# Equivariant Message Passing Neural Network for Crystal Material Discovery

arXiv: https://arxiv.org/abs/2302.00485 · HTML: https://mlsanity.com/paper/2302.00485/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [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)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [CrystalGAN: Learning to Discover Crystallographic Structures with Generative Adversarial Networks](https://mlsanity.com/paper/1810.11203/) (2018)
- [Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials](https://mlsanity.com/paper/1806.03146/) (2018)

## Built on by (most cited first, 10 of 10)

- [All that structure matches does not glitter](https://mlsanity.com/paper/2509.12178/) (2025)
- [Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey](https://mlsanity.com/paper/2505.16379/) (2025)
- [Vector Field Oriented Diffusion Model for Crystal Material Generation](https://mlsanity.com/paper/2401.05402/) (2023)
- [Unified Model for Crystalline Material Generation](https://mlsanity.com/paper/2306.04510/) (2023)
- [C2NP: A Benchmark for Learning Scale-Dependent Geometric Invariances in 3D Materials Generation](https://mlsanity.com/paper/2601.19076/) (2026)
- [Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling](https://mlsanity.com/paper/2602.12045/) (2026)
- [Optimized Crystallographic Graph Generation for Material Science](https://mlsanity.com/paper/2307.05380/) (2023)
- [Local Max-Entropy and Free Energy Principles, Belief Diffusions and their Singularities](https://mlsanity.com/paper/2310.02946/) (2023)
- [Bond Graphs for multi-physics informed Neural Networks for multi-variate time series](https://mlsanity.com/paper/2405.13586/) (2024)
- [SCALAR: Quantifying Structural Hallucination, Consistency, and Reasoning Gaps in Materials Foundation Models](https://mlsanity.com/paper/2601.22312/) (2026)

## Abstract (arXiv)

Automatic material discovery with desired properties is a fundamental challenge for material sciences. Considerable attention has recently been devoted to generating stable crystal structures. While existing work has shown impressive success on supervised tasks such as property prediction, the progress on unsupervised tasks such as material generation is still hampered by the limited extent to which the equivalent geometric representations of the same crystal are considered. To address this challenge, we propose EMPNN a periodic equivariant message-passing neural network that learns crystal lattice deformation in an unsupervised fashion. Our model equivalently acts on lattice according to the deformation action that must be performed, making it suitable for crystal generation, relaxation and optimisation. We present experimental evaluations that demonstrate the effectiveness of our approach.