  Applications of neural networks to condensed matter physics are becoming
popular and beginning to be well accepted. Obtaining and representing the
ground and excited state wave functions are examples of such applications.
Another application is analyzing the wave functions and determining their
quantum phases. Here, we review the recent progress of using the multilayer
convolutional neural network, so-called deep learning, to determine the quantum
phases in random electron systems. After training the neural network by the
supervised learning of wave functions in restricted parameter regions in known
phases, the neural networks can determine the phases of the wave functions in
wide parameter regions in unknown phases; hence, the phase diagrams are
obtained. We demonstrate the validity and generality of this method by drawing
the phase diagrams of two- and higher dimensional Anderson metal-insulator
transitions and quantum percolations as well as disordered topological systems
such as three-dimensional topological insulators and Weyl semimetals. Both
real-space and Fourier space wave functions are analyzed. The advantages and
disadvantages over conventional methods are discussed.
