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Accurate Molecular Dynamics Enabled by Efficient Physically Constrained Machine Learning Approaches

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Machine Learning Meets Quantum Physics

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

Abstract

We develop a combined machine learning (ML) and quantum mechanics approach that enables data-efficient reconstruction of flexible molecular force fields from high-level ab initio calculations, through the consideration of fundamental physical constraints. We discuss how such constraints are recovered and incorporated into ML models. Specifically, we use conservation of energy—a fundamental property of closed classical and quantum mechanical systems—to derive an efficient gradient-domain machine learning (GDML) model. The challenge of constructing conservative force fields is accomplished by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. We proceed with the development of a multi-partite matching algorithm that enables a fully automated recovery of physically relevant point group and fluxional symmetries from the training dataset into a symmetric variant of our model. The symmetric GDML (sGDML) approach is able to faithfully reproduce global force fields at the accuracy high-level ab initio methods, thus enabling sample intensive tasks like molecular dynamics simulations at that level of accuracy. (This chapter is adapted with permission from Chmiela (Towards exact molecular dynamics simulations with invariant machine-learned models, PhD thesis. Technische Universität, Berlin, 2019).)

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Notes

  1. 1.

    For illustrative purposes, we use the definition of curl in three dimensions here, but the theory directly generalizes to arbitrary dimension. One way to prove this is via path-independence of conservative vector fields: the circulation of a gradient along any closed curve is zero and the curl is the limit of such circulations.

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Authors and Affiliations

  1. Machine Learning Group, Technische Universität Berlin, Berlin, Germany

    Stefan Chmiela, Huziel E. Sauceda & Klaus-Robert Müller

  2. Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg, Luxembourg

    Alexandre Tkatchenko

Authors
  1. Stefan Chmiela
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  2. Huziel E. Sauceda
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  3. Alexandre Tkatchenko
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  4. Klaus-Robert Müller
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Correspondence to Stefan Chmiela .

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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Chmiela, S., Sauceda, H.E., Tkatchenko, A., Müller, KR. (2020). Accurate Molecular Dynamics Enabled by Efficient Physically Constrained Machine Learning Approaches. 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_7

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