IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v16y2025i1d10.1038_s41467-025-60095-8.html
   My bibliography  Save this article

Image super-resolution inspired electron density prediction

Author

Listed:
  • Chenghan Li

    (California Institute of Technology)

  • Or Sharir

    (California Institute of Technology)

  • Shunyue Yuan

    (California Institute of Technology)

  • Garnet Kin-Lic Chan

    (California Institute of Technology)

Abstract

Predicting ground-state electron densities of chemical systems has recently received growing attention in machine learning quantum chemistry, given their fundamental importance as highlighted by the Hohenberg-Kohn theorem. Drawing inspiration from the domain of image super-resolution, we view the electron density as a 3D grayscale image and use a convolutional residual network to transform a crude and trivially generated guess of the molecular density into an accurate ground-state quantum mechanical density. Here we show that this model produces more accurate predictions than all prior density prediction approaches. Due to its simplicity, the model is directly applicable to unseen molecular conformations and chemical elements. We show that fine-tuning on limited new data provides high accuracy even in challenging cases of exotic elements and charge states.

Suggested Citation

  • Chenghan Li & Or Sharir & Shunyue Yuan & Garnet Kin-Lic Chan, 2025. "Image super-resolution inspired electron density prediction," Nature Communications, Nature, vol. 16(1), pages 1-9, December.
  • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-60095-8
    DOI: 10.1038/s41467-025-60095-8
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41467-025-60095-8
    File Function: Abstract
    Download Restriction: no

