Abstract
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.
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Alrachid, H., Lelièvre, T.: Long-time convergence of an adaptive biasing force method: variance reduction by Helmholtz projection. SMAI J. Comput. Math. 1, 55–82 (2015)
Darve, E., Pohorille, A.: Calculating free energy using average forces. J. Chem. Phys. 115, 9169–9183 (2001)
Hénin, J., Chipot, C.: Overcoming free energy barriers using unconstrained molecular dynamics simulations. J. Chem. Phys. 121, 2904 (2004)
Lelièvre, T., Rousset M., Stoltz, G.: Computation of free energy profiles with adaptive parallel dynamics. J. Chem. Phys. 126, 134111 (2007)
Lelièvre, T., Rousset M., Stoltz, G.: Long-time convergence of an adaptive biasing force method. Nonlinearity 21, 1155–1181 (2008)
Lelièvre, T., Rousset, M., Stoltz, G.: Free Energy Computations: A Mathematical Perspective. Imperial College Press, London (2010)
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AlRachid, H., Lelièvre, T. (2017). Variance Reduction Result for a Projected Adaptive Biasing Force Method. In: Mateos, M., Alonso, P. (eds) Computational Mathematics, Numerical Analysis and Applications. SEMA SIMAI Springer Series, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-49631-3_10
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DOI: https://doi.org/10.1007/978-3-319-49631-3_10
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