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arxiv: 2606.02507 · v1 · pith:EJK2PHB3new · submitted 2026-06-01 · ❄️ cond-mat.mtrl-sci · cs.ET· cs.LG· physics.app-ph· physics.comp-ph

Towards Automated Discovery: A Review of Generative Models, Multimodal Learning and Closed-Loop Workflows in Inverse Materials Design

Anand Babu , Rog\'erio Almeida Gouv\^ea , Gian-Marco Rignanese This is my paper

Pith reviewed 2026-06-28 13:29 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cs.ETcs.LGphysics.app-phphysics.comp-ph
keywords inverse materials designgenerative modelscrystal structuresmultimodal learningclosed-loop workflowsmaterials discoverydiffusion modelsstability gap
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The pith

Generative models learn chemical-structural priors from databases to enable controllable sampling of periodic crystal structures for inverse materials design.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review establishes that inverse materials design is moving from forward prediction toward targeted generation of candidate crystals that meet specific objectives while respecting physical constraints. A sympathetic reader would care because the approach promises to make materials discovery more efficient by using data-driven models to propose structures instead of exhaustive search. The paper surveys how models such as variational autoencoders, normalizing flows, autoregressive networks, and diffusion models acquire priors from large databases and how feasibility is enforced through representation choices, training objectives, sampling guidance, and post-processing. It further examines the fusion of multiple data modalities into unified representations and the integration of generation with optimization loops such as Bayesian methods and reinforcement learning. The review also catalogs recurring failure modes including surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap, while advocating staged evaluation metrics of validity, novelty, uniqueness, stability, and cost.

Core claim

Modern generators learn chemical-structural priors from large databases to enable controllable sampling of periodic structures, with multimodal learning and closed-loop integration advancing inverse design while recurring failure modes include surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap.

What carries the argument

Generative crystal structure models (variational autoencoders, normalizing flows, autoregressive formulations, diffusion models) that acquire priors from databases and enforce physical constraints via representation, objectives, guidance, and screening.

If this is right

  • Controllable sampling of periodic structures follows from learning priors in the listed model classes.
  • Multimodal fusion of structures, thermodynamics, spectra, and text produces more transferable representations of chemical space.
  • Integration of conditional generation with latent optimization, Bayesian optimization, reinforcement learning, and active learning yields concrete inverse-design strategies.
  • Staged reporting of validity, novelty, uniqueness, stability, and cost becomes the required standard for discovery-grade evaluation.
  • Mitigation of surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap is necessary for reliable automated discovery.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the stability-synthesizability gap narrows through these workflows, experimental validation cycles could shorten substantially.
  • Distribution shift between generated and real-world databases implies that models trained on current data may require periodic retraining on new experimental results.
  • Closed-loop integration could extend naturally to processing parameters and device-level performance once multimodal representations include those modalities.
  • The emphasis on post-generation relaxation and screening suggests that purely generative approaches may still need hybrid physics-based refinement steps.

Load-bearing premise

The surveyed literature and model classes comprehensively represent leading approaches and the identified failure modes apply broadly across the field.

What would settle it

A new generative model that produces high novelty, uniqueness, and stability scores on held-out databases without diversity collapse or surrogate exploitation would challenge the claim that these failure modes are recurring.

Figures

Figures reproduced from arXiv: 2606.02507 by Anand Babu, Gian-Marco Rignanese, Rog\'erio Almeida Gouv\^ea.

Figure 1
Figure 1. Figure 1: Overview of the four principal crystal structure generation model families. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of a multimodal materials machine learning workflow. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Algorithm selection guide for inverse-design optimization. [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Failure-mode map for crystal inverse-design systems with algorithm-exposure [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The self-driving laboratory as an orchestrated closed-loop system for inverse [PITH_FULL_IMAGE:figures/full_fig_p028_5.png] view at source ↗
read the original abstract

