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Crystal structure representations for machine learning models of formation energies
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- Faber, Felix (author)
- University of Basel, Switzerland; University of Basel, Switzerland; University of Basel, Switzerland
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- Lindmaa, Alexander (author)
- Linköpings universitet,Teoretisk Fysik,Tekniska fakulteten
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- von Lilienfeld, O. Anatole (author)
- University of Basel, Switzerland; Argonne Leadership Comp Facil, IL 60439 USA; Argonne National Lab, IL 60439 USA
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- Armiento, Rickard (author)
- Linköpings universitet,Teoretisk Fysik,Tekniska fakulteten
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(creator_code:org_t)
- 2015-04-20
- 2015
- English.
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In: International Journal of Quantum Chemistry. - : Wiley. - 0020-7608 .- 1097-461X. ; 115:16, s. 1094-1101
- Related links:
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https://rss.onlineli...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences (hsv//eng)
Keyword
- machine learning; formation energies; representations; crystal structure; periodic systems
Publication and Content Type
- ref (subject category)
- art (subject category)
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