# Deep Generative Model for Periodic Graphs

arXiv: https://arxiv.org/abs/2201.11932 · HTML: https://mlsanity.com/paper/2201.11932/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 81 references that are in the map.
- First posted on arXiv 28 Jan 2022.

## Builds on (most cited first, 23 of 23)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [Graph Representation Learning: A Survey](https://mlsanity.com/paper/1909.00958/) (2019)
- [Disentangled Representation Learning in Cardiac Image Analysis](https://mlsanity.com/paper/1903.09467/) (2019)
- [A Survey on Graph Neural Networks for Knowledge Graph Completion](https://mlsanity.com/paper/2007.12374/) (2020)
- [Toward Subgraph-Guided Knowledge Graph Question Generation with Graph Neural Networks](https://mlsanity.com/paper/2004.06015/) (2020)
- [Interpretable Deep Graph Generation with Node-Edge Co-Disentanglement](https://mlsanity.com/paper/2006.05385/) (2020)
- [Look Across Elapse: Disentangled Representation Learning and Photorealistic Cross-Age Face Synthesis for Age-Invariant Face Recognition](https://mlsanity.com/paper/1809.00338/) (2018)
- [Deep Graph Translation](https://mlsanity.com/paper/1805.09980/) (2018)

## Built on by (most cited first, 20 of 20)

- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [Beyond Text: A Deep Dive into Large Language Models' Ability on Understanding Graph Data](https://mlsanity.com/paper/2310.04944/) (2023)
- [Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materials](https://mlsanity.com/paper/2306.09375/) (2023)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [MatSciML: A Broad, Multi-Task Benchmark for Solid-State Materials Modeling](https://mlsanity.com/paper/2309.05934/) (2023)
- [ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splitting](https://mlsanity.com/paper/2205.13700/) (2022)
- [Multi-objective Deep Data Generation with Correlated Property Control](https://mlsanity.com/paper/2210.01796/) (2022)
- [Curriculum Learning for Graph Neural Networks: Which Edges Should We Learn First](https://mlsanity.com/paper/2310.18735/) (2023)
- [Materials Informatics Transformer: A Language Model for Interpretable Materials Properties Prediction](https://mlsanity.com/paper/2308.16259/) (2023)
- [SGOOD: Substructure-enhanced Graph-Level Out-of-Distribution Detection](https://mlsanity.com/paper/2310.10237/) (2023)
- [Retrieval-based Disentangled Representation Learning with Natural Language Supervision](https://mlsanity.com/paper/2212.07699/) (2022)
- [Deep representation learning: Fundamentals, Perspectives, Applications, and Open Challenges](https://mlsanity.com/paper/2211.14732/) (2022)
- [GraphRCG: Self-Conditioned Graph Generation](https://mlsanity.com/paper/2403.01071/) (2024)
- [Representation Learning of Geometric Trees](https://mlsanity.com/paper/2408.08799/) (2024)
- [Disentangled Generative Graph Representation Learning](https://mlsanity.com/paper/2408.13471/) (2024)
- [Non-Euclidean Spatial Graph Neural Network](https://mlsanity.com/paper/2312.10808/) (2023)
- [Fine-Grained Graph Generation through Latent Mixture Scheduling](https://mlsanity.com/paper/2605.02780/) (2026)

## Abstract (arXiv)

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.