Molecular simulations are widely applied in the study of chemical and bio-physical problems. However, the accessible timescales of atomistic simulations are limited, and extracting equilibrium properties of systems containing rare events remains challenging. Two distinct strategies are usually adopted in this regard: either sticking to the atomistic level and performing enhanced sampling or trading details for speed by leveraging coarse-grained models. Although both strategies are promising, either of them, if adopted individually, exhibits severe limitations. In this paper, we propose a machine-learning approach to ally both strategies so that simulations on different scales can benefit mutually from their crosstalks: Accurate coarse-grained (CG) models can be inferred from the fine-grained (FG) simulations through deep generative learning; in turn, FG simulations can be boosted by the guidance of CG models via deep reinforcement learning. Our method defines a variational and adaptive training objective, which allows end-to-end training of parametric molecular models using deep neural networks. Through multiple experiments, we show that our method is efficient and flexible and performs well on challenging chemical and bio-molecular systems.
REFERENCES
1.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation: From Algorithms to Applications
(Elsevier
, 2001
).2.
M. E.
Tuckerman
, J. Phys.: Condens. Matter
14
(50
), R1297
(2002
).3.
G.
Fiorin
, M. L.
Klein
, and J.
Hénin
, Mol. Phys.
111
(22-23
), 3345
–3362
(2013
).4.
G. A.
Voth
, Coarse-Graining of Condensed Phase and Biomolecular Systems
(CRC Press
, 2008
).5.
W. G.
Noid
, J.-W.
Chu
, G. S.
Ayton
, V.
Krishna
, S.
Izvekov
, G. A.
Voth
, A.
Das
, and H. C.
Andersen
, J. Chem. Phys.
128
(24
), 244114
(2008
).6.
G. M.
Torrie
and J. P.
Valleau
, J. Comput. Phys.
23
(2
), 187
–199
(1977
).7.
B. W.
Silverman
, Density Estimation for Statistics and Data Analysis
(Routledge
, 2018
).8.
R.
Bellman
, “Adaptive control processes: a guided tour
,” (Princeton
, New Jersey, USA,
1961
).9.
J. J.
Crabbe
, “Handling the curse of dimensionality in multivariate kernel density estimation
,” Ph.D. dissertation, Oklahoma State University
, 2013
.10.
Y.
LeCun
, Y.
Bengio
, and G.
Hinton
, Nature
521
(7553
), 436
(2015
).11.
12.
E.
Schneider
, L.
Dai
, R. Q.
Topper
, C.
Drechsel-Grau
, and M. E.
Tuckerman
, Phys. Rev. Lett.
119
(15
), 150601
(2017
).13.
J.
Wang
, S.
Olsson
, C.
Wehmeyer
, A.
Pérez
, N. E.
Charron
, G.
De Fabritiis
, F.
Noé
, and C.
Clementi
, ACS Cent. Sci.
5
, 755
(2019
).14.
V. N.
Vapnik
, IEEE Trans. Neural Networks
10
(5
), 988
–999
(1999
).15.
D. P.
Kingma
and M.
Welling
, “Auto-encoding variational bayes
,” 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada (2014
).16.
A.
Van den Oord
, N.
Kalchbrenner
, L.
Espeholt
, O.
Vinyals
, and A.
Graves
, presented at the Advances in Neural Information Processing Systems
, 2016
.17.
18.
D. J.
Rezende
and S.
Mohamed
, “Variational inference with normalizing flows
,” in International Conference on Machine Learning (ICML, 2015), pp. 1530–1538.19.
M. E.
Abbasnejad
, Q.
Shi
, A. v. d.
Hengel
, and L.
Liu
, presented at the The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
.20.
R.
Salakhutdinov
, A.
Mnih
, and G.
Hinton
, presented at the Proceedings of the 24th International Conference on Machine Learning
, 2007
.21.
R.
Salakhutdinov
and G.
Hinton
, in Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics
, edited by D.
David van
and W.
