PMID- 22612086
OWN - NLM
STAT- MEDLINE
DCOM- 20120925
LR  - 20120522
IS  - 1089-7690 (Electronic)
IS  - 0021-9606 (Linking)
VI  - 136
IP  - 19
DP  - 2012 May 21
TI  - The multiscale coarse-graining method. VIII. Multiresolution hierarchical basis 
      functions and basis function selection in the construction of coarse-grained 
      force fields.
PG  - 194113
LID - 10.1063/1.4705384 [doi]
AB  - The multiscale coarse-graining (MS-CG) method is a method for determining the 
      effective potential energy function for a coarse-grained (CG) model of a 
      molecular system using data obtained from molecular dynamics simulation of the 
      corresponding atomically detailed model. The coarse-grained potential obtained 
      using the MS-CG method is a variational approximation for the exact many-body 
      potential of mean force for the coarse-grained sites. Here we propose a new 
      numerical algorithm with noise suppression capabilities and enhanced numerical 
      stability for the solution of the MS-CG variational problem. The new method, 
      which is a variant of the elastic net method [Friedman et al., Ann. Appl. Stat. 
      1, 302 (2007)], allows us to construct a large basis set, and for each value of a 
      so-called "penalty parameter" the method automatically chooses a subset of the 
      basis that is most important for representing the MS-CG potential. The size of 
      the subset increases as the penalty parameter is decreased. The appropriate value 
      to choose for the penalty parameter is the one that gives a basis set that is 
      large enough to fit the data in the simulation data set without fitting the 
      noise. This procedure provides regularization to mitigate potential numerical 
      problems in the associated linear least squares calculation, and it provides a 
      way to avoid fitting statistical error. We also develop new basis functions that 
      are similar to multiresolution Haar functions and that have the differentiability 
      properties that are appropriate for representing CG potentials. We demonstrate 
      the feasibility of the combined use of the elastic net method and the 
      multiresolution basis functions by performing a variational calculation of the CG 
      potential for a relatively simple system. We develop a method to choose the 
      appropriate value of the penalty parameter to give the optimal basis set. The 
      combined effect of the new basis functions and the regularization provided by the 
      elastic net method opens the possibility of using very large basis sets for 
      complicated CG systems with many interaction potentials without encountering 
      numerical problems in the variational calculation.
FAU - Das, Avisek
AU  - Das A
AD  - Department of Chemistry, Stanford University, Stanford, California 94305, USA.
FAU - Andersen, Hans C
AU  - Andersen HC
LA  - eng
PT  - Journal Article
PT  - Research Support, U.S. Gov't, Non-P.H.S.
PL  - United States
TA  - J Chem Phys
JT  - The Journal of chemical physics
JID - 0375360
SB  - IM
MH  - Algorithms
MH  - Linear Models
MH  - Models, Chemical
MH  - *Models, Theoretical
MH  - *Molecular Dynamics Simulation
EDAT- 2012/05/23 06:00
MHDA- 2012/09/26 06:00
CRDT- 2012/05/23 06:00
PHST- 2012/05/23 06:00 [entrez]
PHST- 2012/05/23 06:00 [pubmed]
PHST- 2012/09/26 06:00 [medline]
AID - 10.1063/1.4705384 [doi]
PST - ppublish
SO  - J Chem Phys. 2012 May 21;136(19):194113. doi: 10.1063/1.4705384.