  Supervised machine learning algorithms, such as graph neural networks (GNN),
have successfully predicted material properties. However, the superior
performance of GNN usually relies on end-to-end learning on large material
datasets, which may lose the physical insight of multi-scale information about
materials. And the process of labeling data consumes many resources and
inevitably introduces errors, which constrains the accuracy of prediction. We
propose to train the GNN model by self-supervised learning on the node and edge
information of the crystal graph. Compared with the popular manually
constructed material descriptors, the self-supervised atomic representation can
reach better prediction performance on material properties. Furthermore, it may
provide physical insights by tuning the range information. Applying the
self-supervised atomic representation on the magnetic moment datasets, we show
how they can extract rules and information from the magnetic materials. To
incorporate rich physical information into the GNN model, we develop the node
embedding graph neural networks (NEGNN) framework and show significant
improvements in the prediction performance. The self-supervised material
representation and the NEGNN framework may investigate in-depth information
from materials and can be applied to small datasets with increased prediction
accuracy.
