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International audienceStarting 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

From Mesoscale Back to Microscale: Reconstruction Schemes for Coarse-Grained Stochastic Lattice Systems