Inverse materials design is shifting materials discovery from forward prediction to targeted proposal of candidates that satisfy objectives under physical constraints. Here, we review recent advances in generative crystal structure modeling, multimodal learning, and closed-loop design pipelines for crystalline solids. We survey how modern generators learn chemical-structural priors from large databases to enable controllable sampling of periodic structures, and compare leading model classes including variational autoencoders, normalizing flows, autoregressive formulations, and diffusion models. Particular attention is given to how feasibility constraints and physical priors are enforced across the workflow, through representation choices, training objectives, sampling-time guidance, and post-generation screening and relaxation. We also discuss how multimodal learning fuses diverse materials modalities, including crystal structures, thermodynamic, electronic information, microscopy, spectroscopy, processing context, and scientific text, to construct a more universal, transferable representation of chemical space. In addition, diverse inverse-design strategies are examined, particularly those that integrate conditional generation with latent optimization, Bayesian optimization, reinforcement learning, and active learning. Finally, we highlight recurring failure modes, such as surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap, and outline discovery-grade evaluation practices based on staged reporting of validity, novelty, uniqueness, stability, and cost.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The manuscript is a review surveying recent advances in generative models for crystal structures (VAEs, normalizing flows, autoregressive formulations, diffusion models), multimodal learning that fuses crystal structures with thermodynamic, electronic, microscopy, spectroscopy, processing, and text data, closed-loop inverse-design workflows integrating conditional generation with latent optimization, Bayesian optimization, reinforcement learning and active learning, enforcement of physical constraints via representations, objectives, guidance and post-processing, recurring failure modes including surrogate exploitation, diversity collapse, distribution shift and the stability-synthesizability gap, and staged evaluation practices based on validity, novelty, uniqueness, stability and cost.

Significance. If the coverage is representative, the review provides a timely synthesis of trends in automated inverse materials design, explicitly naming failure modes and evaluation criteria that can help standardize reporting and reduce common pitfalls in the field.

minor comments (1)
  1. The abstract lists model classes and failure modes but does not indicate the number of papers or time window surveyed; adding this in the introduction would help readers gauge scope.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of the manuscript, recognition of its timeliness, and recommendation to accept. We are pleased that the coverage of generative models, multimodal learning, closed-loop workflows, failure modes, and evaluation practices was viewed as representative and useful for standardizing reporting in the field.

Circularity Check

0 steps flagged

Review paper: no derivations or self-referential claims present

full rationale

This is a survey paper summarizing external literature on generative models, multimodal learning, and closed-loop workflows for inverse materials design. No equations, derivations, fitted parameters, predictions, or load-bearing self-citations are present that could reduce to the paper's own inputs. Central claims are descriptive summaries of trends from cited works, with no internal technical assertions that require validation against the paper itself. The weakest assumption (comprehensiveness of surveyed literature) is inherent to review format and does not constitute circularity. Score 0 is the appropriate finding for self-contained survey content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As this is a review paper, no new free parameters, axioms, or invented entities are introduced; the contribution is synthesis of existing methods and literature.

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discussion (0)

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Reference graph

Works this paper leans on

89 extracted references · 62 canonical work pages

  1. [1]

    Curtarolo, S. et al. The high-throughput highway to computational materials design. Nature Mate- rials 12, 191–201 (2013). doi:10.1038/nmat3568. https://doi.org/10.1038/nmat3568

    work page doi:10.1038/nmat3568 2013

  2. [2]

    Jain, A. et al. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Materials 1, 011002 (2013). doi:10.1063/1.4812323. https://doi.org/ 10.1063/1.4812323

    work page doi:10.1063/1.4812323 2013

  3. [3]

    Ward, L. et al. Matminer: An open source toolkit for materials data mining. Computational Materials Science 152, 60–69 (2018). doi:10.1016/j.commatsci.2018.05.018. https://doi.org/10.1016/j.co mmatsci.2018.05.018

    work page doi:10.1016/j.commatsci.2018.05.018 2018

  4. [4]

    Choudhary, K. et al. The joint automated repository for various integrated simulations (JAR VIS) for data-driven materials design. npj Computational Materials 6, 173 (2020). doi:10.1038/s41524-020- 00440-1. https://doi.org/10.1038/s41524-020-00440-1

    work page doi:10.1038/s41524-020- 2020

  5. [5]

