Deep Generative Model for Periodic Graphs

Periodic graphs are graphs consisting of repetitive local structures, such as crystal nets and polygon mesh. Their generative modeling has great potential in real-world applications such as material design and graphics synthesis. Classical models either rely on domain-specific predefined generation principles (e.g., in crystal net design), or follow geometry-based prescribed rules. Recently, deep generative models have shown great promise in automatically generating general graphs. However, their advancement into periodic graphs has not been well explored due to several key challenges in 1) maintaining graph periodicity; 2) disentangling local and global patterns; and 3) efficiency in learning repetitive patterns. To address them, this paper proposes Periodical-Graph Disentangled Variational Auto-encoder (PGD-VAE), a new deep generative model for periodic graphs that can automatically learn, disentangle, and generate local and global graph patterns.