Relative entropy has been shown to provide a principled framework for the selection of coarse-grained potentials. Despite the intellectual appeal of it, its application has been limited by the fact that it requires the solution of an optimization problem with noisy gradients. When using deterministic optimization schemes, one is forced to either decrease the noise by adequate sampling or to resolve to ad hoc modifications in order to avoid instabilities. The former increases the computational demand of the method while the latter is of questionable validity. In order to address these issues and make relative entropy widely applicable, we propose alternative schemes for the solution of the optimization problem using stochastic algorithms.
REFERENCES
1.
W.
Tschöp
, K.
Kremer
, J.
Batoulis
, T.
Bürger
, and O.
Hahn
, “Simulation of polymer melts. I. Coarse-graining procedure for polycarbonates
,” Acta Polym.
49
, 61
–74
(1998
).2.
D.
Reith
, M.
Pütz
, and F.
Müller-Plathe
, “Deriving effective mesoscale potentials from atomistic simulations
,” J. Comput. Chem.
24
, 1624
–1636
(2003
).3.
A. P.
Lyubartsev
and A.
Laaksonen
, “Calculation of effective interaction potentials from radial distribution functions: A reverse Monte Carlo approach
,” Phys. Rev. E
52
, 3730
–3737
(1995
).4.
A. K.
Soper
, “Empirical potential Monte Carlo simulation of fluid structure
,” Chem. Phys.
202
, 295
–306
(1996
).5.
S.
Izvekov
and G. A.
Voth
, “Multiscale coarse graining of liquid-state systems
,” J. Chem. Phys.
123
, 134105
(2005
).6.
W. G.
Noid
, J.
Chu
, G. S.
Ayton
, and G. A.
Voth
, “Multiscale coarse-graining and structural correlations: Connections to liquid-state theory
,” J. Phys. Chem. B
111
, 4116
–4127
(2007
).7.
M. S.
Shell
, “The relative entropy is fundamental to multiscale and inverse thermodynamic problems
,” J. Chem. Phys.
129
, 144108
(2008
).8.
A.
Chaimovich
and M. S.
Shell
, “Coarse-graining errors and numerical optimization using a relative entropy framework
,” J. Chem. Phys.
134
, 094112
(2011
).9.
A.
Chaimovich
and M. S.
Shell
, “Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy
,” Phys. Chem. Chem. Phys.
11
, 1901
–1915
(2009
).10.
A.
Pritchard-Bell
and M. S.
Shell
, “Smoothing protein energy landscapes by integrating folding models with structure prediction
,” Biophys. J.
101
, 2251
–2259
(2011
).11.
S. P.
Carmichael
and M. S.
Shell
, “A new multiscale algorithm and its application to coarse-grained peptide models for self-assembly
,” J. Phys. Chem. B
116
, 8383
–8393
(2012
).12.
J. M.
Ortega
and W. C.
Rheinboldt
, Iterative Solution of Nonlinear Equations in Several Variables
(Academic
, New York
, 1970
).13.
H.
Robbins
and S.
Monro
, “A stochastic approximation method
,” Ann. Math. Stat.
22
, 400
–407
(1951
).14.
J. C.
Spall
, Introduction to Stochastic Search and Optimization
, 1st ed. (Wiley
, New York, NY
, 2003
).15.
R. H.
Byrd
, G. M.
Chin
, W.
Neveitt
, and J.
Nocedal
, “On the use of stochastic Hessian information in optimization methods for machine learning
,” SIAM J. Optim.
21
(3
), 977
–995
(2011
).16.
P. G.
Kusalik
and I. M.
Svishchev
, “The spatial structure in liquid water
,” Science
265
, 1219
–1221
(1994
).17.
H. J. C.
Berendsen
, J. R.
Grigera
, and T. P.
Straatsma
, “The missing term in effective pair potentials
,” J. Phys. Chem.
91
, 6269
–6271
(1987
).18.
V.
Rühle
, C.
Junghans
, A.
Lukyanov
, K.
Kremer
, and D.
Andrienko
, “Versatile object-oriented toolkit for coarse-graining applications
,” J. Chem. Theory Comput.
5
, 3211
–3223
(2009
).19.
B.
Hess
, C.
Kutzner
, D.
van der Spoel
, and E.
Lindahl
, “plbibsc-gromacs 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation
,” J. Chem. Theory Comput.
4
, 435
–447
(2008
).20.
H. J. C.
Berendsen
, J. P. M.
Postma
, W. F.
van Gunsteren
, A.
DiNola
, and J. R.
Haak
, “Molecular dynamics with coupling to an external bath
,” J. Chem. Phys.
81
, 3684
–3690
(1984
).21.
W. F.
van Gunsteren
and H. J. C.
Berendsen
, “A leap-frog algorithm for stochastic dynamics
,” Mol. Simul.
1
, 173
–185
(1988
).22.
23.
M.
Galassi
, J.
Davis
, J.
Theiler
, B.
Gough
, G.
Jungman
, P.
Alken
, M.
Booth
, and F.
Rossi
, GNU Scientific Library Reference Manual (3rd Ed.).© 2013 American Institute of Physics.
2013
American Institute of Physics
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