    Kirklin, S. et al. The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT for- mation energies. npj Computational Materials 1, 15010 (2015). doi:10.1038/npjcompumats.2015.10. https://doi.org/10.1038/npjcompumats.2015.10

    work page doi:10.1038/npjcompumats.2015.10 2015

  6. [6]

    Saal, J. E. et al. Materials design and discovery with high-throughput density functional theory: The Open Quantum Materials Database (OQMD). JOM 65, 1501–1509 (2013). doi:10.1007/s11837-013- 0755-4. https://doi.org/10.1007/s11837-013-0755-4

    work page doi:10.1007/s11837-013- 2013

  7. [7]

    Ong, S. P. et al. Python Materials Genomics (pymatgen): A robust, open-source Python library for materials analysis. Computational Materials Science 68, 314–319 (2013). doi:10.1016/j.commatsci.2012.10.028. https://doi.org/10.1016/j.commatsci.2012.10.028

    work page doi:10.1016/j.commatsci.2012.10.028 2013

  8. [8]

    V., Xue, D

    Lookman, T., Balachandran, P. V., Xue, D. and Yuan, R. Active learning in materials science with emphasis on adaptive sampling using uncertainties for targeted design. npj Computational Materials 5, 21 (2019). doi:10.1038/s41524-019-0153-8. https://doi.org/10.1038/s41524-019-0153-8

    work page doi:10.1038/s41524-019-0153-8 2019

  9. [9]

    Shahriari, B., Swersky, K., Wang, Z., Adams, R. P. and de Freitas, N. Taking the human out of the loop: A review of Bayesian optimization. Proceedings of the IEEE 104, 148–175 (2016). doi:10.1109/JPROC.2015.2494218. https://doi.org/10.1109/JPROC.2015.2494218 31

    work page doi:10.1109/jproc.2015.2494218 2016

  10. [10]

    and Adams, R

    Snoek, J., Larochelle, H. and Adams, R. P. Practical Bayesian optimization of machine learning algorithms. Advances in Neural Information Processing Systems 25 (2012). https://arxiv.org/ab s/1206.2944

    Pith/arXiv arXiv 2012

  11. [11]

    Frazier, P. I. A tutorial on Bayesian optimization. arXiv (2018). arXiv:1807.02811. https://arxiv. org/abs/1807.02811

    Pith/arXiv arXiv 2018

  12. [12]

    Active Learning Literature Survey

    Settles, B. Active Learning Literature Survey. University of Wisconsin-Madison, Computer Sciences Technical Report 1648 (2009). https://minds.wisconsin.edu/handle/1793/60660

    2009

  13. [13]

    Häse, F., Roch, L. M. and Aspuru-Guzik, A. Phoenics: A Bayesian optimizer for chemistry. ACS Central Science 4, 1134–1145 (2018). doi:10.1021/acscentsci.8b00307. https://doi.org/10.1021/ acscentsci.8b00307

    work page doi:10.1021/acscentsci.8b00307 2018

  14. [14]

    Häse, F., Roch, L. M. and Aspuru-Guzik, A. Gryffin: An algorithm for Bayesian optimization of categorical variables informed by physical intuition with applications to chemistry. ACS Central Science 7, 1230–1237 (2021). doi:10.1021/acscentsci.0c01520. https://doi.org/10.1021/acscents ci.0c01520

    work page doi:10.1021/acscentsci.0c01520 2021

  15. [15]

    Luo, X. et al. Deep learning generative model for crystal structure prediction. npj Computational Materials 10, 254 (2024). doi:10.1038/s41524-024-01443-y. https://doi.org/10.1038/s41524-024 -01443-y

    work page doi:10.1038/s41524-024-01443-y 2024

  16. [16]

    Xie, T. et al. Crystal Diffusion Variational Autoencoder for periodic material generation. arXiv (2021). arXiv:2110.06197. https://arxiv.org/abs/2110.06197

    arXiv 2021

  17. [17]

    Jiao, R. et al. Crystal Structure Prediction by Joint Equivariant Diffusion. arXiv (2023). arXiv:2309.04475. https://arxiv.org/abs/2309.04475

    arXiv 2023

  18. [18]

