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Crystal structure representations for machine learning models of formation energies

International journal of quantum chemistry, 2015-08, Vol.115 (16), p.1094-1101 [Peer Reviewed Journal]

2015 Wiley Periodicals, Inc. ;ISSN: 0020-7608 ;ISSN: 1097-461X ;EISSN: 1097-461X ;DOI: 10.1002/qua.24917 ;CODEN: IJQCB2

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  • Title:
    Crystal structure representations for machine learning models of formation energies
  • Author: Faber, Felix ; Lindmaa, Alexander ; von Lilienfeld, O. Anatole ; Armiento, Rickard
  • Subjects: crystal structure ; formation energies ; INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY ; machine learning ; periodic systems ; representations
  • Is Part Of: International journal of quantum chemistry, 2015-08, Vol.115 (16), p.1094-1101
  • Description: We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb‐like matrix that takes into account a number of neighboring unit cells; and (iii) an ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37 eV/atom for the respective representations. © 2015 Wiley Periodicals, Inc. Feature vector representations of crystal structures for machine learning models of formation energies of solids are evaluated. A representation previously found successful for molecules is generalized to periodic systems in three different ways. For training sets of 3000 crystal structures comprising all different elements, the best representation is estimated to predict formation energies of new materials with an average error of 0.37 eV/atom.
  • Publisher: Hoboken: Blackwell Publishing Ltd
  • Language: English;French;German
  • Identifier: ISSN: 0020-7608
    ISSN: 1097-461X
    EISSN: 1097-461X
    DOI: 10.1002/qua.24917
    CODEN: IJQCB2
  • Source: Alma/SFX Local Collection
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