From mesoscale back to microscale: Reconstruction schemes for coarse-grained stochastic lattice systems

José Trashorras and Dimitrios Tsagkarogiannis

Contact the author: Please use for correspondence this email.
Submission date: 25. Apr. 2008
Pages: 26
published in: SIAM journal on numerical analysis, 48 (2010) 5, p. 1647-1677 
DOI number (of the published article): 10.1137/080722382
Bibtex
MSC-Numbers: 65C05, 65C20, 82-08, 82B20, 82B80, 94A17
Keywords and phrases: coarse-graining, microscopic reconstruction, Monte-Carlo simulation, parallel computing, lattice spin systems, Gibbs measure, cluster expansion
Download full preprint: PDF (267 kB)

Abstract:
Starting from a microscopic stochastic lattice spin system and the corresponding coarse-grained model we introduce a mathematical strategy to recover microscopic information given the coarse-grained data. We define ``reconstructed" microscopic measures satisfying two conditions: (i) they are close in specific relative entropy to the initial microscopic equilibrium measure conditioned on the coarse-grained data and (ii) their sampling is computationally advantageous when compared to sampling directly from the conditioned microscopic equilibrium measure.