# Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraints

arXiv: https://arxiv.org/abs/2203.14352 · HTML: https://mlsanity.com/paper/2203.14352/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 27 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [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)
- [Generative adversarial networks (GAN) based efficient sampling of chemical space for inverse design of inorganic materials](https://mlsanity.com/paper/1911.05020/) (2019)
- [Normalizing flows for atomic solids](https://mlsanity.com/paper/2111.08696/) (2021)
- [Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures](https://mlsanity.com/paper/1909.00949/) (2019)
- [CrystalGAN: Learning to Discover Crystallographic Structures with Generative Adversarial Networks](https://mlsanity.com/paper/1810.11203/) (2018)
- [Generative Models for Automatic Chemical Design](https://mlsanity.com/paper/1907.01632/) (2019)
- [Study of Deep Generative Models for Inorganic Chemical Compositions](https://mlsanity.com/paper/1910.11499/) (2019)

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

- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [Structure-based out-of-distribution (OOD) materials property prediction: a benchmark study](https://mlsanity.com/paper/2401.08032/) (2024)
- [Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Data](https://mlsanity.com/paper/2406.10796/) (2024)
- [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)
- [Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling](https://mlsanity.com/paper/2602.20210/) (2026)
- [Graph Diffusion that can Insert and Delete](https://mlsanity.com/paper/2506.15725/) (2025)
- [Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystals](https://mlsanity.com/paper/2510.12405/) (2025)
- [Generative Design of Crystal Structures by Point Cloud Representations and Diffusion Model](https://mlsanity.com/paper/2401.13192/) (2024)
- [InvDesFlow-AL: active learning-based workflow for inverse design of functional materials](https://mlsanity.com/paper/2505.09203/) (2025)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [Self-supervised learning for crystal property prediction via denoising](https://mlsanity.com/paper/2408.17255/) (2024)
- [Efficient Symmetry-Aware Materials Generation via Hierarchical Generative Flow Networks](https://mlsanity.com/paper/2411.04323/) (2024)
- [Towards an automated workflow in materials science for combining multi-modal simulative and experimental information using data mining and large language models](https://mlsanity.com/paper/2502.14904/) (2025)
- [Evaluating the diversity and utility of materials proposed by generative models](https://mlsanity.com/paper/2309.12323/) (2023)
- [Data-Driven Score-Based Models for Generating Stable Structures with Adaptive Crystal Cells](https://mlsanity.com/paper/2310.10695/) (2023)
- [L^2M^3OF: A Large Language Multimodal Model for Metal-Organic Frameworks](https://mlsanity.com/paper/2510.20976/) (2025)
- [PerCNet: Periodic Complete Representation for Crystal Graphs](https://mlsanity.com/paper/2312.14936/) (2023)
- [ADA-GNN: Atom-Distance-Angle Graph Neural Network for Crystal Material Property Prediction](https://mlsanity.com/paper/2401.11768/) (2024)
- [Autonomous Inorganic Materials Discovery via Multi-Agent Physics-Aware Scientific Reasoning](https://mlsanity.com/paper/2508.02956/) (2025)
- [Benchmarking GNNs for OOD Materials Property Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2511.11697/) (2025)
- [Chemical filters for ultra-high-throughput materials screening and generation](https://mlsanity.com/paper/2607.17910/) (2026)
- [Unleashing the power of novel conditional generative approaches for new materials discovery](https://mlsanity.com/paper/2411.03156/) (2024)
- [Design Topological Materials by Reinforcement Fine-Tuned Generative Model](https://mlsanity.com/paper/2504.13048/) (2025)
- [Unified machine-learning framework for property prediction and time-evolution simulation of strained alloy microstructure](https://mlsanity.com/paper/2507.21760/) (2025)
- [Inverse Design of Inorganic Compounds with Generative AI](https://mlsanity.com/paper/2604.11827/) (2026)
- [Neural surrogates for crystal growth dynamics with variable supersaturation: explicit vs. implicit conditioning](https://mlsanity.com/paper/2604.21753/) (2026)
- [Text-guided flow matching enables sample-efficient crystal structure generation](https://mlsanity.com/paper/2609.01076/) (2026)

## Abstract (arXiv)

Discovering new materials is a challenging task in materials science crucial to the progress of human society. Conventional approaches based on experiments and simulations are labor-intensive or costly with success heavily depending on experts' heuristic knowledge. Here, we propose a deep learning based Physics Guided Crystal Generative Model (PGCGM) for efficient crystal material design with high structural diversity and symmetry. Our model increases the generation validity by more than 700% compared to FTCP, one of the latest structure generators and by more than 45% compared to our previous CubicGAN model. Density Functional Theory (DFT) calculations are used to validate the generated structures with 1,869 materials out of 2,000 are successfully optimized and deposited into the Carolina Materials Database urlwww.carolinamatdb.org, of which 39.6% have negative formation energy and 5.3% have energy-above-hull less than 0.25 eV/atom, indicating their thermodynamic stability and potential synthesizability.