Analysis of Kohn-Sham Eigenfunctions Using a Convolutional Neural Network in Simulations of the Metal-Insulator Transition in Doped Semiconductors

Machine learning has recently been applied to many problems in condensed matter physics. A common point of many proposals is to save computational cost by training the machine with data from a simple example and then using the machine to make predictions for a more complicated example. Convolutional neural networks (CNN), which are one of the tools of machine learning, have proved to work well for assessing eigenfunctions in disordered systems. Here we apply a CNN to assess Kohn-Sham eigenfunctions obtained in density functional theory (DFT) simulations of the metal-insulator transition of a doped semiconductor. We demonstrate that a CNN that has been trained using eigenfunctions from a simulation of a doped semiconductor that neglects electron spin successfully predicts the critical concentration when presented with eigenfunctions from simulations that include spin.

Automated summary

Machine learning is increasingly being applied to problems in condensed matter physics to save computational cost by training with data from a simple example and then making predictions for a more complex example. Convolutional neural networks have shown to work well for assessing eigenfunctions in disordered systems, and have successfully been applied in DFT simulations.