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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: 2017-08-15
In thesis
1. Theoretical prediction of properties of atomistic systems: Density functional theory and machine learning
Open this publication in new window or tab >>Theoretical prediction of properties of atomistic systems: Density functional theory and machine learning
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The prediction of ground state properties of atomistic systems is of vital importance in technological advances as well as in the physical sciences. Fundamentally, these predictions are based on a quantum-mechanical description of many-electron systems. One of the hitherto most prominent theories for the treatment of such systems is density functional theory (DFT). The main reason for its success is due to its balance of acceptable accuracy with computational efficiency. By now, DFT is applied routinely to compute the properties of atomic, molecular, and solid state systems.

The general approach to solve the DFT equations is to use a density-functional approximation (DFA). In Kohn-Sham (KS) DFT, DFAs are applied to the unknown exchangecorrelation (xc) energy. In orbital-free DFT on the other hand, where the total energy is minimized directly with respect to the electron density, a DFA applied to the noninteracting kinetic energy is also required. Unfortunately, central DFAs in DFT fail to qualitatively capture many important aspects of electronic systems. Two prime examples are the description of localized electrons, and the description of systems where electronic edges are present.

In this thesis, I use a model system approach to construct a DFA for the electron localization function (ELF). The very same approach is also taken to study the non-interacting kinetic energy density (KED) in the slowly varying limit of inhomogeneous electron densities, where the effect of electronic edges are effectively included. Apart from the work on model systems, extensions of an exchange energy functional with an improved KS orbital description are presented: a scheme for improving its description of energetics of solids, and a comparison of its description of an essential exact exchange feature known as the derivative discontinuity with numerical data for exact exchange.

An emerging alternative route towards the prediction of the properties of atomistic systems is machine learning (ML). I present a number of ML methods for the prediction of solid formation energies, with an accuracy that is on par with KS DFT calculations, and with orders-of-magnitude lower computational cost.

Abstract [sv]

Att kunna förutsäga egenskaper hos atomistiska system utgör en viktigdel av vår teknologiska utveckling, samt spelar en betydande roll i defysikaliska vetenskaperna. Sådana förutsägelser bygger på en kvantmekaniskbeskrivning av mångelektronsystem. En av de mest framståendeteorierna för att behandla den här typen av system är täthetsfunktionalteorin(DFT). Den främsta orsaken till dess framgång är attden lyckas kombinera skaplig noggrannhet med en bra beräkningseffektivitet.DFT används numera rutinmässigt för att beräkna storheterhos atomer, molekyler, och fasta kroppar.

Generellt sett löses ekvationerna inom DFT genom att man inför entäthetsfunktionalapproximation (DFA). I Kohn-Sham (KS) DFT, användsDFAer för att approximera utbytes-korrelationsenergin. Inom orbitalfriDFT, där målet är att direkt minimera den totala energin med avseendepå elektrontätheten, så approximerar man också den icke-interageranderörelseenergin hos elektronerna. Dessvärre så fallerar många centralaDFAer att kvalitativt beskriva många viktiga aspekter hos elektronsystem.Två viktiga exempel är beskrivningen av lokaliserade elektroner,samt beskrivningen av system där det förekommer elektronytor.

I denna avhandling använder jag modellsystem för att konstruera enDFAför elektronlokaliseringsfunktionen (ELF). Samma tillvägagångssättappliceras sedan för att studera den kinetiska energitätheten i gränsen avlångsamt varierande elektrontätheter, där effekten av elektronytor effektivtinkluderas. Förutom arbetet som berör modellsystem, så presenterasen utökad variant av en utbytes-energifunktional med en förbättrad KSorbitalbeskrivning: ett schema för att förbättra dess energiegenskaperför solida material, samt en jämförelse av dess beskrivning av en viktigegenskap hos den exakta utbytesenergin, vilket utgörs av diskontinuiteteri dess derivata.

Ett mera nyligen uppkommet samt alternativt sätt att kunna förutsägaegenskaper hos atomistiska system utgörs av maskinlärning (ML).Jag presenterar ett antal ML-modeller för att kunna förutsäga formeringsenergierhos fasta material med en noggrannhet som är i linje medresultat som uppnås av beräkningar med hjälp av KS DFT, och med enberäkningseffektivitet som är flera storleksordningar snabbare.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. 68 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1868
National Category
Theoretical Chemistry Other Physics Topics Condensed Matter Physics Control Engineering Other Engineering and Technologies not elsewhere specified
Identifiers
urn:nbn:se:liu:diva-139767 (URN)10.3384/diss.diva-139767 (DOI)978-91-7685-486-0 (ISBN)
Public defence
2017-09-08, Planck, Fysikhuset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2017-08-15 Created: 2017-08-15 Last updated: 2017-08-18Bibliographically approved

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