A machine learning approach based on the artificial neural network (ANN) is applied for the configuration problem in solids. The proposed method provides a direct mapping from configuration vectors to energies. The benchmark conducted for the M1 phase of Mo–V–Te–Nb oxide showed that only a fraction of configurations needs to be calculated, thus the computational burden significantly decreased, by a factor of 20–50, with R2 = 0.96 and MAD = 0.12 eV. It is shown that ANN can also handle the effects of geometry relaxation when properly trained, resulting in R2 = 0.95 and MAD = 0.13 eV.
REFERENCES
1.
P.
Hohenberg
and W.
Kohn
, Phys. Rev.
136
, B864
(1964
).2.
W.
Kohn
and L. J.
Sham
, Phys. Rev.
140
, A1133
(1965
).3.
4.
G.
Hautier
, C. C.
Fischer
, A.
Jain
, T.
Mueller
, and G.
Ceder
, Chem. Mater.
22
, 3762
(2010
).5.
H.
Kim
and Y.
Jung
, Int. J. Quantum Chem.
115
, 1141
(2015
).6.
A. K.
Rappé
, C. J.
Casewit
, K. S.
Colwell
, W. A.
Goddard
III, and W. M.
Skiff
, J. Am. Chem. Soc.
114
, 10024
(1992
).7.
C. J.
Casewit
, K. S.
Colwell
, and A. K.
Rappé
, J. Am. Chem. Soc.
114
, 10046
(1992
).8.
K.
Gundertofte
, T.
Liljefors
, P.
Norrby
, and I.
Pettersson
, J. Comput. Chem.
17
, 429
(1996
).9.
J. M.
Sanchez
, F.
Ducastelle
, and D.
Gratias
, Physica A
128
, 334
(1984
).10.
D.
Fontaine
, Solid State Phys.
47
, 33
(1994
).11.
J. W. D.
Connolly
and A. R.
Williams
, Phys. Rev. B
27
, 5169
(1983
).12.
D. B.
Laks
, L. G.
Ferreira
, S.
Froyen
, and A.
Zunger
, Phys. Rev. B
46
, 12587
(1992
).13.
N. A.
Zarkevich
and D. D.
Johnson
, Phys. Rev. Lett.
92
, 255702
(2004
).14.
A.
Seko
, Y.
Koyama
, and I.
Tanaka
, Phys. Rev. B
80
, 165122
(2009
).15.
L. J.
Nelson
, V.
Ozoliņš
, C. S.
Reese
, F.
Zhou
, and G. L. W.
Hart
, Phys. Rev. B
88
, 155105
(2013
).16.
C.
Wolverton
and V.
Ozoliņš
, Phys. Rev. Lett.
86
, 5518
(2001
).17.
A.
van de Walle
and G.
Ceder
, J. Phase Equilib.
23
, 348
(2002
).18.
B. C.
Han
, A.
Van der Ven
, G.
Ceder
, and B.
Hwang
, Phys. Rev. B
72
, 205409
(2005
).19.
V.
Blum
and A.
Zunger
, Phys. Rev. B
69
, 020103(R)
(2004
).20.
T.
Mueller
and G.
Ceder
, Phys. Rev. B
80
, 204103
(2009
).21.
W. S.
McCulloch
and W.
Pitts
, Bull. Math. Biophys.
5
, 115
(1943
).22.
F.
Rosenblatt
, Psychol. Rev.
65
, 386
(1958
).23.
B. G.
Sumpter
, C.
Getino
, and D. W.
Noid
, Annu. Rev. Phys. Chem.
45
, 439
(1994
).24.
G.
Cybenko
, Math. Control Signals Syst.
2
, 303
(1989
).25.
K.
Funahashi
, Neural Networks
2
, 183
(1989
).26.
V.
Maiorov
and A.
Pinkus
, Neurocomputing
25
, 81
(1999
).27.
M.
Rupp
, A.
Tkatchenko
, K.-R.
Müller
, and O. A.
von Lilienfeld
, Phys. Rev. Lett.
