# Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures

arXiv: https://arxiv.org/abs/1909.00949 · HTML: https://mlsanity.com/paper/1909.00949/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 30 of 34)

- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Scalable Diffusion for Materials Generation](https://mlsanity.com/paper/2311.09235/) (2023)
- [LLMatDesign: Autonomous Materials Discovery with Large Language Models](https://mlsanity.com/paper/2406.13163/) (2024)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [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)
- [MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworks](https://mlsanity.com/paper/2410.17270/) (2024)
- [A Periodic Bayesian Flow for Material Generation](https://mlsanity.com/paper/2502.02016/) (2025)
- [Periodic Materials Generation using Text-Guided Joint Diffusion Model](https://mlsanity.com/paper/2503.00522/) (2025)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [Generative Hierarchical Materials Search](https://mlsanity.com/paper/2409.06762/) (2024)
- [DenseGNN: universal and scalable deeper graph neural networks for high-performance property prediction in crystals and molecules](https://mlsanity.com/paper/2501.03278/) (2025)
- [LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generation](https://mlsanity.com/paper/2510.23040/) (2025)
- [Vector Field Oriented Diffusion Model for Crystal Material Generation](https://mlsanity.com/paper/2401.05402/) (2023)
- [Kinetic Langevin Diffusion for Crystalline Materials Generation](https://mlsanity.com/paper/2507.03602/) (2025)
- [Equivariant Diffusion for Crystal Structure Prediction](https://mlsanity.com/paper/2512.07289/) (2025)
- [M2Hub: Unlocking the Potential of Machine Learning for Materials Discovery](https://mlsanity.com/paper/2307.05378/) (2023)
- [Generative Inverse Design of Crystal Structures via Diffusion Models with Transformers](https://mlsanity.com/paper/2406.09263/) (2024)
- [Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling](https://mlsanity.com/paper/2602.20210/) (2026)
- [Atomic structure generation from reconstructing structural fingerprints](https://mlsanity.com/paper/2207.13227/) (2022)
- [Generative Design of Crystal Structures by Point Cloud Representations and Diffusion Model](https://mlsanity.com/paper/2401.13192/) (2024)
- [Crystal-LSBO: Automated Design of De Novo Crystals with Latent Space Bayesian Optimization](https://mlsanity.com/paper/2405.17881/) (2024)
- [ParticleGrid: Enabling Deep Learning using 3D Representation of Materials](https://mlsanity.com/paper/2211.08506/) (2022)
- [Neural Structure Fields with Application to Crystal Structure Autoencoders](https://mlsanity.com/paper/2212.13120/) (2022)
- [Data-Driven Score-Based Models for Generating Stable Structures with Adaptive Crystal Cells](https://mlsanity.com/paper/2310.10695/) (2023)
- [SLayerGen: a Crystal Generative Model for all Space and Layer Groups](https://mlsanity.com/paper/2605.08262/) (2026)
- [Artificial Intelligence in Material Engineering: A review on applications of AI in Material Engineering](https://mlsanity.com/paper/2209.11234/) (2022)
- [Towards End-to-End Structure Solutions from Information-Compromised Diffraction Data via Generative Deep Learning](https://mlsanity.com/paper/2312.15136/) (2023)

## Abstract (arXiv)

Generative models have achieved impressive results in many domains including image and text generation. In the natural sciences, generative models have led to rapid progress in automated drug discovery. Many of the current methods focus on either 1-D or 2-D representations of typically small, drug-like molecules. However, many molecules require 3-D descriptors and exceed the chemical complexity of commonly used dataset. We present a method to encode and decode the position of atoms in 3-D molecules from a dataset of nearly 50,000 stable crystal unit cells that vary from containing 1 to over 100 atoms. We construct a smooth and continuous 3-D density representation of each crystal based on the positions of different atoms. Two different neural networks were trained on a dataset of over 120,000 three-dimensional samples of single and repeating crystal structures, made by rotating the single unit cells. The first, an Encoder-Decoder pair, constructs a compressed latent space representation of each molecule and then decodes this description into an accurate reconstruction of the input. The second network segments the resulting output into atoms and assigns each atom an atomic number. By generating compressed, continuous latent spaces representations of molecules we are able to decode random samples, interpolate between two molecules, and alter known molecules.