    File URL: https://libkey.io/10.1038/s41467-025-60095-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Simon Batzner & Albert Musaelian & Lixin Sun & Mario Geiger & Jonathan P. Mailoa & Mordechai Kornbluth & Nicola Molinari & Tess E. Smidt & Boris Kozinsky, 2022. "E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    2. Sebastian Dick & Marivi Fernandez-Serra, 2020. "Machine learning accurate exchange and correlation functionals of the electronic density," Nature Communications, Nature, vol. 11(1), pages 1-10, December.
    3. Felix Brockherde & Leslie Vogt & Li Li & Mark E. Tuckerman & Kieron Burke & Klaus-Robert Müller, 2017. "Bypassing the Kohn-Sham equations with machine learning," Nature Communications, Nature, vol. 8(1), pages 1-10, December.
    4. K. T. Schütt & M. Gastegger & A. Tkatchenko & K.-R. Müller & R. J. Maurer, 2019. "Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    5. Albert Musaelian & Simon Batzner & Anders Johansson & Lixin Sun & Cameron J. Owen & Mordechai Kornbluth & Boris Kozinsky, 2023. "Learning local equivariant representations for large-scale atomistic dynamics," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    6. Justin S. Smith & Benjamin T. Nebgen & Roman Zubatyuk & Nicholas Lubbers & Christian Devereux & Kipton Barros & Sergei Tretiak & Olexandr Isayev & Adrian E. Roitberg, 2019. "Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning," Nature Communications, Nature, vol. 10(1), pages 1-8, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuanming Bai & Leslie Vogt-Maranto & Mark E. Tuckerman & William J. Glover, 2022. "Machine learning the Hohenberg-Kohn map for molecular excited states," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    2. Zechen Tang & He Li & Peize Lin & Xiaoxun Gong & Gan Jin & Lixin He & Hong Jiang & Xinguo Ren & Wenhui Duan & Yong Xu, 2024. "A deep equivariant neural network approach for efficient hybrid density functional calculations," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    3. Keke Song & Rui Zhao & Jiahui Liu & Yanzhou Wang & Eric Lindgren & Yong Wang & Shunda Chen & Ke Xu & Ting Liang & Penghua Ying & Nan Xu & Zhiqiang Zhao & Jiuyang Shi & Junjie Wang & Shuang Lyu & Zezhu, 2024. "General-purpose machine-learned potential for 16 elemental metals and their alloys," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    4. Juno Nam & Jiayu Peng & Rafael Gómez-Bombarelli, 2025. "Interpolation and differentiation of alchemical degrees of freedom in machine learning interatomic potentials," Nature Communications, Nature, vol. 16(1), pages 1-14, December.
    5. Bin Han & Kuang Yu, 2025. "Refining potential energy surface through dynamical properties via differentiable molecular simulation," Nature Communications, Nature, vol. 16(1), pages 1-12, December.
    6. Yusong Wang & Tong Wang & Shaoning Li & Xinheng He & Mingyu Li & Zun Wang & Nanning Zheng & Bin Shao & Tie-Yan Liu, 2024. "Enhancing geometric representations for molecules with equivariant vector-scalar interactive message passing," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    7. Stefano Falletta & Andrea Cepellotti & Anders Johansson & Chuin Wei Tan & Marc L. Descoteaux & Albert Musaelian & Cameron J. Owen & Boris Kozinsky, 2025. "Unified differentiable learning of electric response," Nature Communications, Nature, vol. 16(1), pages 1-12, December.
    8. Jonathan P. Mailoa & Xin Li & Shengyu Zhang, 2024. "3T-VASP: fast ab-initio electrochemical reactor via multi-scale gradient energy minimization," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    9. J. Thorben Frank & Oliver T. Unke & Klaus-Robert Müller & Stefan Chmiela, 2024. "A Euclidean transformer for fast and stable machine learned force fields," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    10. Adil Kabylda & Valentin Vassilev-Galindo & Stefan Chmiela & Igor Poltavsky & Alexandre Tkatchenko, 2023. "Efficient interatomic descriptors for accurate machine learning force fields of extended molecules," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    11. Junjie Wang & Yong Wang & Haoting Zhang & Ziyang Yang & Zhixin Liang & Jiuyang Shi & Hui-Tian Wang & Dingyu Xing & Jian Sun, 2024. "E(n)-Equivariant cartesian tensor message passing interatomic potential," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    12. Xiaoxun Gong & He Li & Nianlong Zou & Runzhang Xu & Wenhui Duan & Yong Xu, 2023. "General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    13. Ziduo Yang & Yi-Ming Zhao & Xian Wang & Xiaoqing Liu & Xiuying Zhang & Yifan Li & Qiujie Lv & Calvin Yu-Chian Chen & Lei Shen, 2024. "Scalable crystal structure relaxation using an iteration-free deep generative model with uncertainty quantification," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    14. Chao Liang & Yilimiranmu Rouzhahong & Caiyuan Ye & Chong Li & Biao Wang & Huashan Li, 2023. "Material symmetry recognition and property prediction accomplished by crystal capsule representation," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    15. Laura Lewis & Hsin-Yuan Huang & Viet T. Tran & Sebastian Lehner & Richard Kueng & John Preskill, 2024. "Improved machine learning algorithm for predicting ground state properties," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    16. Chen, Xin & Zhang, Lin & Huang, JiangBo & Jin, Lei & Song, YongShi & Zheng, XianHua & Zou, ZhiXiong, 2025. "A thermodynamics-consistent machine learning approach for ammonia-water thermal cycles," Energy, Elsevier, vol. 315(C).
    17. Peikun Zheng & Roman Zubatyuk & Wei Wu & Olexandr Isayev & Pavlo O. Dral, 2021. "Artificial intelligence-enhanced quantum chemical method with broad applicability," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    18. Amin Alibakhshi & Bernd Hartke, 2022. "Implicitly perturbed Hamiltonian as a class of versatile and general-purpose molecular representations for machine learning," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    19. Daniel Schwalbe-Koda & Sebastien Hamel & Babak Sadigh & Fei Zhou & Vincenzo Lordi, 2025. "Model-free estimation of completeness, uncertainties, and outliers in atomistic machine learning using information theory," Nature Communications, Nature, vol. 16(1), pages 1-13, December.
    20. Changwei Zhang & Yang Zhong & Zhi-Guo Tao & Xinming Qin & Honghui Shang & Zhenggang Lan & Oleg V. Prezhdo & Xin-Gao Gong & Weibin Chu & Hongjun Xiang, 2025. "Advancing nonadiabatic molecular dynamics simulations in solids with E(3) equivariant deep neural hamiltonians," Nature Communications, Nature, vol. 16(1), pages 1-13, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-60095-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.