Incorporating long-range physics in atomic-scale machine learning

Authors: Andrea Grisafi1, Michele Ceriotti1*

  1. Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
  • Corresponding author email:

DOI10.24435/materialscloud:2019.0090/v1 (version v1, submitted on 18 December 2019)

How to cite this entry

Andrea Grisafi, Michele Ceriotti, Incorporating long-range physics in atomic-scale machine learning, Materials Cloud Archive (2019), doi: 10.24435/materialscloud:2019.0090/v1.


The most successful and popular machine learning models of atomic-scale properties derive their transferability from a locality ansatz. The properties of a large molecule or a bulk material are written as a sum over contributions that depend on the configurations within finite atom-centered environments. The obvious downside of this approach is that it cannot capture nonlocal, nonadditive effects such as those arising due to long-range electrostatics or quantum interference. We propose a solution to this problem by introducing nonlocal representations of the system, which are remapped as feature vectors that are defined locally and are equivariant in O(3). We consider, in particular, one form that has the same asymptotic behavior as the electrostatic potential. We demonstrate that this framework can capture nonlocal, long-range physics by building a model for the electrostatic energy of randomly distributed point-charges, for the unrelaxed binding curves of charged organic molecular dimers, and for the electronic dielectric response of liquid water. By combining a representation of the system that is sensitive to long-range correlations with the transferability of an atom-centered additive model, this method outperforms current state-of-the-art machine-learning schemes and provides a conceptual framework to incorporate nonlocal physics into atomistic machine learning.

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File name Size Description
MD5MD5: 6421bec70027a9f349f868fa5d7b8019
247.8 KiB Binding energies of molecular dimers.
MD5MD5: fb7ee4cbfb6cdd75cbdb7b632850a2a3
1.1 KiB README file.
MD5MD5: e38dfea4ccc41ea1dc400eb58ca56d3a
6.9 MiB Atomic coordinates of molecular dimers.


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External references

Journal reference (Paper in which the method is described)
Preprint (Preprint where the method is described.)


ERC MARVEL/DD1 machine learning long-range interactions

Version history

18 December 2019 [This version]