108
, 058301
(2012
).28.
K.
Hansen
, F.
Biegler
, R.
Ramakrishnan
, W.
Pronobis
, O. A.
von Lilienfeld
, K.-R.
Müller
, and A.
Tkatchenko
, J. Phys. Chem. Lett.
6
, 2326
(2015
).29.
J.
Hachmann
, R.
Olivares-Amaya
, S.
Atahan-Evrenk
, C.
Amador-Bedolla
, R. S.
Sánchez-Carrera
, A.
Gold-Parker
, L.
Vogt
, A. M.
Brockway
, and A.
Aspuru-Guzik
, J. Phys. Chem. Lett.
2
, 2241
(2011
).30.
J.
Wu
, Y.
Zhou
, and X.
Xu
, Int. J. Quantum Chem.
115
, 1021
(2015
).31.
A.
Seko
, T.
Maekawa
, K.
Tsuda
, and I.
Tanaka
, Phys. Rev. B
89
, 054303
(2014
).32.
S.
Manzhos
and T.
Carrington
, Jr., J. Chem. Phys.
125
, 084109
(2006
).33.
C. M.
Handley
and P. L.
Popelier
, J. Phys. Chem. A
114
, 3371
(2010
).34.
J.
Behler
, Phys. Chem. Chem. Phys.
13
, 17930
(2011
).35.
L.
Yang
, S.
Dacek
, and G.
Ceder
, Phys. Rev. B
90
, 054102
(2014
).36.
M.
Riedmiller
and H.
Braun
, “Rprop—A fast adaptive learning algorithm
,” in Proceedings of ISCIS VII
, Technical Report (Universitat
, 1992
).37.
C.
Igel
and M.
Hüsken
, Neurocomputing
50
, 105
(2003
).38.
M.
Aouine
, J. L.
Dubois
, and J. M. M.
Millet
, Chem. Commun.
2001
, 1180
.39.
J. M. M.
Millet
, H.
Roussel
, A.
Pigamo
, J. L.
Dubois
, and J. C.
Jumas
, Appl. Catal., A
232
, 77
(2002
).40.
P.
DeSanto
, D. J.
Buttrey
, R. K.
Grasseli
, C. G.
Lugmair
, A. F.
Volpe
, B. H.
Toby
, and T.
Vogt
, Z. Kristallogr. - Cryst. Mater.
219
, 152
(2004
).41.
H.
Murayama
, D.
Vitry
, W.
Ueda
, G.
Fuchs
, M.
Anne
, and J. L.
Dubois
, Appl. Catal., A
317
, 137
(2007
).42.
X.
Li
, D. J.
Buttrey
, D. A.
Blom
, and T.
Vogt
, Top. Catal.
54
, 614
(2011
).43.
W. A.
Goddard
III, J. E.
Mueller
, K.
Chenoweth
, and A. C. T.
van Duin
, Catal. Today
157
, 71
(2010
).44.
G.
Fu
, X.
Xu
, and P.
Sautet
, Angew. Chem., Int. Ed.
51
, 12854
(2012
).45.
46.
G.
Kresse
and J.
Furthmüller
, Comput. Mater. Sci.
6
, 15
(1996
).47.
G.
Kresse
and J.
Furthmüller
, Phys. Rev. B
65
, 11169
(1996
).48.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
77
, 3865
(1996
).49.
P. E.
Blöchl
, Phys. Rev. B
50
, 17953
(1994
).50.
G.
Kresse
and D.
Joubert
, Phys. Rev. B
59
, 1758
(1999
).51.
H. J.
Monkhorst
and J. D.
Pack
, Phys. Rev. B
13
, 5188
(1976
).52.
G.
Buesing
, Neural Networks (in ruby).53.
S.
Geman
, E.
Bienenstock
, and R.
Doursat
, Neural Comput.
4
, 1
(1992
).54.
G.
Huang
, IEEE Trans. Neural Networks
14
, 274
(2003
).© 2017 Author(s).
2017
Author(s)
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