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Crystal structure representations for machine learning models of formation energies
University of Basel, Switzerland; University of Basel, Switzerland; University of Basel, Switzerland.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-5439-711X
University of Basel, Switzerland; University of Basel, Switzerland; University of Basel, Switzerland; Argonne Leadership Comp Facil, IL 60439 USA; Argonne National Lab, IL 60439 USA.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-5571-0814
2015 (English)In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 115, no 16, 1094-1101 p.Article in journal (Refereed) Published
Abstract [en]

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) 0.37eV/atom for the respective representations.

Place, publisher, year, edition, pages
Wiley , 2015. Vol. 115, no 16, 1094-1101 p.
Keyword [en]
machine learning; formation energies; representations; crystal structure; periodic systems
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:liu:diva-120326DOI: 10.1002/qua.24917ISI: 000357606000010OAI: oai:DiVA.org:liu-120326DiVA: diva2:843917
Note

Funding Agencies|Swedish Research Council (VR) [621-2011-4249]; Linnaeus Environment at Linkoping on Nanoscale Functional Materials - VR; Swiss National Science foundation [PP00P2_138932]; Office of Science of the U.S. DOE [DE-AC02-06CH11357]; Air Force Office of Scientific Research, Air Force Material Command, USAF [FA9550-15-1-0026]

Available from: 2015-07-31 Created: 2015-07-31 Last updated: 2015-07-31

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Lindmaa, AlexanderArmiento, Rickard
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