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Machine-Learning of Atomic-Scale Properties Based on Physical Principles

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Machine Learning Meets Quantum Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 968))

Abstract

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the smooth overlap of atomic positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalizations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels—applicable to comparing entire molecules or periodic systems—that go beyond an additive combination of local environments. (This chapter is adapted with permission from Ceriotti et al. (Handbook of materials modeling. Springer, Cham, 2019).)

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Author information

Authors and Affiliations

  1. Engineering Laboratory, University of Cambridge, Cambridge, UK

    Gábor Csányi

  2. Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Michael J. Willatt & Michele Ceriotti

Authors
  1. Gábor Csányi
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  2. Michael J. Willatt
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  3. Michele Ceriotti
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Corresponding author

Correspondence to Michele Ceriotti .

Editor information

Editors and Affiliations

  1. Machine Learning, Technical University of Berlin, Berlin, Germany

    Kristof T. Schütt

  2. Machine Learning Group, Technical University of Berlin, Berlin, Germany

    Stefan Chmiela

  3. Institute of Physical Chemistry and MARVEL, University of Basel, Basel, Switzerland

    O. Anatole von Lilienfeld

  4. Department of Physics and Materials Science, University of Luxembourg, Luxembourg, Luxembourg

    Alexandre Tkatchenko

  5. Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Japan

    Koji Tsuda

  6. Computer Science, Technical University of Berlin, Berlin, Germany

    Klaus-Robert Müller

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Csányi, G., Willatt, M.J., Ceriotti, M. (2020). Machine-Learning of Atomic-Scale Properties Based on Physical Principles. In: Schütt, K., Chmiela, S., von Lilienfeld, O., Tkatchenko, A., Tsuda, K., Müller, KR. (eds) Machine Learning Meets Quantum Physics. Lecture Notes in Physics, vol 968. Springer, Cham. https://doi.org/10.1007/978-3-030-40245-7_6

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