Atomic-Scale Representation and Statistical Learning of Tensorial Properties

Andrea Grisafi, David Wilkins, Michael Willatt, Michele Ceriotti*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
36 Downloads (Pure)


This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability, the hyperpolarizability, and the ground-state electron density of a molecule.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalACS Symposium Series
Publication statusPublished - 01 Jan 2019
Externally publishedYes


  • Machine Learning
  • Symmetry
  • Gaussian Process Regression

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)


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