# Learning Ordering in Crystalline Materials with Symmetry-Aware Graph Neural Networks

arXiv: https://arxiv.org/abs/2409.13851 · HTML: https://mlsanity.com/paper/2409.13851/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 63 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## Builds on (most cited first, 13 of 13)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Matbench Discovery -- A framework to evaluate machine learning crystal stability predictions](https://mlsanity.com/paper/2308.14920/) (2023)
- [Practical Bayesian optimization in the presence of outliers](https://mlsanity.com/paper/1712.04567/) (2017)
- [Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution](https://mlsanity.com/paper/2310.02299/) (2023)
- [Incompleteness of graph neural networks for points clouds in three dimensions](https://mlsanity.com/paper/2201.07136/) (2022)

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

- [Atomistic Modeling of Chemical Disorder in Materials: Bridging Conventional Methods and AI-Assisted Approaches](https://mlsanity.com/paper/2605.19124/) (2026)

## Abstract (arXiv)

Graph convolutional neural networks (GCNNs) have become a machine learning workhorse for screening the chemical space of crystalline materials in fields such as catalysis and energy storage, by predicting properties from structures. Multicomponent materials, however, present a unique challenge since they can exhibit chemical (dis)order, where a given lattice structure can encompass a variety of elemental arrangements ranging from highly ordered structures to fully disordered solid solutions. Critically, properties like stability, strength, and catalytic performance depend not only on structures but also on orderings. To enable rigorous materials design, it is thus critical to ensure GCNNs are capable of distinguishing among atomic orderings. However, the ordering-aware capability of GCNNs has been poorly understood. Here, we benchmark various neural network architectures for capturing the ordering-dependent energetics of multicomponent materials in a custom-made dataset generated with high-throughput atomistic simulations. Conventional symmetry-invariant GCNNs were found unable to discern the structural difference between the diverse symmetrically inequivalent atomic orderings of the same material, while symmetry-equivariant model architectures could inherently preserve and differentiate the distinct crystallographic symmetries of various orderings.