TY - GEN
T1 - Variance reduction result for a projected adaptive biasing force method
AU - AlRachid, Houssam
AU - Lelièvre, Tony
N1 - Publisher Copyright:
© 2017, Springer International Publishing AG.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - This paper is committed to investigate an extension of the classical adaptive biasing force method, which is used to compute the free energy related to the Boltzmann-Gibbs measure and a reaction coordinate function. The issue of this technique is that the approximated gradient of the free energy, called biasing force, is not a gradient. The commitment to this field is to project the estimated biasing force on a gradient using the Helmholtz decomposition. The variance of the biasing force is reduced using this technique, which makes the algorithm more efficient than the standard ABF method. We prove exponential convergence to equilibrium of the estimated free energy, with a precise rate of convergence in function of Logarithmic Sobolev inequality constants.
AB - This paper is committed to investigate an extension of the classical adaptive biasing force method, which is used to compute the free energy related to the Boltzmann-Gibbs measure and a reaction coordinate function. The issue of this technique is that the approximated gradient of the free energy, called biasing force, is not a gradient. The commitment to this field is to project the estimated biasing force on a gradient using the Helmholtz decomposition. The variance of the biasing force is reduced using this technique, which makes the algorithm more efficient than the standard ABF method. We prove exponential convergence to equilibrium of the estimated free energy, with a precise rate of convergence in function of Logarithmic Sobolev inequality constants.
UR - https://www.scopus.com/pages/publications/85031767928
U2 - 10.1007/978-3-319-49631-3_10
DO - 10.1007/978-3-319-49631-3_10
M3 - Conference contribution
AN - SCOPUS:85031767928
SN - 9783319496306
T3 - SEMA SIMAI Springer Series
SP - 221
EP - 227
BT - Computational Mathematics, Numerical Analysis and Applications - Lecture Notes of the XVII ‘Jacques-Louis Lions’ Spanish-French School
A2 - Mateos, Mariano
A2 - Alonso, Pedro
PB - Springer International Publishing
T2 - 17th 'Jacques-Louis Lions' Spanish-French School on Computational Mathematics, Numerical Analysis and Applications, 2016
Y2 - 6 June 2016 through 10 June 2016
ER -