The committor function is a central object of study in understanding transitions between metastable states in complex systems. However, computing the committor function for realistic systems at low temperatures is a challenging task due to the curse of dimensionality and the scarcity of transition data. In this paper, we introduce a computational approach that overcomes these issues and achieves good performance on complex benchmark problems with rough energy landscapes or in high dimensions. The new approach combines deep learning, data sampling, and feature engineering techniques. This establishes an alternative practical method for studying rare transition events between metastable states in complex, high dimensional systems.
REFERENCES
1.
H.
Jónsson
, G.
Mills
, and K. W.
Jacobsen
, “Nudged elastic band method for finding minimum energy paths of transitions
,” in Classical and Quantum Dynamics in Condensed Phase Simulations
, edited by B. J.
Berne
, G.
Ciccotti
and D. F.
Coker
(World Scientific
, Singapore
, 1998
), pp. 385
–404
.2.
W.
E
, W.
Ren
, and E.
Vanden-Eijnden
, “String method for the study of rare events
,” Phys. Rev. B
66
, 052301
(2002
).3.
W.
E
, W.
Ren
, and E.
Vanden-Eijnden
, “Simplified and improved string method for computing the minimum energy paths in barrier-crossing events
,” J. Chem. Phys.
126
, 164103
(2007
).4.
W.
Ren
, E.
Vanden-Eijnden
, P.
Maragakis
, and W.
E
, “Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide
,” J. Chem. Phys.
123
, 134109
(2005
).5.
R.
Olender
and R.
Elber
, “Calculation of classical trajectories with a very large time step: Formalism and numerical examples
,” J. Chem. Phys.
105
, 9299
–9315
(1996
).6.
P. G.
Bolhuis
, D.
Chandler
, C.
Dellago
, and P. L.
Geissler
, “Transition path sampling: Throwing ropes over rough mountain passes, in the dark
,” Annu. Rev. Phys. Chem.
53
, 291
–318
(2002
).7.
C.
Dellago
, P. G.
Bolhuis
, and P. L.
Geissler
, “Transition path sampling
,” Adv. Chem. Phys.
123
, 1
–78
(2002
).8.
A. F.
Voter
, “Hyperdynamics: Accelerated molecular dynamics of infrequent events
,” Phys. Rev. Lett.
78
, 3908
(1997
).9.
W.
E
, W.
Ren
, and E.
Vanden-Eijnden
, “Transition pathways in complex systems: Reaction coordinates, isocommittor surfaces, and transition tubes
,” Chem. Phys. Lett.
413
, 242
–247
(2005
).10.
W.
E
and E.
Vanden-Eijnden
, “Transition-path theory and path-finding algorithms for the study of rare events
,” Annu. Rev. Phys. Chem.
61
, 391
–420
(2010
).11.
R.
Lai
and J.
Lu
, “Point cloud discretization of fokker-planck operators for committor functions
,” Multiscale Model. Simul.
16
, 710
–726
(2018
).12.
Y.
Khoo
, J.
Lu
, and L.
Ying
, “Solving for high-dimensional committor functions using artificial neural networks
,” Res. Math. Sci.
6
, 1
(2019
).13.
C. W.
Gardiner
, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences
(Springer
, New York
, 1997
).14.
A.
Laio
and M.
Parrinello
, “Escaping free-energy minima
,” Proc. Natl. Acad. Sci. U. S. A.
99
, 12562
–12566
(2002
).15.
A.
Barducci
, M.
Bonomi
, and M.
Parrinello
, “Metadynamics
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
1
, 826
–843
(2011
).16.
F.
Hecht
, “New development in FreeFem++
,” J. Numer. Math.
20
, 251
–265
(2012
).17.
M.
Abadi
, A.
Agarwal
, P.
Barham
, E.
Brevdo
, Z.
Chen
, C.
Citro
, G. S.
Corrado
, A.
Davis
, J.
Dean
, M.
Devin
, S.
Ghemawat
, I.
Goodfellow
, A.
Harp
, G.
Irving
, M.
Isard
, Y.
Jia
, R.
Jozefowicz
, L.
Kaiser
, M.
Kudlur
, J.
Levenberg
, D.
Mané
, R.
Monga
, S.
Moore
, D.
Murray
, C.
Olah
, M.
Schuster
, J.
Shlens
, B.
Steiner
, I.
Sutskever
, K.
Talwar
, P.
Tucker
, V.
Vanhoucke
, V.
Vasudevan
, F.
Viégas
, O.
Vinyals
, P.
Warden
, M.
Wattenberg
, M.
Wicke
, Y.
Yu
, and X.
Zheng
, TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems, 2015
, software available from tensorflow.org.18.
D. P.
Kingma
and J.
Ba
, “Adam: A method for stochastic optimization
,” in Proceedings of International Conference on Learning Representations
(ICLR
, San Diego
, 2015
).19.
W.
E
, W.
Ren
, and E.
Vanden-Eijnden
, “Minimum action method for the study of rare events
,” Commun. Pure Appl. Math.
57
, 637
–656
(2004
).20.
J.
Apostolakis
, P.
Ferrara
, and A.
Caflisch
, “Calculation of conformational transitions and barriers in solvated systems: Application to the alanine dipeptide in water
,” J. Chem. Phys.
110
, 2099
–2108
(1999
).21.
P. G.
Bolhuis
, C.
Dellago
, and D.
Chandler
, “Reaction coordinates of biomolecular isomerization
,” Proc. Natl. Acad. Sci. U. S. A.
97
, 5877
–5882
(2000
).22.
A.
Ma
and A. R.
Dinner
, “Automatic method for identifying reaction coordinates in complex systems
,” J. Phys. Chem. B
109
, 6769
–6779
(2005
).23.
J. C.
Phillips
, R.
Braun
, W.
Wang
, J.
Gumbart
, E.
Tajkhorshid
, E.
Villa
, C.
Chipot
, R. D.
Skeel
, L.
Kalé
, and K.
Schulten
, “Scalable molecular dynamics with NAMD
,” J. Comput. Chem.
26
, 1781
–1802
(2005
).24.
G.
Fiorin
, M. L.
Klein
, and J.
Hénin
, “Using collective variables to drive molecular dynamics simulations
,” Mol. Phys.
111
, 3345
–3362
(2013
).25.
L.
Maragliano
, A.
Fischer
, E.
Vanden-Eijnden
, and G.
Ciccotti
, “String method in collective variables: Minimum free energy paths and isocommittor surfaces
,” J. Chem. Phys.
125
, 024106
(2006
).© 2019 Author(s).
2019
Author(s)
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