  Manipulation of material properties via precise doping affords enormous
tunable phenomena to explore. Recent advance shows that in the atomic and nano
scales topological states of dopants play crucial roles in determining their
properties. However, such determination is largely unknown due to the
incredible size of topological states. Here, we present a case study of
developing deep learning algorithms to predict bandgaps of boron-nitrogen pair
doped graphene with arbitrary dopant topologies. A material descriptor system
that enables to correlate structures with the bandgaps was developed for
convolutional neuron networks (CNNs). Bandgaps calculated by the ab initio
calculations and the corresponding structures were fed as input datasets to
train VGG16 convolutional network, residual convolutional network, and
concatenate convolutional network. Then these trained CNNs were used to predict
bandgaps of doped graphene with various dopant topologies. All of them afford
great prediction accuracy, showing square of the coefficient of correlation
(R2) of > 90% and root-mean-square errors of ~ 0.1 eV for the predicted
bandgaps. They are much better than those predicted by a shallow machine
learning method - support vector machine. The transfer learning was further
performed by leveraging data generated from smaller systems to improve the
prediction for large systems. Success of this work provides a cornerstone for
future investigation of topologically doped graphene and other 2D materials.
Moreover, given ubiquitous existence of topologies in materials, this work will
stimulate widespread interests in applying deep learning algorithms to
topological design of materials crossing atomic, nano-, meso-, and macro-
scales.
