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Atomic energy mapping of neural network potential

Dongsun Yoo, Kyuhyun Lee, Wonseok Jeong, Dongheon Lee, Satoshi Watanabe, and Seungwu Han
Phys. Rev. Materials 3, 093802 – Published 3 September 2019
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  • INTRODUCTION
  • METHODS
  • RESULTS AND DISCUSSIONS
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    We investigate the atomic energy mapping inferred by machine-learning potentials, in particular neural network potentials. We first show that the transferable atomic energy can be defined within the density functional theory, which means that the core of machine-learning potentials is to deduce a reference atomic-energy function from the given set of total energies. By utilizing invariant points in the feature space at which the atomic energy has a fixed reference value, we examine the atomic energy mapping of neural network potentials. Examples on Si consistently support that NNPs are capable of learning correct atomic energies. However, we also find that the neural network potential is vulnerable to ‘ad hoc’ mapping in which the total energy appears to be trained accurately while the atomic energy mapping is incorrect in spite of its capability. We show that the energy mapping can be improved by choosing the training set carefully and monitoring the atomic energy at the invariant points during the training procedure. The energy mapping in multicomponent systems is also discussed.

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    • Received 12 March 2019
    • Revised 25 July 2019

    DOI:https://doi.org/10.1103/PhysRevMaterials.3.093802

    ©2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    First-principles calculationsInteratomic & molecular potentials
    1. Techniques
    Density functional theoryMachine learningMolecular dynamics
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Dongsun Yoo1, Kyuhyun Lee1, Wonseok Jeong1, Dongheon Lee1, Satoshi Watanabe2, and Seungwu Han1,*

    • 1Department of Materials Science and Engineering, Seoul National University, Seoul 08826, Korea
    • 2Department of Materials Engineering, The University of Tokyo, Bunkyo, Tokyo 113-8656, Japan

    • *hansw@snu.ac.kr

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    Issue

    Vol. 3, Iss. 9 — September 2019

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    Images

    • Figure 1
      Figure 1

      (a) Structure of the Ni85 octahedron that consist of 6 corner, 36 edge, 24 surface, and 19 bulk atoms. (b) Correlation between atomic energy of EAM and NNP.

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    • Figure 2
      Figure 2

      (a) The distribution of dNN for the training set. (b) The distribution of G in the training set (dots) and the equation of state (EOS) (solid disks), projected onto principal component (PC) axes. (c) The dNN for each point in EOS. In both (b) and (c), the square bracket indicates the same range for EOS where the dNN is lower than 0.2. (d) The EOS for Si crystal compared between DFT and NNP. The blue and red solid lines are the average EOS over five NNPs that are trained with NVT- and NPT-MD snapshots, respectively. The shades are one standard deviation from the average, corresponding to the prediction uncertainty. The squared bracket indicates the volume range where corresponding G's lie in the proximity of the training set.

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    • Figure 3
      Figure 3

      (a) The structure of Si(100)-(2×2) slab. The atoms in bulk and surface regions are marked in blue and red, respectively. rc is the cutoff radius of symmetry functions. (b) The average of atomic-energy difference between DFT and NNPs for bulk and surface groups, plotted against the temperature of the training set. (c) Scatter plot along principal components (PC) of G vectors in the training set. (d) Schematic illustration of ad hoc mapping due to separate groups of training points.

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    • Figure 4
      Figure 4

      (a) rg−1 against the temperature of training set and (b) absolute atomic-energy error (bulk) versus rg−1 for the Si slab model.

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    • Figure 5
      Figure 5

      (a) Si239 nanocluster relaxed at 0 K. (b) Change of RMSE for energy and force, and mapping errors for surface and bulk regions of Si(100)-(2×2) slab in Fig. 3, with respect to the training epoch.

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    • Figure 6
      Figure 6

      (a) Average atomic energies of Ge and Te when the training set encompasses the whole composition range (Ge, Ge3Te, GeTe, GeTe3, and Te; filled circles), or when the training set includes only compositions near 1:1 (empty squares). Error bars indicate one standard deviation in atomic energies for MD snapshots. (b) The unphysical phase separation results with NNP that is trained over only compositions near 1:1.

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