Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

Hong Duong, Agnes Lamacz, Mark A. Peletier, André Schlichting, Upanshu Sharma

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Abstract

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained dynamics and an effective dynamics. The effective dynamics is a Markov process on the coarse-grained state space obtained by a closure procedure from the coarse-grained coefficients. We obtain error estimates both in relative entropy and Wasserstein distance, for both Langevin and overdamped Langevin dynamics. The approach allows for vectorial coarse-graining maps. Hereby, the quality of the chosen coarse-graining is measured by certain
functional inequalities encoding the scale separation of the Gibbs measure. The method is based on error estimates between solutions of (kinetic) Fokker-Planck equations in terms of large-deviation rate functionals.
Original languageEnglish
Pages (from-to)4517-4566
Number of pages50
JournalNonlinearity
Volume31
Issue number10
Early online date21 Aug 2018
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • coarse-graining
  • relative entropy techniques
  • effective dynamics for SDEs
  • functional inequalities
  • Langevin equation
  • large-deviation rate functionals

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