    Zhao, Y. et al. Probabilistic constrained graph variational autoencoders for crystal generation. npj Computational Materials 9, 30 (2023). doi:10.1038/s41524-023-00987-9. https://doi.org/10.103 8/s41524-023-00987-9

    work page doi:10.1038/s41524-023-00987-9 2023

  19. [19]

    Qiu, J. et al. VQCrystal: A vector-quantized diffusion framework for crystal generation. npj Com- putational Materials 11, 63 (2025). doi:10.1038/s41524-025-01613-6. https://doi.org/10.1038/s4 1524-025-01613-6

    work page doi:10.1038/s41524-025-01613-6 2025

  20. [20]

    Zeni, C. et al. A generative model for inorganic materials design (MatterGen). Nature (2025). https://www.nature.com/articles/s41586-025-08628-5

    2025

  21. [21]

    Luo, X. et al. CrystalFlow: a flow-based generative model for crystal structure prediction and mate- rials discovery. Nature Communications (2025). https://www.nature.com/articles/s41467-025 -64364-4

    2025

  22. [22]

    Park, C. W. et al. Exploration of crystal chemical space using text-guided generative artificial intelli- gence. Nature Communications (2025). doi:10.1038/s41467-025-59636-y. https://www.nature.com /articles/s41467-025-59636-y

    work page doi:10.1038/s41467-025-59636-y 2025

  23. [23]

    Ren, Z. et al. An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties. Matter 5, 314–335 (2022). doi:10.1016/j.matt.2021.11.032. https: //doi.org/10.1016/j.matt.2021.11.032

    work page doi:10.1016/j.matt.2021.11.032 2022

  24. [24]

    and Abbeel, P

    Ho, J., Jain, A. and Abbeel, P. Denoising diffusion probabilistic models. arXiv (2020). arXiv:2006.11239. https://arxiv.org/abs/2006.11239

    Pith/arXiv arXiv 2020

  25. [25]

    P., Kumar, A., Ermon, S

    Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S. and Poole, B. Score-based generative modeling through stochastic differential equations. arXiv (2020). arXiv:2011.13456. https://arxiv.org/abs/2011.13456

    Pith/arXiv arXiv 2020

  26. [26]

    Wu, Y. et al. A versatile multimodal learning framework bridging multiscale knowledge for material design. npj Computational Materials (2025). doi:10.1038/s41524-025-01767-3. https://doi.org/10 .1038/s41524-025-01767-3

    work page doi:10.1038/s41524-025-01767-3 2025

  27. [27]

    Moro, V. et al. Multimodal foundation models for material property prediction and discovery. Newton (2025). PII: S2950636025000088. https://www.sciencedirect.com/science/article/pii/S295 0636025000088 32

    2025

  28. [28]

    Babu, A. et al. MEIDNet: Multimodal generative AI framework for inverse materials design. arXiv (2026). arXiv:2601.22009. doi:10.48550/arXiv.2601.22009. https://arxiv.org/abs/2601.22009

    work page doi:10.48550/arxiv.2601.22009 2026

  29. [29]

    Kononova, O. et al. Text-mined dataset of inorganic materials synthesis recipes. Scientific Data 6, 203 (2019). doi:10.1038/s41597-019-0224-1. https://doi.org/10.1038/s41597-019-0224-1

    work page doi:10.1038/s41597-019-0224-1 2019

  30. [30]

    Tshitoyan, V. et al. Unsupervised word embeddings capture latent knowledge from materials science literature. Nature 571, 95–98 (2019). doi:10.1038/s41586-019-1335-8. https://doi.org/10.1038/ s41586-019-1335-8

    work page doi:10.1038/s41586-019-1335-8 2019

  31. [31]

    Olivetti, E. A. et al. Data-driven materials research enabled by natural language processing and information extraction. Applied Physics Reviews 7, 041317 (2020). doi:10.1063/5.0021106. https: //doi.org/10.1063/5.0021106

    work page doi:10.1063/5.0021106 2020

  32. [32]

    and Olivetti, E

    Venugopal, V. and Olivetti, E. A. MatKG: A knowledge graph for materials science. Scientific Data 11, 141 (2024). doi:10.1038/s41597-024-03039-z. https://doi.org/10.1038/s41597-024-03039-z

    work page doi:10.1038/s41597-024-03039-z 2024

  33. [34]

