Diffusion Monte Carlo method : numerical analysis in a simple case
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 2, p. 189-213
The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove the convergence of the method for a fixed number of reconfigurations when the number of walkers tends to $+\infty$ while the timestep tends to $0$. We confirm our theoretical rates of convergence by numerical experiments. Various resampling algorithms are investigated, both theoretically and numerically.
DOI : https://doi.org/10.1051/m2an:2007017
Classification:  81Q05,  65C35,  60K35,  35P15
@article{M2AN_2007__41_2_189_0,
author = {Makrini, Mohamed El and Jourdain, Benjamin and Leli\evre, Tony},
title = {Diffusion Monte Carlo method : numerical analysis in a simple case},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {41},
number = {2},
year = {2007},
pages = {189-213},
doi = {10.1051/m2an:2007017},
zbl = {1135.81379},
mrnumber = {2339625},
language = {en},
url = {http://www.numdam.org/item/M2AN_2007__41_2_189_0}
}

Makrini, Mohamed El; Jourdain, Benjamin; Lelièvre, Tony. Diffusion Monte Carlo method : numerical analysis in a simple case. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 2, pp. 189-213. doi : 10.1051/m2an:2007017. http://www.numdam.org/item/M2AN_2007__41_2_189_0/`

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