Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

A universal graph deep learning interatomic potential for the periodic table

Nature Computational Science volume 2, pages 718–728 (2022)Cite this article

Subjects

A preprint version of the article is available at arXiv.

Abstract

Interatomic potentials (IAPs), which describe the potential energy surface of atoms, are a fundamental input for atomistic simulations. However, existing IAPs are either fitted to narrow chemistries or too inaccurate for general applications. Here we report a universal IAP for materials based on graph neural networks with three-body interactions (M3GNet). The M3GNet IAP was trained on the massive database of structural relaxations performed by the Materials Project over the past ten years and has broad applications in structural relaxation, dynamic simulations and property prediction of materials across diverse chemical spaces. About 1.8 million materials from a screening of 31 million hypothetical crystal structures were identified to be potentially stable against existing Materials Project crystals based on M3GNet energies. Of the top 2,000 materials with the lowest energies above the convex hull, 1,578 were verified to be stable using density functional theory calculations. These results demonstrate a machine learning-accelerated pathway to the discovery of synthesizable materials with exceptional properties.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Schematic of the many-body graph potential and the major computational blocks.
Fig. 2: The distribution of the MPF.2021.2.8 dataset.
Fig. 3: The model predictions on the test dataset compared to DFT calculations.
Fig. 4: Relaxation of crystal structures with M3GNet.
Fig. 5: Discovery of stable materials using M3GNet.

Similar content being viewed by others

Data availability

The training data for the universal IAP are available at https://doi.org/10.6084/m9.figshare.19470599 (ref. 61). The phonon dispersion curves of 328 dynamically stable materials are available at https://doi.org/10.6084/m9.figshare.20217212 (ref. 62). The ICSD database used in this study is a commercial product and cannot be shared. All generated hypothetical compounds and their corresponding M3GNet predictions are provided at http://matterverse.ai. Each material can be accessed via a detail page at https://matterverse.ai/details/mv-id, where id ranges from 0 to 31,664,854. Source Data are provided with this paper.

Code availability

The source code for M3GNet is available at https://github.com/materialsvirtuallab/m3gnet and https://doi.org/10.5281/zenodo.7141391 (ref. 63).

References

  1. Weiner, P. K. & Kollman, P. A. AMBER: assisted model building with energy refinement. A general program for modeling molecules and their interactions. J. Comput. Chem. 2, 287–303 (1981).

    Article  Google Scholar 

  2. Case, D. A. et al. The AMBER biomolecular simulation programs. J. Comput. Chem. 26, 1668–1688 (2005).

    Article  Google Scholar 

  3. Rappe, A. K., Casewit, C. J., Colwell, K. S., Goddard, W. A. & Skiff, W. M. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114, 10024–10035 (1992).

    Article  Google Scholar 

  4. Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).

    Article  Google Scholar 

  5. Bartók, A. P., Payne, M. C., Kondor, R. & Csányi, G. Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104, 136403 (2010).

    Article  Google Scholar 

  6. Thompson, A. P., Swiler, L. P., Trott, C. R., Foiles, S. M. & Tucker, G. J. Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials. J. Comput. Phys. 285, 316–330 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  7. Shapeev, A. V. Moment tensor potentials: a class of systematically improvable interatomic potentials. Multiscale Model. Simul. 14, 1153–1173 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhang, L., Han, J., Wang, H., Car, R. & E, W. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 120, 143001 (2018).

    Article  Google Scholar 

  9. Zuo, Y. et al. Performance and cost assessment of machine learning interatomic potentials. J. Phys. Chem. A 124, 731–745 (2020).

    Article  Google Scholar 

  10. Schütt, K. et al. SchNet: a continuous-filter convolutional neural network for modeling quantum interactions. In Proc. 31st International Conference on Neural Information Processing Systems Advances in Neural Information Processing Systems 992–1002 (NIPS, 2017).

  11. Klicpera, J., Groß, J. & Günnemann, S. Directional message passing for molecular graphs. Preprint at https://arxiv.org/abs/2003.03123 (2020).