    Burger, B. et al. A mobile robotic chemist. Nature 583, 237–241 (2020). doi:10.1038/s41586-020- 2442-2. https://doi.org/10.1038/s41586-020-2442-2

    work page doi:10.1038/s41586-020- 2020

  34. [35]

    MacLeod, B. P. et al. Self-driving laboratory for accelerated discovery of thin-film materials. Science Advances 6, eaaz8867 (2020). doi:10.1126/sciadv.aaz8867. https://doi.org/10.1126/sciadv.aaz 8867

    work page doi:10.1126/sciadv.aaz8867 2020

  35. [36]

    Flores-Leonar, M. M. et al. Materials acceleration platforms: On the way to autonomous experi- mentation. Nature Reviews Materials 5, 575–590 (2020). doi:10.1038/s41578-020-0226-2. https: //doi.org/10.1038/s41578-020-0226-2

    work page doi:10.1038/s41578-020-0226-2 2020

  36. [37]

    De Breuck, W. et al. Generative AI for crystal structures: a review. npj Computational Materials (2025). doi:10.1038/s41524-025-01881-2. https://doi.org/10.1038/s41524-025-01881-2

    work page doi:10.1038/s41524-025-01881-2 2025

  37. [38]

    Wagner, J. et al. Benchmarking machine learning in self-driving laboratories. Digital Discovery (2026). doi:10.1039/D5DD00337G. https://doi.org/10.1039/D5DD00337G

    work page doi:10.1039/d5dd00337g 2026

  38. [39]

    Dunn, A. et al. Benchmarking materials property prediction methods: the Matbench test set and Automatminer reference algorithm. npj Computational Materials 6, 138 (2020). doi:10.1038/s41524- 020-00406-3. https://doi.org/10.1038/s41524-020-00406-3

    work page doi:10.1038/s41524- 2020

  39. [40]

    Kent, P. et al. Foundation models for materials discovery – current state and future directions. npj Computational Materials (2025). doi:10.1038/s41524-025-01538-0. https://www.nature.com/artic les/s41524-025-01538-0

    work page doi:10.1038/s41524-025-01538-0 2025

  40. [41]

    T., Davies, D

    Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. and Walsh, A. Machine learning for molecular and materials science. Nature 559, 547–555 (2018). doi:10.1038/s41586-018-0337-2. https://doi. org/10.1038/s41586-018-0337-2

    work page doi:10.1038/s41586-018-0337-2 2018

  41. [42]

    Schmidt, J., Marques, M. R. G., Botti, S. and Marques, M. A. L. Recent advances and applica- tions of machine learning in solid-state materials science. npj Computational Materials 5, 83 (2019). doi:10.1038/s41524-019-0221-0. https://doi.org/10.1038/s41524-019-0221-0

    work page doi:10.1038/s41524-019-0221-0 2019

  42. [43]

    and Ramprasad, R

    Batra, R., Song, L. and Ramprasad, R. Emerging materials intelligence ecosystems propelled by machine learning. Nature Reviews Materials 6, 655–678 (2021). doi:10.1038/s41578-020-00255-y. https://doi.org/10.1038/s41578-020-00255-y

    work page doi:10.1038/s41578-020-00255-y 2021

  43. [44]

    Chen, C. et al. Generative models for inverse design of inorganic solid materials. Journal of Materials Informatics (2021). https://www.oaepublish.com/articles/jmi.2021.07

    2021

  44. [45]

    Jha, D. et al. ElemNet: Deep learning the chemistry of materials from only elemental composition. Scientific Reports 8, 17593 (2018). doi:10.1038/s41598-018-35934-y. https://doi.org/10.1038/s4 1598-018-35934-y

    work page doi:10.1038/s41598-018-35934-y 2018

  45. [46]

    Fudge, B. et al. Design and implementation of self-driving laboratories. Digital Discovery (2024). https://doi.org/10.1039/D4DD00059E 33

    work page doi:10.1039/d4dd00059e 2024

  46. [47]

