mlsanityData to 14 Oct 2026

Crystal-GFN: sampling crystals with desirable properties and constraints

arXiv 2310.04925 ↗First posted 7 Oct 2023cs.LGcited by 31

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Abstract (arXiv)

The discovery of novel solid-state materials, such as electrocatalysts, super-ionic conductors, or photovoltaic materials, plays a critical role in addressing various global challenges. It has, for instance, the potential to significantly improve the efficiency of renewable energy production and storage, thereby making substantial contributions to climate crisis mitigation strategies. In this paper, we introduce Crystal-GFN, a generative model of crystal structures possessing desirable properties and constraints. Operating as a multi-environment, continuous-discrete GFlowNet, it sequentially samples structural attributes of crystalline materials, namely space group, composition and lattice parameters. This domain-inspired approach enables the flexible incorporation of physicochemical and geometric hard constraints. We demonstrate the capabilities of Crystal-GFN to efficiently discover diverse and valid crystals with various properties: low predicted formation energy (median -3.2 eV/atom), band gap close to a target value and high density. Overall, Crystal-GFN is a crystal generation method that addresses several existing challenges in the literature and opens promising paths for accelerating materials discovery with machine learning.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 22 of its 51 references that are in the map. First posted on arXiv 7 Oct 2023.

Builds on

22 of 51 references.

References · 22

  1. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 516
  2. 2018MolGAN: An implicit generative model for small molecular graphscited by 393
  3. 2021Flow Network based Generative Models for Non-Iterative Diverse Candidate Generationcited by 392
  4. 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 305
  5. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 270
  6. 2022Trajectory balance: Improved credit assignment in GFlowNetscited by 251
  7. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 204
  8. 2022Biological Sequence Design with GFlowNetscited by 174
  9. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 172
  10. 2021E(n) Equivariant Normalizing Flowscited by 165
  11. 2023A theory of continuous generative flow networkscited by 101
  12. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 73
10 more
  1. 2023GFlowNets for AI-Driven Scientific Discoverycited by 63
  2. 2020An invertible crystallographic representation for general inverse design of inorganic crystals with targeted propertiescited by 53
  3. 2020An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storagecited by 45
  4. 2019Data-Driven Approach to Encoding and Decoding 3-D Crystal Structurescited by 34
  5. 2018CrystalGAN: Learning to Discover Crystallographic Structures with Generative Adversarial Networkscited by 31
  6. 2022Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraintscited by 30
  7. 2023Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learningcited by 26
  8. 2023Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modelingcited by 17
  9. 2023Multi-Fidelity Active Learning with GFlowNetscited by 15
  10. 2022PhAST: Physics-Aware, Scalable, and Task-specific GNNs for Accelerated Catalyst Designcited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 10; 2025: 14; 2026: 5.

31 papers.

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  1. 2024FlowMM: Generating Materials with Riemannian Flow Matchingcited by 109
  2. 2023MatterGen: a generative model for inorganic materials designcited by 98
  3. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 68
  4. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 51
  5. 2024Discrete Probabilistic Inference as Control in Multi-path Environmentscited by 44
  6. 2024Space Group Informed Transformer for Crystalline Materials Generationcited by 41
  7. 2025Open Materials Generation with Stochastic Interpolantscited by 28
  8. 2025Wyckoff Transformer: Generation of Symmetric Crystalscited by 27
  9. 2025LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Modelscited by 23
  10. 2025A Periodic Bayesian Flow for Material Generationcited by 16
  11. 2024Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximizationcited by 14
  12. 2024Improved Off-policy Reinforcement Learning in Biological Sequence Designcited by 13
19 more
  1. 2024RetroGFN: Diverse and Feasible Retrosynthesis using GFlowNetscited by 12
  2. 2024Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materialscited by 9
  3. 2025Artificial Intelligence and Generative Models for Materials Discovery -- A Reviewcited by 8
  4. 2024Generative Inverse Design of Crystal Structures via Diffusion Models with Transformerscited by 7
  5. 2025Space Group Conditional Flow Matchingcited by 7
  6. 2026Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modelingcited by 7
  7. 2024Towards DNA-Encoded Library Generation with GFlowNetscited by 5
  8. 2025OBELiX: A Curated Dataset of Crystal Structures and Experimentally Measured Ionic Conductivities for Lithium Solid-State Electrolytescited by 5
  9. 2025CrystalGym: A New Benchmark for Materials Discovery Using Reinforcement Learningcited by 4
  10. 2025MiAD: Mirage Atom Diffusion for De Novo Crystal Generationcited by 4
  11. 2025Generative Models for Crystalline Materialscited by 4
  12. 2025Catalyst GFlowNet for electrocatalyst design: A hydrogen evolution reaction case studycited by 3
  13. 2026Rooted Absorbed Prefix Trajectory Balance with Submodular Replay for GFlowNet Trainingcited by 3
  14. 2025Discrete Compositional Generation via General Soft Operators and Robust Reinforcement Learningcited by 2
  15. 2025Irresponsible AI: big tech's influence on AI research and associated impactscited by 1
  16. 2026Fourier Transformers for Latent Crystallographic Diffusion and Generative Modelingcited by 1
  17. 2024Dynamic Backtracking in GFlowNets: Enhancing Decision Steps with Reward-Dependent Adjustment Mechanismscited by 0
  18. 2026Reinforcement Learning on the Discrete Composition Channel of a Crystal Generator: Validated Gains and Reward Hackingcited by 0
  19. 2026OxiGen: Oxidation-State-Aware Crystal Generationcited by 0