  12. Haghighatlari, M. et al. NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces. Digit. Discov. 1, 333–343 (2022).

    Article  Google Scholar 

  13. Park, C. W. et al. Accurate and scalable graph neural network force field and molecular dynamics with direct force architecture. npj Comput. Mater. 7, 1–9 (2021).

    Article  Google Scholar 

  14. Cheon, G., Yang, L., McCloskey, K., Reed, E. J. & Cubuk, E. D. Crystal structure search with random relaxations using graph networks. Preprint at https://arxiv.org/abs/2012.02920 (2020).

  15. Lejaeghere, K. et al. Reproducibility in density functional theory calculations of solids. Science 351, aad3000 (2016).

    Article  Google Scholar 

  16. Ong, S. P. et al. Python Materials Genomics (pymatgen): a robust, open-source Python library for materials analysis. Comput. Mater. Sci. 68, 314–319 (2013).

    Article  Google Scholar 

  17. Jain, A. et al. FireWorks: a dynamic workflow system designed for high-throughput applications. Concurr. Comput. 27, 5037–5059 (2015).

    Article  Google Scholar 

  18. Pizzi, G., Cepellotti, A., Sabatini, R., Marzari, N. & Kozinsky, B. AiiDA: automated interactive infrastructure and database for computational science. Comput. Mater. Sci. 111, 218–230 (2016).

    Article  Google Scholar 

  19. Mathew, K. et al. Atomate: a high-level interface to generate, execute, and analyze computational materials science workflows. Comput. Mater. Sci. 139, 140–152 (2017).

    Article  Google Scholar 

  20. Jain, A. et al. Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).

    Article  Google Scholar 

  21. Curtarolo, S. et al. AFLOWLIB.ORG: a distributed materials properties repository from high-throughput ab initio calculations. Comput. Mater. Sci. 58, 227–235 (2012).

    Article  Google Scholar 

  22. Kirklin, S. et al. The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies. npj Comput. Mater. 1, 1–15 (2015).

    Article  Google Scholar 

  23. Draxl, C. & Scheffler, M. The NOMAD laboratory: from data sharing to artificial intelligence. J. Phys. Mater. 2, 036001 (2019).

    Article  Google Scholar 

  24. Xie, T. & Grossman, J. C. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett. 120, 145301 (2018).

    Article  Google Scholar 

  25. Chen, C., Ye, W., Zuo, Y., Zheng, C. & Ong, S. P. Graph networks as a universal machine learning framework for molecules and crystals. Chem. Mater. 31, 3564–3572 (2019).

    Article  Google Scholar 

  26. Chen, C., Zuo, Y., Ye, W., Li, X. & Ong, S. P. Learning properties of ordered and disordered materials from multi-fidelity data. Nat. Comput. Sci. 1, 46–53 (2021).

    Article  Google Scholar 

  27. Choudhary, K. & DeCost, B. Atomistic line graph neural network for improved materials property predictions. npj Comput. Mater. 7, 1–8 (2021).

    Article  Google Scholar 

  28. Tersoff, J. New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37, 6991–7000 (1988).

    Article  Google Scholar 

  29. Petretto, G. et al. High-throughput density-functional perturbation theory phonons for inorganic materials. Sci. Data 5, 180065 (2018).

    Article  Google Scholar 

  30. Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).

    Article  Google Scholar 

  31. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

    Article  Google Scholar 

  32. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Article  Google Scholar 

  33. Dunn, A., Wang, Q., Ganose, A., Dopp, D. & Jain, A. Benchmarking materials property prediction methods: the Matbench test set and Automatminer reference algorithm. npj Comput. Mater. 6, 1–10 (2020).

    Google Scholar 

  34. Sun, W. et al. The thermodynamic scale of inorganic crystalline metastability. Sci. Adv. 2, e160022 (2016).

    Article  Google Scholar 

  35. Qi, J. et al. Bridging the gap between simulated and experimental ionic conductivities in lithium superionic conductors. Mater. Today Phys. 21, 100463 (2021).

