# AI-Assisted Rapid Crystal Structure Generation Towards a Target Local Environment

arXiv: https://arxiv.org/abs/2506.08224 · HTML: https://mlsanity.com/paper/2506.08224/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 94 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Fine-Tuned Language Models Generate Stable Inorganic Materials as Text](https://mlsanity.com/paper/2402.04379/) (2024)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [SV4D 2.0: Enhancing Spatio-Temporal Consistency in Multi-View Video Diffusion for High-Quality 4D Generation](https://mlsanity.com/paper/2503.16396/) (2025)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Wyckoff Transformer: Generation of Symmetric Crystals](https://mlsanity.com/paper/2503.02407/) (2025)

## Built on by (most cited first, 2 of 2)

- [CrystalGRPO: Target-Aligned and Coverage-Preserving Reinforcement Learning for Flow-Based Crystal Structure Prediction](https://mlsanity.com/paper/2608.06582/) (2026)
- [Crystal Generation using the Fully Differentiable Pipeline and Latent Space Optimization](https://mlsanity.com/paper/2601.04606/) (2026)

## Abstract (arXiv)

In the field of material design, traditional crystal structure prediction approaches require extensive structural sampling through computationally expensive energy minimization methods using either force fields or quantum mechanical simulations. While emerging artificial intelligence (AI) generative models have shown great promise in generating realistic crystal structures more rapidly, most existing models fail to account for the unique symmetries and periodicity of crystalline materials, and they are limited to handling structures with only a few tens of atoms per unit cell. Here, we present a symmetry-informed AI generative approach called Local Environment Geometry-Oriented Crystal Generator (LEGO-xtal) that overcomes these limitations. Our method generates initial structures using AI models trained on an augmented small dataset, and then optimizes them using machine learning structure descriptors rather than traditional energy-based optimization. We demonstrate the effectiveness of LEGO-xtal by expanding from 25 known low-energy sp2 carbon allotropes to over 1,700, all within 0.5 eV/atom of the ground-state energy of graphite. This framework offers a generalizable strategy for the targeted design of materials with modular building blocks, such as metal-organic frameworks and next-generation battery materials.