Materials design based on a material-motif network and heterogeneous graphs

Machine learning models for functional materials design require precise and informative representations of material systems. Common representations encode atomic composition and bonding but often do not include local coordination environments across chemically diverse crystals. Recurring structural motifs provide a motif level description of crystalline solids and can serve as interpretable descriptors for structure property learning. To analyze the motif connectivity in materials, we construct a bipartite material motif network from 131,548 Materials Project entries, with materials and motifs as the two node sets. Edges connect materials to their constituent motifs and are weighted by motif distortion, which quantifies the strength of each material motif association. Network connectivity is analyzed to identify motif-defined material clusters that capture recurring local geometries relevant to structure property trends. Most shared motifs act as hubs that connect otherwise disconnected regions of the network, enabling motif guided screening by expanding from known motifs to nearby materials in the same neighborhoods. A network embedding step converts this weighted connectivity into vector representations of materials. Using these motif informed embeddings, property prediction yields a formation energy mean absolute error (MAE) of 0.157 eV per atom and a bandgap MAE of 0.601 eV. These results indicate that motif connectivity provides a compact, interpretable representation that complements existing descriptors for scalable screening and structure property modeling.