    P., Kalinin, S

    Hysmith, H., Foadian, E., Padhy, S. P., Kalinin, S. V., Moore, R. G., Ovchinnikova, O. S. and Ahmadi, M. The future of self-driving laboratories: from human in the loop interactive AI to gamification. Digital Discovery (2024). doi:10.1039/D4DD00040D. https://doi.org/10.1039/D4DD00040D

    work page doi:10.1039/d4dd00040d 2024

  47. [48]

    Han, X.-Q. et al. InvDesFlow-AL: active learning-based workflow for inverse design of functional materials. npj Computational Materials (2025). doi:10.1038/s41524-025-01830-z. https://doi.org/ 10.1038/s41524-025-01830-z

    work page doi:10.1038/s41524-025-01830-z 2025

  48. [49]

    Antunes, L. M. et al. CrystaLLM: data-efficient autoregressive generation of inorganic crystal structures. Nature Communications 15, 10570 (2024). doi:10.1038/s41467-024-54639-7. https: //www.nature.com/articles/s41467-024-54639-7

    work page doi:10.1038/s41467-024-54639-7 2024

  49. [50]

    and Ghosh, P

    Chenebuah, C., Qi, Y. and Ghosh, P. Learning crystal morphology with graph autoencoders for inverse design. npj Computational Materials 10, 129 (2024). doi:10.1038/s41524-024-01381-9. https: //doi.org/10.1038/s41524-024-01381-9

    work page doi:10.1038/s41524-024-01381-9 2024

  50. [51]

    Davies, D. W. et al. SMACT: Semiconducting materials by analogy and chemical theory. Journal of Open Source Software 4, 1361 (2019). doi:10.21105/joss.01361. https://doi.org/10.21105/joss. 01361

    work page doi:10.21105/joss.01361 2019

  51. [52]

    Wang, A. Y.-T. et al. Compositionally restricted attention-based network for materials property prediction. npj Computational Materials 7, 77 (2021). doi:10.1038/s41524-021-00545-1. https: //doi.org/10.1038/s41524-021-00545-1

    work page doi:10.1038/s41524-021-00545-1 2021

  52. [53]

    Goodall, R. E. A. and Lee, A. A. Predicting materials properties without crystal structure: Deep representation learning from stoichiometry. npj Computational Materials 6, 148 (2020). doi:10.1038/s41524-020-00381-w. https://doi.org/10.1038/s41524-020-00381-w

    work page doi:10.1038/s41524-020-00381-w 2020

  53. [54]

    Court, C. J. and Cole, J. M. 3-D inorganic crystal structure generation and property prediction via representation learning. J. Chem. Inf. Model. (2020). https://pubs.acs.org/doi/10.1021/acs.j cim.0c00048

    work page doi:10.1021/acs.j 2020

  54. [55]

    Kim, B. et al. Generative adversarial network for crystal structure prediction. ACS Central Science (2020). https://pubs.acs.org/doi/10.1021/acscentsci.0c00426

    work page doi:10.1021/acscentsci.0c00426 2020

  55. [56]

    Gao, Y. et al. ConditionCDV AE+: physically informed conditional crystal generation. Scientific Reports (2025). https://www.nature.com/articles/s41598-025-06432-9

    2025

  56. [57]

    and Laine, S

    Karras, T., Aittala, M., Aila, T. and Laine, S. Elucidating the design space of diffusion-based gener- ative models. arXiv (2022). arXiv:2206.00364. https://arxiv.org/abs/2206.00364

    Pith/arXiv arXiv 2022

  57. [58]

    Karpovich, C. et al. Deep reinforcement learning for inverse inorganic materials design. npj Compu- tational Materials (2024). doi:10.1038/s41524-024-01474-5. https://doi.org/10.1038/s41524-024 -01474-5

    work page doi:10.1038/s41524-024-01474-5 2024

  58. [59]

    Isayev, O. et al. Universal fragment descriptors for predicting properties of inorganic crystals. Nature Communications 8, 15679 (2017). doi:10.1038/ncomms15679. https://doi.org/10.1038/ncomms 15679

    work page doi:10.1038/ncomms15679 2017

  59. [60]

