From mesoscale back to microscale: Reconstruction schemes for coarse-grained stochastic lattice systems
José Trashorras and Dimitrios Tsagkarogiannis
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Submission date: 25. Apr. 2008
published in: SIAM journal on numerical analysis, 48 (2010) 5, p. 1647-1677
DOI number (of the published article): 10.1137/080722382
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
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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.