• Open Access

Machine Learning a General-Purpose Interatomic Potential for Silicon

Albert P. Bartók, James Kermode, Noam Bernstein, and Gábor Csányi
Phys. Rev. X 8, 041048 – Published 14 December 2018
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Abstract

The success of first-principles electronic-structure calculation for predictive modeling in chemistry, solid-state physics, and materials science is constrained by the limitations on simulated length scales and timescales due to the computational cost and its scaling. Techniques based on machine-learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the physically relevant space of configurations remains a challenging goal. Here, we present a Gaussian approximation potential for silicon that achieves this milestone, accurately reproducing density-functional-theory reference results for a wide range of observable properties, including crystal, liquid, and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calculations such as finite-temperature phase-boundary lines, self-diffusivity in the liquid, formation of the amorphous by slow quench, and dynamic brittle fracture, all of which are very expensive with a first-principles method. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qualitative estimate of the potential’s accuracy for a given atomic configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interatomic potential that comprehensively describes a material on the atomic scale and serves as a template for the development of such models in the future.

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  • Received 26 May 2018
  • Revised 11 October 2018

DOI:https://doi.org/10.1103/PhysRevX.8.041048

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Albert P. Bartók

  • Scientific Computing Department, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot, OX11 0QX, United Kingdom

James Kermode

  • Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry, CV4 7AL, United Kingdom

Noam Bernstein

  • Center for Materials Physics and Technology, U.S. Naval Research Laboratory, Washington, D.C. 20375, USA

Gábor Csányi

  • Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, United Kingdom

Popular Summary

Computer simulation of electrons in the potential of atomic nuclei is the workhorse of modeling material properties such as phase stability, mechanical behavior, and thermal conductivity. However, these simulations are limited by their computational cost. A new approach might break through this limitation: interpolating within a large database of already-solved quantum-mechanical calculations. This could allow for accurate energy estimates for a collection of atoms in a particular spatial configuration without having to recalculate the electronic structure for a new, possibly quite similar, configuration of positions. Here, we explore whether it is possible to construct a database that covers the entire physically relevant set of configurations for a material so that the interpolation is accurate enough to completely bypass costly quantum calculations in future simulations.

We construct a candidate database for silicon. We show that uncertainty quantification can be used to give confidence about the prospects for success and failure depending on the encountered atomic configurations, and it can also be used to extend the database. Our model for silicon can immediately be used to study material properties that have hitherto been out of reach, such as the thermal conductivity of nanostructures, medium-range order in amorphous materials, and the stability of large complexes of various point and line defects in the crystal structure.

The fitting methodology, the approach to building the database, and its general performance represent a milestone in creating comprehensive machine-learning models of materials, and it can serve as a template for future models of many other materials.

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Vol. 8, Iss. 4 — October - December 2018

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