    Suzuki, H. et al. Bridging text and crystal structures: literature-driven contrastive learning for materials science. AI4Mat @ NeurIPS (2024). OpenReview: JPL2XhDqeM. https://openreview.n et/forum?id=JPL2XhDqeM

    2024

  60. [61]

    Ozawa, N. et al. Graph-text contrastive learning of inorganic crystal structure toward a foundation model of inorganic materials. STAM Methods (2024). doi:10.1080/27660400.2024.2406219. https: //doi.org/10.1080/27660400.2024.2406219

    work page doi:10.1080/27660400.2024.2406219 2024

  61. [62]

    Das, K. et al. CrysMMNet: Multimodal Representation for Crystal Property Prediction. Proceedings of Machine Learning Research (UAI) 216 (2023). https://proceedings.mlr.press/v216/das23 a.html

    2023

  62. [63]

    J., Jain, A

    Court, C. J., Jain, A. and Cole, J. M. Inverse Design of Materials That Exhibit the Magnetocaloric Effect by Text-Mining of the Scientific Literature and Generative Deep Learning. Chemistry of Materials 33, 7217–7230 (2021). doi:10.1021/acs.chemmater.1c01368. https://pubs.acs.org/doi /10.1021/acs.chemmater.1c01368 34

    work page doi:10.1021/acs.chemmater.1c01368 2021

  63. [64]

    N., Duvenaud, D., Hernández -Lobato, J

    Gómez-Bombarelli, R., Wei, J. N., Duvenaud, D., Hernández-Lobato, J. M., Sánchez-Lengeling, B., Sheberla, D., Aguilera-Iparraguirre, J., Hirzel, T. D., Adams, R. P. and Aspuru-Guzik, A. Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules. ACS Central Science 4(2), 268–276 (2018). doi:10.1021/acscentsci.7b00572. https://doi...

    work page doi:10.1021/acscentsci.7b00572 2018

  64. [65]

    and Xu, L

    Xiao, H., Li, R., Shi, Q., Chen, Y., Zheng, L., Chen, F. and Xu, L. An invertible, invariant crystal representation for inverse design of solid-state materials using generative deep learning. Nature Com- munications 14, 7027 (2023). doi:10.1038/s41467-023-42870-7. https://doi.org/10.1038/s41467 -023-42870-7

    work page doi:10.1038/s41467-023-42870-7 2023

  65. [66]

    The CMA Evolution Strategy: A Tutorial

    Hansen, N. The CMA Evolution Strategy: A Tutorial. arXiv (2016). arXiv:1604.00772. https: //arxiv.org/abs/1604.00772

    Pith/arXiv arXiv 2016

  66. [67]

    and Teh, Y

    Welling, M. and Teh, Y. W. Bayesian Learning via Stochastic Gradient Langevin Dynamics. In Proceedings of the 28th International Conference on Machine Learning , 681–688 (2011). https: //icml.cc/2011/papers/398_icmlpaper.pdf

    2011

  67. [68]

    and Carin, L

    Li, C., Chen, C., Carlson, D. and Carin, L. Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks. In Proceedings of the 30th AAAI Conference on Artificial Intelligence 30(1), 1788–1794 (2016). https://ojs.aaai.org/index.php/AAAI/article/view/10200

    2016

  68. [69]

    and Salimans, T

    Ho, J. and Salimans, T. Classifier-Free Diffusion Guidance. arXiv preprint arXiv:2207.12598 (2022). https://arxiv.org/abs/2207.12598

    Pith/arXiv arXiv 2022

  69. [70]

    and Klimov, O

    Schulman, J., Wolski, F., Dhariwal, P., Radford, A. and Klimov, O. Proximal Policy Optimization Algorithms. arXiv preprint arXiv:1707.06347 (2017). https://arxiv.org/abs/1707.06347

    Pith/arXiv arXiv 2017

  70. [71]

    and Sankaranarayanan, S

    Banik, S., Dhabal, D., Chan, H., Manna, S., Cherukara, M., Molinero, V. and Sankaranarayanan, S. K. R. S. CATING: Crystal structure generation from composition using attention-based neural networks. npj Computational Materials 9, 117 (2023). doi:10.1038/s41524-023-01094-5. https: //doi.org/10.1038/s41524-023-01094-5

    work page doi:10.1038/s41524-023-01094-5 2023

  71. [72]

