Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mechanical interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chemical compound space. Here we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chemical space for molecules and materials, where our model learns chemically plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for molecular dynamics simulations of small molecules and perform an exemplary study on the quantum-mechanical properties of C20-fullerene that would have been infeasible with regular ab initio molecular dynamics.

1.
M.
Rupp
,
A.
Tkatchenko
,
K.-R.
Müller
, and
O. A.
von Lilienfeld
,
Phys. Rev. Lett.
108
,
058301
(
2012
).
2.
G.
Montavon
,
M.
Rupp
,
V.
Gobre
,
A.
Vazquez-Mayagoitia
,
K.
Hansen
,
A.
Tkatchenko
,
K.-R.
Müller
, and
O. A.
von Lilienfeld
,
New J. Phys.
15
,
095003
(
2013
).
3.
K.
Hansen
,
G.
Montavon
,
F.
Biegler
,
S.
Fazli
,
M.
Rupp
,
M.
Scheffler
,
O. A.
von Lilienfeld
,
A.
Tkatchenko
, and
K.-R.
Müller
,
J. Chem. Theory Comput.
9
,
3404
(
2013
).
4.
K. T.
Schütt
,
H.
Glawe
,
F.
Brockherde
,
A.
Sanna
,
K.-R.
Müller
, and
E.
Gross
,
Phys. Rev. B
89
,
205118
(
2014
).
5.
F.
Faber
,
A.
Lindmaa
,
O. A.
von Lilienfeld
, and
R.
Armiento
,
Int. J. Quantum Chem.
115
,
1094
(
2015
).
6.
R.
Ramakrishnan
,
P. O.
Dral
,
M.
Rupp
, and
O. A.
von Lilienfeld
,
J. Chem. Theory Comput.
11
,
2087
(
2015
).
7.
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
).
8.
F. A.
Faber
,
A.
Lindmaa
,
O. A.
von Lilienfeld
, and
R.
Armiento
,
Phys. Rev. Lett.
117
,
135502
(
2016
).
9.
M.
Hirn
,
S.
Mallat
, and
N.
Poilvert
,
Multiscale Model. Simul.
15
,
827
(
2017
).
10.
F. A.
Faber
,
L.
Hutchison
,
B.
Huang
,
J.
Gilmer
,
S. S.
Schoenholz
,
G. E.
Dahl
,
O.
Vinyals
,
S.
Kearnes
,
P. F.
Riley
, and
O. A.
von Lilienfeld
,
J. Chem. Theory Comput.
13
(
11
),
5255
5264
(
2017
).
11.
H.
Huo
and
M.
Rupp
, preprint arXiv:1704.06439 (
2017
).
12.
M.
Eickenberg
,
G.
Exarchakis
,
M.
Hirn
, and
S.
Mallat
,
Advances in Neural Information Processing Systems 30
(
Curran Associates, Inc.
,
2017
), pp.
6522
6531
.
13.
O.
Isayev
,
C.
Oses
,
C.
Toher
,
E.
Gossett
,
S.
Curtarolo
, and
A.
Tropsha
,
Nat. Commun.
8
,
15679
(
2017
).
14.
K.
Ryczko
,
K.
Mills
,
I.
Luchak
,
C.
Homenick
, and
I.
Tamblyn
, preprint arXiv:1706.09496 (
2017
).
15.
I.
Luchak
,
K.
Mills
,
K.
Ryczko
,
A.
Domurad
, and
I.
Tamblyn
, preprint arXiv:1708.06686 (
2017
).
16.
J.
Behler
and
M.
Parrinello
,
Phys. Rev. Lett.
98
,
146401
(
2007
).
17.
J.
Behler
,
J. Chem. Phys.
134
,
074106
(
2011
).
18.
A. P.
Bartók
,
M. C.
Payne
,
R.
Kondor
, and
G.
Csányi
,
Phys. Rev. Lett.
104
,
136403
(
2010
).
19.
A. P.
Bartók
,
R.
Kondor
, and
G.
Csányi
,
Phys. Rev. B
87
,
184115
(
2013
).
20.
A. V.
Shapeev
,
Multiscale Model. Simul.
14
,
1153
(
2016
).
21.
S.
Chmiela
,
A.
Tkatchenko
,
H. E.
Sauceda
,
I.
Poltavsky
,
K. T.
Schütt
, and
K.-R.
Müller
,
Sci. Adv.
3
,
e1603015
(
2017
).
22.
F.
Brockherde
,
L.
Voigt
,
L.
Li
,
M. E.
Tuckerman
,
K.
