# An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties

arXiv: https://arxiv.org/abs/2005.07609 · HTML: https://mlsanity.com/paper/2005.07609/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2020.

## Built on by (most cited first, 30 of 53)

- [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)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [LLMatDesign: Autonomous Materials Discovery with Large Language Models](https://mlsanity.com/paper/2406.13163/) (2024)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (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)
- [Hypothesis Generation for Materials Discovery and Design Using Goal-Driven and Constraint-Guided LLM Agents](https://mlsanity.com/paper/2501.13299/) (2025)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [Data-driven discovery of novel 2D materials by deep generative models](https://mlsanity.com/paper/2206.12159/) (2022)
- [Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling](https://mlsanity.com/paper/2308.02165/) (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)
- [Capturing long-range interaction with reciprocal space neural network](https://mlsanity.com/paper/2211.16684/) (2022)
- [Equivariant Message Passing Neural Network for Crystal Material Discovery](https://mlsanity.com/paper/2302.00485/) (2023)
- [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)
- [Establishing baselines for generative discovery of inorganic crystals](https://mlsanity.com/paper/2501.02144/) (2025)
- [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)
- [Unified Cross-Scale 3D Generation and Understanding via Autoregressive Modeling](https://mlsanity.com/paper/2503.16278/) (2025)
- [Generative Inverse Design of Crystal Structures via Diffusion Models with Transformers](https://mlsanity.com/paper/2406.09263/) (2024)
- [Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystals](https://mlsanity.com/paper/2510.12405/) (2025)
- [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)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization](https://mlsanity.com/paper/2512.08987/) (2025)

## Abstract (arXiv)

Realizing general inverse design could greatly accelerate the discovery of new materials with user-defined properties. However, state-of-the-art generative models tend to be limited to a specific composition or crystal structure. Herein, we present a framework capable of general inverse design (not limited to a given set of elements or crystal structures), featuring a generalized invertible representation that encodes crystals in both real and reciprocal space, and a property-structured latent space from a variational autoencoder (VAE). In three design cases, the framework generates 142 new crystals with user-defined formation energies, bandgap, thermoelectric (TE) power factor, and combinations thereof. These generated crystals, absent in the training database, are validated by first-principles calculations. The success rates (number of first-principles-validated target-satisfying crystals/number of designed crystals) ranges between 7.1% and 38.9%. These results represent a significant step toward property-driven general inverse design using generative models, although practical challenges remain when coupled with experimental synthesis.