# Connectivity Optimized Nested Graph Networks for Crystal Structures

arXiv: https://arxiv.org/abs/2302.14102 · HTML: https://mlsanity.com/paper/2302.14102/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 60 references that are in the map.
- First posted on arXiv 27 Feb 2023.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [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)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalysts](https://mlsanity.com/paper/2206.08917/) (2022)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [DeepSphere: a graph-based spherical CNN](https://mlsanity.com/paper/2012.15000/) (2020)
- [Orbital Graph Convolutional Neural Network for Material Property Prediction](https://mlsanity.com/paper/2008.06415/) (2020)

## Built on by (most cited first, 11 of 11)

- [From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Prediction](https://mlsanity.com/paper/2310.16802/) (2023)
- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction](https://mlsanity.com/paper/2406.12888/) (2024)
- [Materials Informatics Transformer: A Language Model for Interpretable Materials Properties Prediction](https://mlsanity.com/paper/2308.16259/) (2023)
- [CrysToGraph: A Comprehensive Predictive Model for Crystal Materials Properties and the Benchmark](https://mlsanity.com/paper/2407.16131/) (2024)
- [CLOUD: A Scalable and Physics-Informed Foundation Model for Crystal Representation Learning](https://mlsanity.com/paper/2506.17345/) (2025)
- [Graph Transformer Networks for Accurate Band Structure Prediction: An End-to-End Approach](https://mlsanity.com/paper/2411.16483/) (2024)
- [Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computations](https://mlsanity.com/paper/2507.01131/) (2025)
- [Combining feature-based approaches with graph neural networks and symbolic regression for synergistic performance and interpretability](https://mlsanity.com/paper/2509.03547/) (2025)
- [Addressing the Accuracy-Cost Tradeoff in Material Property Prediction: A Teacher-Student Strategy](https://mlsanity.com/paper/2309.04482/) (2023)
- [Towards Efficient Large Language Models for Scientific Text: A Review](https://mlsanity.com/paper/2408.10729/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) have been applied to a large variety of applications in materials science and chemistry. Here, we recapitulate the graph construction for crystalline (periodic) materials and investigate its impact on the GNNs model performance. We suggest the asymmetric unit cell as a representation to reduce the number of atoms by using all symmetries of the system. This substantially reduced the computational cost and thus time needed to train large graph neural networks without any loss in accuracy. Furthermore, with a simple but systematically built GNN architecture based on message passing and line graph templates, we introduce a general architecture (Nested Graph Network, NGN) that is applicable to a wide range of tasks. We show that our suggested models systematically improve state-of-the-art results across all tasks within the MatBench benchmark. Further analysis shows that optimized connectivity and deeper message functions are responsible for the improvement. Asymmetric unit cells and connectivity optimization can be generally applied to (crystal) graph networks, while our suggested nested graph framework will open new ways of systematic comparison of GNN architectures.