Incompleteness of Atomic Structure Representations

Sergey N. Pozdnyakov, Michael J. Willatt, Albert P. Bartók, Christoph Ortner, Gábor Csányi, and Michele Ceriotti
Phys. Rev. Lett. 125, 166001 – Published 12 October 2020
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Abstract

Many-body descriptors are widely used to represent atomic environments in the construction of machine-learned interatomic potentials and more broadly for fitting, classification, and embedding tasks on atomic structures. There is a widespread belief in the community that three-body correlations are likely to provide an overcomplete description of the environment of an atom. We produce several counterexamples to this belief, with the consequence that any classifier, regression, or embedding model for atom-centered properties that uses three- (or four)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centered contributions mitigates the impact of this fundamental deficiency—explaining the success of current “machine-learning” force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.

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  • Received 27 January 2020
  • Accepted 9 September 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.166001

© 2020 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Sergey N. Pozdnyakov1,*, Michael J. Willatt1,*, Albert P. Bartók2, Christoph Ortner3,†, Gábor Csányi4,‡, and Michele Ceriotti1,§

  • 1Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
  • 2Department of Physics and Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 3Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 4Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom

  • *These two authors contributed equally to this work.
  • c.ortner@warwick.ac.uk
  • gc121@cam.ac.uk
  • §michele.ceriotti@epfl.ch

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Issue

Vol. 125, Iss. 16 — 16 October 2020

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