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A universal graph deep learning interatomic potential for the periodic table

A preprint version of the article is available at arXiv.


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.

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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.

Data availability

The training data for the universal IAP are available at (ref. 61). The phonon dispersion curves of 328 dynamically stable materials are available at (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 Each material can be accessed via a detail page at, 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 and (ref. 63).


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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



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.

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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.

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Extended data

Supplementary information

Supplementary Information

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

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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.

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Chen, C., Ong, S.P. A universal graph deep learning interatomic potential for the periodic table. Nat Comput Sci 2, 718–728 (2022).

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