We consider a Preconditioned Overdamped Langevin algorithm that does not alter the invariant distribution (up to controllable discretisation errors) and ask whether preconditioning improves the standard model in terms of reducing the asymptotic variance and of accelerating convergence to equilibrium. We present a detailed study of the dependence of the asymptotic variance on preconditioning in some elementary toy models related to molecular simulation. Our theoretical results are supported by numerical simulations.

DOI: https://doi.org/10.5802/smai-jcm.29

Keywords: Preconditioned Overdamped Langevin algorithm, Asymptotic Variance, Central Limit Theorem, Model Hamiltonians, Lattice Model

@article{SMAI-JCM_2018__4__57_0, author = {Houssam AlRachid and Letif Mones and Christoph Ortner}, title = {Some {Remarks} on {Preconditioning} {Molecular} {Dynamics}}, journal = {The SMAI journal of computational mathematics}, pages = {57--80}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {4}, year = {2018}, doi = {10.5802/smai-jcm.29}, mrnumber = {3774648}, zbl = {1416.82020}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.29/} }

Houssam AlRachid; Letif Mones; Christoph Ortner. Some Remarks on Preconditioning Molecular Dynamics. The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 57-80. doi : 10.5802/smai-jcm.29. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.29/

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