Burke
, and
K.-R.
Müller
,
Nat. Commun.
8
,
872
(
2017
).
23.
J. S.
Smith
,
O.
Isayev
, and
A. E.
Roitberg
,
Chem. Sci.
8
,
3192
(
2017
).
24.
E. V.
Podryabinkin
and
A. V.
Shapeev
,
Comput. Mater. Sci.
140
,
171
(
2017
).
25.
P.
Rowe
,
G.
Csányi
,
D.
Alfè
, and
A.
Michaelides
,
Phys. Rev. B
97
(
5
),
054303
(
2018
).
26.
D. K.
Duvenaud
,
D.
Maclaurin
,
J.
Iparraguirre
,
R.
Bombarell
,
T.
Hirzel
,
A.
Aspuru-Guzik
, and
R. P.
Adams
, in
Conference on Neural Information Processing Systems
, edited by
C.
Cortes
,
N. D.
Lawrence
,
D. D.
Lee
,
M.
Sugiyama
, and
R.
Garnett
(
Curran Associates, Inc.
,
2015
), pp.
2224
2232
.
27.
S.
Kearnes
,
K.
McCloskey
,
M.
Berndl
,
V.
Pande
, and
P. F.
Riley
,
J. Comput.-Aided Mol. Des.
30
,
595
(
2016
).
28.
K. T.
Schütt
,
F.
Arbabzadah
,
S.
Chmiela
,
K.-R.
Müller
, and
A.
Tkatchenko
,
Nat. Commun.
8
,
13890
(
2017
).
29.
J.
Gilmer
,
S. S.
Schoenholz
,
P. F.
Riley
,
O.
Vinyals
, and
G. E.
Dahl
, in
Proceedings of the 34th International Conference on Machine Learning
(
PMLR
,
2017
), pp.
1263
1272
.
30.
K. T.
Schütt
,
P.-J.
Kindermans
,
H. E.
Sauceda
,
S.
Chmiela
,
A.
Tkatchenko
, and
K.-R.
Müller
, in
Advances in Neural Information Processing Systems 30
(
Curran Associates, Inc.
,
2017
), pp.
992
1002
.
31.
D.
Baehrens
,
T.
Schroeter
,
S.
Harmeling
,
M.
Kawanabe
,
K.
Hansen
, and
K.-R.
Müller
,
J. Mach. Learn. Res.
11
,
1803
1831
(
2010
).
32.
K.
Simonyan
,
A.
Vedaldi
, and
A.
Zisserman
, eprint arXiv:1312.6034 (
2013
).
33.
S.
Bach
,
A.
Binder
,
G.
Montavon
,
F.
Klauschen
,
K.-R.
Müller
, and
W.
Samek
,
PLoS One
10
,
e0130140
(
2015
).
34.
L. M.
Zintgraf
,
T. S.
Cohen
,
T.
Adel
, and
M.
Welling
, in
International Conference on Learning Representations
,
2017
.
35.
G.
Montavon
,
S.
Lapuschkin
,
A.
Binder
,
W.
Samek
, and
K.-R.
Müller
,
Pattern Recognit.
65
,
211
(
2017
).
36.
P.-J.
Kindermans
,
K. T.
Schütt
,
M.
Alber
,
K.-R.
Müller
,
D.
Erhan
,
B.
Kim
, and
S.
Dähne
, eprint arXiv:1705.05598 (
2017
).
37.
G.
Montavon
,
W.
Samek
, and
K.-R.
Müller
,
Digital Signal Process.
73
,
1
(
2018
).
38.
K.
Xu
,
J.
Ba
,
R.
Kiros
,
K.
Cho
,
A.
Courville
,
R.
Salakhudinov
,
R.
Zemel
, and
Y.
Bengio
, in
International Conference on Machine Learning
(
PMLR
,
2015
), pp.
2048
2057
.
39.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
40.
A.
Tkatchenko
and
M.
Scheffler
,
Phys. Rev. Lett.
102
,
073005
(
2009
).
41.
I.
Poltavsky
and
A.
Tkatchenko
,
Chem. Sci.
7
,
1368
(
2016
).
42.
G. W.
Taylor
and
G. E.
Hinton
, in
Proceedings of the 26th Annual International Conference on Machine Learning ICML 09
(
ACM
,
2009
), Vol. 49, p.
1
.
43.
D.
Yu
,
L.
Deng
, and
F.
Seide
,
IEEE Trans. Audio, Speech, Lang. Process.
21
,
388
(
2013
).
44.
R.
Socher
,
A.