    Article  Google Scholar 

  36. Glass, C. W., Oganov, A. R. & Hansen, N. USPEX—evolutionary crystal structure prediction. Comput. Phys. Commun. 175, 713–720 (2006).

    Article  MATH  Google Scholar 

  37. Wang, Y., Lv, J., Zhu, L. & Ma, Y. CALYPSO: a method for crystal structure prediction. Comput. Phys. Commun. 183, 2063–2070 (2012).

    Article  Google Scholar 

  38. Xie, T., Fu, X., Ganea, O.-E., Barzilay, R. & Jaakkola, T. Crystal diffusion variational autoencoder for periodic material generation. Preprint at https://arxiv.org/abs/2110.06197 (2021).

  39. Chmiela, S. et al. Machine learning of accurate energy-conserving molecular force fields. Sci. Adv. 3, e1603015 (2017).

    Article  Google Scholar 

  40. Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R. & Tkatchenko, A. Quantum-chemical insights from deep tensor neural networks. Nat. Commun. 8, 13890 (2017).

    Article  Google Scholar 

  41. Chmiela, S., Sauceda, H. E., Müller, K.-R. & Tkatchenko, A. Towards exact molecular dynamics simulations with machine-learned force fields. Nat. Commun. 9, 3887 (2018).

    Article  Google Scholar 

  42. Zhang, Y., Hu, C. & Jiang, B. Embedded atom neural network potentials: efficient and accurate machine learning with a physically inspired representation. J. Phys. Chem. Lett. 10, 4962–4967 (2019).

    Article  Google Scholar 

  43. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  Google Scholar 

  44. Anisimov, V. I., Zaanen, J. & Andersen, O. K. Band theory and Mott insulators: Hubbard U instead of stoner I. Phys. Rev. B 44, 943–954 (1991).

    Article  Google Scholar 

  45. Hellenbrandt, M. The Inorganic Crystal Structure Database (ICSD)—present and future. Crystallogr. Rev. 10, 17–22 (2004).

    Article  Google Scholar 

  46. Wang, L., Maxisch, T. & Ceder, G. Oxidation energies of transition metal oxides within the GGU+U framework. Phys. Rev. B 73, 195107 (2006).

    Article  Google Scholar 

  47. Singraber, A., Behler, J. & Dellago, C. Library-based LAMMPS implementation of high-dimensional neural network potentials. J. Chem. Theory Comput. 15, 1827–1840 (2019).

    Article  Google Scholar 

  48. Ramachandran, P., Zoph, B. & Le, Q. V. Searching for activation functions. Preprint at https://arxiv.org/abs/1710.05941 (2017).

  49. Kocer, E., Mason, J. K. & Erturk, H. A novel approach to describe chemical environments in high-dimensional neural network potentials. J. Chem. Phys. 150, 154102 (2019).

    Article  Google Scholar 

  50. Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint https://arxiv.org/abs/1412.6980 (2017).

  51. Huber, P. J. Robust estimation of a location parameter. Ann. Math. Stat. 35, 73–101 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  52. Abadi, M. et al. TensorFlow: a system for large-scale machine learning. In 12th Symposium on Operating Systems Design and Implementation 265–283 (OSDI, 2016).

  53. Bitzek, E., Koskinen, P., Gähler, F., Moseler, M. & Gumbsch, P. Structural relaxation made simple. Phys. Rev. Lett. 97, 170201 (2006).

    Article  Google Scholar 

  54. Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys. 29, 273002 (2017).

    Google Scholar 

  55. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scripta Materialia 108, 1–5 (2015).

    Article  Google Scholar 

  56. Pedregosa, F. et al. Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).

    MathSciNet  MATH  Google Scholar 

  57. Seabold, S. & Perktold, J. Statsmodels: econometric and statistical modeling with Python. In Proc. 9th Python in Science Conference 92–96 (SciPy, 2010).