Max
(PMLR, Proceedings of Machine Learning Research
, 2009
), Vol. 5, pp. 448
–455
.22.
J. J.
Hopfield
, Proc. Natl. Acad. Sci. U. S. A.
79
(8
), 2554
–2558
(1982
).23.
D.
Wales
, Energy Landscapes: Applications to Clusters, Biomolecules and Glasses
(Cambridge University Press
, 2003
).24.
25.
A. P.
Lyubartsev
, Eur. Biophys. J.
35
(1
), 53
(2005
).26.
M. S.
Shell
, J. Chem. Phys.
129
(14
), 144108
(2008
).27.
D.
Reith
, M.
Pütz
, and F.
Müller-Plathe
, J. Comput. Chem.
24
(13
), 1624
–1636
(2003
).28.
I.
Goodfellow
, J.
Pouget-Abadie
, M.
Mirza
, B.
Xu
, D.
Warde-Farley
, S.
Ozair
, A.
Courville
, and Y.
Bengio
, presented at the Advances in Neural Information Processing Systems
, 2014
.29.
S.
Kullback
and R. A.
Leibler
, Ann. Math. Stat.
22
(1
), 79
–86
(1951
).30.
M.
Arjovsky
, S.
Chintala
, and L.
Bottou
, presented at the International Conference on Machine Learning
, 2017
.31.
A.
Chaimovich
and M. S.
Shell
, J. Chem. Phys.
134
(9
), 094112
(2011
).32.
O.
Valsson
and M.
Parrinello
, Phys. Rev. Lett.
113
(9
), 090601
(2014
).33.
J.
Zhang
, Y. I.
Yang
, and F.
Noé
, J. Phys. Chem. Lett.
10
(19
), 5791
–5797
(2019
).34.
D. M.
Blei
, A.
Kucukelbir
, and J. D.
McAuliffe
, J. Am. Stat. Assoc.
112
(518
), 859
–877
(2017
).35.
D.
Wu
, L.
Wang
, and P.
Zhang
, Phys. Rev. Lett.
122
(8
), 080602
(2019
).36.
F.
Noé
, S.
Olsson
, J.
Köhler
, and H.
Wu
, Science
365
(6457
), eaaw1147
(2019
).37.
L.
Dinh
, J.
Sohl-Dickstein
, and S.
Bengio
, in International Conference on Learning Representations
, 2017
.38.
G.
Papamakarios
, T.
Pavlakou
, and I.
Murray
, in Neural Information Processing Systems
(NIPS
, 2017
), pp. 2338
–2347
.39.
T. Q.
Chen
, Y.
Rubanova
, J.
Bettencourt
, and D.
Duvenaud
, in Neural Information Processing Systems
(NIPS
, 2018
), pp. 6572
–6583
.40.
W.
Grathwohl
, R. T. Q.
Chen
, J.
Bettencourt
, I.
Sutskever
, and D.
Duvenaud
, in International Conference on Learning Representations
, 2019
.41.
M. E.
Abbasnejad
, Q.
Shi
, A. v. d.
Hengel
, and L.
Liu
, in Computer Vision and Pattern Recognition
(IEEE
, 2019
), pp. 10782
–10791
.42.
C.
Abrams
and G.
Bussi
, Entropy
16
(1
), 163
–199
(2014
).43.
Y.
Okamoto
, J. Mol. Graphics Modell.
22
(5
), 425
–439
(2004
).44.
Y. I.
Yang
, Q.
Shao
, J.
Zhang
, L.
Yang
, and Y. Q.
Gao
, J. Chem. Phys.
151
(7
), 070902
(2019
).45.
A.
Laio
and M.
Parrinello
, Proc. Natl. Acad. Sci. U. S. A.
99
(20
), 12562
–12566
(2002
).46.
R. S.
Sutton
and A. G.
Barto
, Reinforcement Learning: An Introduction
(MIT Press
, 2018
).47.
I.
Grondman
, L.
Busoniu
, G. A. D.
