# Efficient Symmetry-Aware Materials Generation via Hierarchical Generative Flow Networks

arXiv: https://arxiv.org/abs/2411.04323 · HTML: https://mlsanity.com/paper/2411.04323/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Builds on (most cited first, 11 of 11)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Data-Efficient Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1805.08296/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraints](https://mlsanity.com/paper/2203.14352/) (2022)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [CFlowNets: Continuous Control with Generative Flow Networks](https://mlsanity.com/paper/2303.02430/) (2023)

## Built on by (most cited first, 3 of 3)

- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [MiAD: Mirage Atom Diffusion for De Novo Crystal Generation](https://mlsanity.com/paper/2511.14426/) (2025)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)

## Abstract (arXiv)

Discovering new solid-state materials requires rapidly exploring the vast space of crystal structures and locating stable regions. Generating stable materials with desired properties and compositions is extremely difficult as we search for very small isolated pockets in the exponentially many possibilities, considering elements from the periodic table and their 3D arrangements in crystal lattices. Materials discovery necessitates both optimized solution structures and diversity in the generated material structures. Existing methods struggle to explore large material spaces and generate diverse samples with desired properties and requirements. We propose the Symmetry-aware Hierarchical Architecture for Flow-based Traversal (SHAFT), a novel generative model employing a hierarchical exploration strategy to efficiently exploit the symmetry of the materials space to generate crystal structures given desired properties. In particular, our model decomposes the exponentially large materials space into a hierarchy of subspaces consisting of symmetric space groups, lattice parameters, and atoms. We demonstrate that SHAFT significantly outperforms state-of-the-art iterative generative methods, such as Generative Flow Networks (GFlowNets) and Crystal Diffusion Variational AutoEncoders (CDVAE), in crystal structure generation tasks, achieving higher validity, diversity, and stability of generated structures optimized for target properties and requirements.