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 has shown great promise in automatically generating general graphs. However, their advancement into periodic graphs have 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 models for periodic graphs that can automatically learn, disentangle, and generate local and global graph patterns. Specifically, we develop a new periodic graph encoder consisting of global-pattern encoder and local-pattern encoder that ensures to disentangle the representation into global and local semantics. We then propose a new periodic graph decoder consisting of local structure decoder, neighborhood decoder, and global structure decoder, as well as the assembler of their outputs that guarantees periodicity. Moreover, we design a new model learning objective that helps ensure the invariance of local-semantic representations for the graphs with the same local structure. Comprehensive experimental evaluations have been conducted to demonstrate the effectiveness of the proposed method. The code of proposed PGD-VAE is availabe at https://github.com/shi-yu-wang/PGD-VAE.
翻译:定期图形是由重复的地方结构(如水晶网和多边形网状)组成的图表。它们的基因模型在材料设计和图形合成等真实世界应用中具有巨大的潜力。古典模型要么依靠特定域的预定义生成原则(如水晶网设计),要么遵循基于几何的既定规则。最近,深层基因模型在自动生成一般图形方面显示出很大的希望。然而,由于在1) 保持图形周期性方面的若干关键挑战,没有很好地探索它们进入定期图表的进度;2 扭曲当地和全球模式;3 学习重复模式的效率。为了解决这些问题,本文提议了周期-Graph Disentangled Variational-encational-cocarder 自动编码(如水晶网设计),或采用新的深度模型模型,可以自动学习、分解,并生成本地和全球性图表模式。我们开发一个新的定期图形编码,用来确保本地和本地的图形的显示全球和本地的图解变数据。我们随后提议了一个新的直径结构,用来进行新的直径结构的计算。