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Information‐Theoretic Approach to Bidirectional Scaling

We present an information‐theoretic approach for integration of multiresolution data into multiscale simulations. This general framework is used to upscale and downscale equations of fluid flow in heterogeneous porous media. Fine‐scale information can comprise observational data and/or simulation results related to both system states and system parameters. It is aggregated into its coarse‐scale representation by setting a probabilistic equivalence between the two scales, with parameters that are determined via minimization of observable error and mutual information across scales. The same quantities facilitate the use of coarse‐scale data to constrain compatible fine‐scale distributions.