Lopes
, and R.
Babuska
, IEEE Trans. Syst. Man, Cybernetics, Part C
42
(6
), 1291
–1307
(2012
).48.
A.
Barducci
, G.
Bussi
, and M.
Parrinello
, Phys. Rev. Lett.
100
(2
), 020603
(2008
).49.
M.
Heusel
, H.
Ramsauer
, T.
Unterthiner
, B.
Nessler
, and S.
Hochreiter
, presented at the Advances in Neural Information Processing Systems
, 2017
.50.
H.
Van Hasselt
, A.
Guez
, and D.
Silver
, presented at the Thirtieth AAAI Conference on Artificial Intelligence
, 2016
.51.
A. v. d.
Oord
, Y.
Li
, I.
Babuschkin
, K.
Simonyan
, O.
Vinyals
, k.
kavukcuoglu
, G. v. d.
Driessche
, E.
Lockhart
, L.
Cobo
, F.
Stimberg
, N.
Casagrande
, D.
Grewe
, S.
Noury
, S.
Dieleman
, E.
Elsen
, N.
Kalchbrenner
, H.
Zen
, A.
Graves
, H.
King
, T.
Walters
, D.
Belov
, and D.
Hassabis
, in International Conference on Machine Learning
(ICML
, 2018
), pp. 3915
–3923
.52.
L.
Bonati
, Y.-Y.
Zhang
, and M.
Parrinello
, Proc. Natl. Acad. Sci. U. S. A.
116
(36
), 17641
–17647
(2019
).53.
P.
Tiwary
and B. J.
Berne
, J. Chem. Phys.
147
(15
), 152701
(2017
).54.
S.
Singer
and J.
Nelder
, Scholarpedia
4
(7
), 2928
(2009
).55.
S.
Kmiecik
, D.
Gront
, M.
Kolinski
, L.
Wieteska
, A. E.
Dawid
, and A.
Kolinski
, Chem. Rev.
116
(14
), 7898
–7936
(2016
).56.
K.
Lindorff-Larsen
, S.
Piana
, R. O.
Dror
, and D. E.
Shaw
, Science
334
(6055
), 517
, 520
(2011
).57.
S.
Piana
and A.
Laio
, J. Phys. Chem. B
111
(17
), 4553
–4559
(2007
).58.
C. M.
Davis
, S.
Xiao
, D. P.
Raleigh
, and R. B.
Dyer
, J. Am. Chem. Soc.
134
(35
), 14476
–14482
(2012
).59.
H.
Nguyen
, J.
Maier
, H.
Huang
, V.
Perrone
, and C.
Simmerling
, J. Am. Chem. Soc.
136
(40
), 13959
–13962
(2014
).60.
P.
Shaffer
, O.
Valsson
, and M.
Parrinello
, Proc. Natl. Acad. Sci. U. S. A.
113
(5
), 1150
–1155
(2016
).61.
J.
Zhang
, Y.-K.
Lei
, X.
Che
, Z.
Zhang
, Y. I.
Yang
, and Y. Q.
Gao
, J. Phys. Chem. Lett.
10
(18
), 5571
–5576
(2019
).62.
F.
Palazzesi
, O.
Valsson
, and M.
Parrinello
, J. Phys. Chem. Lett.
8
(19
), 4752
–4756
(2017
).63.
H.
Wu
, A.
Mardt
, L.
Pasquali
, and F.
Noe
, presented at the Advances in Neural Information Processing Systems
, 2018
.64.
H.
Sidky
, W.
Chen
, and A. L.
Ferguson
, Chem. Sci.
11
(35
), 9459
–9467
(2020
).65.
J. M. L.
Ribeiro
, P.
Bravo
, Y.
Wang
, and P.
Tiwary
, J. Chem. Phys.
149
(7
), 072301
(2018
).66.
L.
Zhang
, H.
Wang
, and W.
E
, J. Chem. Phys.
148
(12
), 124113
(2018
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
