Using the multilayer convolutional neural network (CNN), we can detect the quantum phases in random electron systems, and phase diagrams of two and higher dimensional Anderson transitions and quantum percolations as well as disordered topological systems have been obtained. Here, instead of using CNN to analyze the wave functions, we analyze the dynamics of wave packets via long short-term memory network (LSTM). We adopt the quasi-periodic quantum kicked rotors, which simulate the three and four dimensional Anderson transitions. By supervised training, we let LSTM extract the features of the time series of wave packet displacements in localized and delocalized phases. We then simulate the wave packets in unknown phases and let LSTM classify the time series to localized and delocalized phases. We compare the phase diagrams obtained by LSTM and those obtained by CNN.

使用多层卷积神经网络（CNN），我们可以检测随机电子系统中的量子相，并获得了二维及更高维安德森跃迁和量子渗流以及无序拓扑系统的相图。在这里，我们不是使用CNN分析波函数，而是通过长短期存储网络（LSTM）分析了波包的动态。我们采用准周期的量子踢转子，该转子模拟了三维维和安德森跃迁。通过监督训练，我们让LSTM提取了局部和非局部相位中波包位移的时间序列特征。然后，我们模拟未知相位中的波包，并让LSTM将时间序列分类为本地化和非本地化阶段。