Perelygin
,
J. Y.
Wu
,
J.
Chuang
,
C. D.
Manning
,
A. Y.
Ng
, and
C.
Potts
, in
Conference on Empirical Methods in Natural Language Processing
(
ACL
,
2013
), Vol. 1631, p.
1642
.
45.
X.
Jia
,
B.
De Brabandere
,
T.
Tuytelaars
, and
L. V.
Gool
, in
Advances in Neural Information Processing Systems 29
, edited by
D. D.
Lee
,
M.
Sugiyama
,
U. V.
Luxburg
,
I.
Guyon
, and
R.
Garnett
(
Curran Associates, Inc.
,
2016
), pp.
667
675
.
46.
Y.
LeCun
,
B.
Boser
,
J. S.
Denker
,
D.
Henderson
,
R. E.
Howard
,
W.
Hubbard
, and
L. D.
Jackel
,
Neural Comput.
1
,
541
(
1989
).
47.
A.
Krizhevsky
,
I.
Sutskever
, and
G. E.
Hinton
,
Advances in Neural Information Processing Systems
(
Curran Associates, Inc.
,
2012
), pp.
1097
1105
.
48.
A.
van den Oord
,
S.
Dieleman
,
H.
Zen
,
K.
Simonyan
,
O.
Vinyals
,
A.
Graves
,
N.
Kalchbrenner
,
A.
Senior
,
K.
Kavukcuoglu
. “
WaveNet: A Generative Model for Raw Audio,
arXiv:1609.03499 (
2016
).
49.
F.
Chollet
,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
(
IEEE
,
2017
), pp.
1251
1258
.
50.
K.
He
,
X.
Zhang
,
S.
Ren
, and
J.
Sun
, in
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
(
IEEE
,
2016
), pp.
770
778
.
51.
A.
Pukrittayakamee
,
M.
Malshe
,
M.
Hagan
,
L.
Raff
,
R.
Narulkar
,
S.
Bukkapatnum
, and
R.
Komanduri
,
J. Chem. Phys.
130
,
134101
(
2009
).
52.
D. P.
Kingma
and
J.
Ba
, in
International Conference on Learning Representations
,
2015
.
53.
R.
Ramakrishnan
,
P. O.
Dral
,
M.
Rupp
, and
O. A.
von Lilienfeld
,
Sci. Data
1
,
140022
(
2014
).
54.
L. C.
Blum
and
J.-L.
Reymond
,
J. Am. Chem. Soc.
131
,
8732
(
2009
).
55.
J.-L.
Reymond
,
Acc. Chem. Res.
48
,
722
(
2015
).
56.
O.
Vinyals
,
S.
Bengio
, and
M.
Kudlur
, eprint arXiv:1511.06391 (
2015
).
57.
M.
Gastegger
,
J.
Behler
, and
P.
Marquetand
,
Chem. Sci.
8
(
10
),
6924
6935
(
2017
).
58.
A.
Jain
,
S. P.
Ong
,
G.
Hautier
,
W.
Chen
,
W. D.
Richards
,
S.
Dacek
,
S.
Cholia
,
D.
Gunter
,
D.
Skinner
,
G.
Ceder
, and
K. A.
Persson
,
APL Mater.
1
,
011002
(
2013
).
59.
S. P.
Ong
,
W. D.
Richards
,
A.
Jain
,
G.
Hautier
,
M.
Kocher
,
S.
Cholia
,
D.
Gunter
,
V. L.
Chevrier
,
K. A.
Persson
, and
G.
Ceder
,
Comput. Mater. Sci.
68
,
314
(
2013
).
60.
P.
Ramachandran
and
G.
Varoquaux
,
Comput. Sci. Eng.
13
,
40
(
2011
).
61.
Code and trained models are available at: https://github.com/atomistic-machine-learning/SchNet.
62.
I.
Poltavsky
,
R. A.
DiStasio
, Jr.
, and
A.
Tkatchenko
,
J. Chem. Phys.
148
,
102325
(
2018
).
63.
V.
Blum
,
R.
Gehrke
,
F.
Hanke
,
P.
Havu
,
V.
Havu
,
X.
Ren
,
K.
Reuter
, and
M.
Scheffler
,
Comput. Phys. Commun.
180
,
2175
(
2009
).
64.
M.
Ceriotti
,
J.
More
, and
D. E.
Manolopoulos
,
Comput. Phys. Commun.
185
,
1019
(
2014
).
65.
M.
Ceriotti
,
M.
Parrinello
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
133
,
124104
(
2010
).
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