    G., Yu, H., Wu, C., Zhang, H., Hattrick-Simpers, J., DeCost, B., Sarker, S., Oses, C., Toher, C., Curtarolo, S., Davydov, A

    Kusne, A. G., Yu, H., Wu, C., Zhang, H., Hattrick-Simpers, J., DeCost, B., Sarker, S., Oses, C., Toher, C., Curtarolo, S., Davydov, A. V., Agarwal, R., Bendersky, L. A., Li, M., Mehta, A. and Takeuchi, I. On-the-fly closed-loop materials discovery via Bayesian active learning. Nature Communications 11, 5966 (2020). doi:10.1038/s41467-020-19597-w. https://...

    work page doi:10.1038/s41467-020-19597-w 2020

  72. [73]

    S., Aykol, M., Cheon, G

    Merchant, A., Batzner, S., Schoenholz, S. S., Aykol, M., Cheon, G. and Cubuk, E. D. Scaling deep learning for materials discovery. Nature 624, 80–85 (2023). doi:10.1038/s41586-023-06735-9. https: //doi.org/10.1038/s41586-023-06735-9

    work page doi:10.1038/s41586-023-06735-9 2023

  73. [74]

    Volk, A. A. and Abolhasani, M. Autonomous flow chemistry platforms: benchmarking and assessment criteria. Nature Communications 15, 5433 (2024). doi:10.1038/s41467-024-49716-4. https://doi. org/10.1038/s41467-024-49716-4

    work page doi:10.1038/s41467-024-49716-4 2024

  74. [75]

    Szymanski, N. J. et al. An autonomous laboratory for the accelerated synthesis of novel materials. Nature 624, 86–91 (2023). doi:10.1038/s41586-023-06734-w. https://doi.org/10.1038/s41586-0 23-06734-w

    work page doi:10.1038/s41586-023-06734-w 2023

  75. [76]

    and Moon, Seonghyeon and Yoon, Sejong and Kapadia, Mubbasir and Pavlovic, Vladimir , month = jun, year =

    Rombach, R., Blattmann, A., Lorenz, D., Esser, P. and Ommer, B. High-resolution image synthesis with latent diffusion models. CVPR (2022). doi:10.1109/CVPR52688.2022.01042. https://doi.or g/10.1109/CVPR52688.2022.01042

    work page doi:10.1109/cvpr52688.2022.01042 2022

  76. [77]

    Diwale, S. et al. Bayesian optimization for material discovery processes with noisy and unreliable measurements. Molecular Systems Design & Engineering (2022). https://doi.org/10.1039/D1ME 00154J

    work page doi:10.1039/d1me 2022

  77. [78]

    Tian, K. et al. Materials design with target-oriented Bayesian optimization (t-EGO). npj Computa- tional Materials (2025). doi:10.1038/s41524-025-01704-4. https://doi.org/10.1038/s41524-025 -01704-4

    work page doi:10.1038/s41524-025-01704-4 2025

  78. [79]

    Chitturi, K. et al. Targeted materials discovery using Bayesian algorithm execution. npj Computa- tional Materials 10, 126 (2024). doi:10.1038/s41524-024-01326-2. https://doi.org/10.1038/s415 24-024-01326-2 35

    work page doi:10.1038/s41524-024-01326-2 2024

  79. [80]

    Riebesell, J., Goodall, R. E. A., Benner, P., Chiang, Y., Deng, B., Ceder, G., Asta, M., Lee, A. A., Jain, A. and Persson, K. A. A framework to evaluate machine learning crystal stability predictions. Nature Machine Intelligence 7, 836–847 (2025). doi:10.1038/s42256-025-01055-3. https://doi.org/ 10.1038/s42256-025-01055-3

    work page doi:10.1038/s42256-025-01055-3 2025

  80. [81]

    Skalse, J., Howe, N. H. R., Krasheninnikov, D. and Krueger, D. Defining and Characterizing Reward Gaming. Advances in Neural Information Processing Systems 35 (2022). https://arxiv.org/abs/ 2209.13085

    arXiv 2022

Showing first 80 references.