  Incorporation of physical principles in a network-based machine learning (ML)
architecture is a fundamental step toward the continued development of
artificial intelligence for materials science and condensed matter physics. In
this work, as inspired by the Pauling rule, we propose that structure motifs
(polyhedral formed by cations and surrounding anions) in inorganic crystals can
serve as a central input to a machine learning framework for crystalline
inorganic materials. Taking metal oxides as examples, we demonstrated that, an
unsupervised learning algorithm Motif2Vec is able to convert the presence of
structure motifs and their connections in a large set of crystalline compounds
into unique vector representations. The connections among complex materials can
be largely determined by the presence of different structure motifs and their
clustering information are identified by our Motif2Vec algorithm. To
demonstrate the novel use of structure motif information, we show that a
motif-centric learning framework can be effectively created by combining motif
information with the recently developed atom-based graph neural networks to
form an atom-motif dual graph network (AMDNet). Taking advantage of node and
edge information on both atomic and motif level, the AMDNet is more accurate
than an atom graph network in predicting electronic structure related material
properties of metal oxides such as band gaps. The work illustrates the route
toward fundamental design of graph neural network learning architecture for
complex material properties by incorporating beyond-atom physical principles.