  58. Hunter, J. D. Matplotlib: a 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).

    Article  Google Scholar 

  59. Waskom, M. L. Seaborn: statistical data visualization. J. Open Source Softw. 6, 3021 (2021).

    Article  Google Scholar 

  60. Pandas Development Team Pandas-Dev/Pandas: Pandas (Zenodo, 2020).

  61. Chen, C. & Ong, S. P. MPF.2021.2.8. (FigShare, 2022); https://doi.org/10.6084/m9.figshare.19470599.v3

  62. Chen, C. m3gnet Phonon Dispersion Curve of 328 Materials (FigShare, 2022); https://doi.org/10.6084/m9.figshare.20217212.v1

  63. Ong, S. P. et al. materialsvirtuallab/m3gnet: v0.1.0. 2022 (FigShare, 2022); https://doi.org/10.5281/zenodo.7141391

  64. de Jong, M. et al. Charting the complete elastic properties of inorganic crystalline compounds. Sci. Data 2, 150009 (2015).

    Article  Google Scholar 

Download references

Acknowledgements

This work was primarily supported by the Materials Project, funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02-05-CH11231: Materials Project program KC23MP. The lithium superionic conductor analysis portion of the work was funded by the LG Energy Solution through the Frontier Research Laboratory (FRL) Program. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation (grant no ACI-1548562). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Authors and Affiliations

  1. Department of NanoEngineering, University of California, San Diego, CA, USA

    Chi Chen & Shyue Ping Ong

Authors
  1. Chi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shyue Ping Ong
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

C.C. and S.P.O. conceived the idea and designed the work. C.C. implemented the models and performed the analysis. C.C. and S.P.O. wrote the manuscript and contributed to the discussion and revision.

Corresponding authors

Correspondence to Chi Chen or Shyue Ping Ong.

Ethics declarations

Competing interests

The authors declare no financial interests.

Peer review

Peer review information

Nature Computational Science thanks Ekin Cubuk and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Handling editor: Jie Pan, in collaboration with the Nature Computational Science team. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Supplementary information

Supplementary Information

Supplementary Figs. 1–13, Sections 1–7 and Tables 1–5.

Peer Review File

Source data

Source Data Fig. 2

Sheet Figure_2a: 2D energy-force distribution counts Sheet Figure_2b: 2D energy-stress distribution counts Sheet Figure_2c: Radial distribution Sheet Figure_2d: Element counts in the dataset.

Source Data Fig. 3

Sheet Figure_3a: DFT energy vs M3GNet energy Sheet Figure_3b: DFT force vs M3GNet force Sheet Figure_3c: DFT stress vs M3GNet stress Sheet Figure_3g: DFT DOS center vs M3GNet DOS center Sheet Figure_3h: DFT Debye temperature vs M3GNet Debye temperature.

Source Data Fig. 4

Sheet Figure_4a: Volume change with model relax vs no model relax Sheet Figure_4b: Energy difference between M3GNet energies and DFT ground-state energies using DFT initial structures, M3GNet-relaxed structures and DFT-relaxed structures.

Source Data Fig. 5

Sheet Figure_5a: Signed Ehull of M3GNet and DFT for all cases and oxide cases Sheet Figure_5b: Stable materials ratio for all and oxide cases as a function of DFT ehull thresholds. Sheet Figure_5c: M3GNet energy vs DFT energy for the all cases. Sheet Figure_5d: M3GNet energy vs DFT energy for the oxide cases.

Source Data Extended Data Fig. 1

Sheet a-special_points: special high symmetry points of phonon dispersion curve and their high symmetry labels Sheet a-high_symmetry_line-{d}: distance and the frequency for different vibration modes. d goes from 0 to the max number of symmetry lines considered for this phonon dispersion curve. Panels b, c, d are stored in Sheet {x}-special points, Sheet {x}-high_symmetry_line-{d}, where x = b, c, or d.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, C., Ong, S.P. A universal graph deep learning interatomic potential for the periodic table. Nat Comput Sci 2, 718–728 (2022). https://doi.org/10.1038/s43588-022-00349-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s43588-022-00349-3

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing