# PerCNet: Periodic Complete Representation for Crystal Graphs

arXiv: https://arxiv.org/abs/2312.14936 · HTML: https://mlsanity.com/paper/2312.14936/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 3 Dec 2023.

## Builds on (most cited first, 25 of 25)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Building powerful and equivariant graph neural networks with structural message-passing](https://mlsanity.com/paper/2006.15107/) (2020)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [DIG: A Turnkey Library for Diving into Graph Deep Learning Research](https://mlsanity.com/paper/2103.12608/) (2021)
- [ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs](https://mlsanity.com/paper/2206.08515/) (2022)
- [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://mlsanity.com/paper/2106.09575/) (2021)
- [Advanced Graph and Sequence Neural Networks for Molecular Property Prediction and Drug Discovery](https://mlsanity.com/paper/2012.01981/) (2020)
- [Topology-Aware Graph Pooling Networks](https://mlsanity.com/paper/2010.09834/) (2020)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)
- [Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraints](https://mlsanity.com/paper/2203.14352/) (2022)
- [Deep Learning of High-Order Interactions for Protein Interface Prediction](https://mlsanity.com/paper/2007.09334/) (2020)
- [Geometric Transformers for Protein Interface Contact Prediction](https://mlsanity.com/paper/2110.02423/) (2021)
- [Multi-task Joint Strategies of Self-supervised Representation Learning on Biomedical Networks for Drug Discovery](https://mlsanity.com/paper/2201.04437/) (2022)

## Built on by (most cited first, 1 of 1)

- [Universal crystal material property prediction via multi-view geometric fusion in graph transformers](https://mlsanity.com/paper/2507.15303/) (2025)

## Abstract (arXiv)

Crystal material representation is the foundation of crystal material research. Existing works consider crystal molecules as graph data with different representation methods and leverage the advantages of techniques in graph learning. A reasonable crystal representation method should capture the local and global information. However, existing methods only consider the local information of crystal molecules by modeling the bond distance and bond angle of first-order neighbors of atoms, which leads to the issue that different crystals will have the same representation. To solve this many-to-one issue, we consider the global information by further considering dihedral angles, which can guarantee that the proposed representation corresponds one-to-one with the crystal material. We first propose a periodic complete representation and calculation algorithm for infinite extended crystal materials. A theoretical proof for the representation that satisfies the periodic completeness is provided. Based on the proposed representation, we then propose a network for predicting crystal material properties, PerCNet, with a specially designed message passing mechanism. Extensive experiments are conducted on two real-world material benchmark datasets. The PerCNet achieves the best performance among baseline methods in terms of MAE. In addition, our results demonstrate the importance of the periodic scheme and completeness for crystal representation learning.