolutional
neural network. The vacancies in topological insulators are especially
interesting since peculiar bound states are formed around the vacancies. We
show that only a few percent of vacancies are required for a topological phase
transition. The results are confirmed by independent calculations of
localization length, density of states, and wave packet dynamics.
