Elements of information theory
Elements of information theory
Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems
Journal of Computational Physics
Error Analysis of Coarse-Graining for Stochastic Lattice Dynamics
SIAM Journal on Numerical Analysis
Numerical and Statistical Methods for the Coarse-Graining of Many-Particle Stochastic Systems
Journal of Scientific Computing
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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. By using different techniques we consider the cases of both short and long range microscopic models.