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Information‐Theoretic Approach to Bidirectional Scaling
Author(s) -
Boso Francesca,
Tartakovsky Daniel M.
Publication year - 2018
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2017wr021993
Subject(s) - scaling , observable , probabilistic logic , equivalence (formal languages) , scale (ratio) , computer science , representation (politics) , mutual information , observational equivalence , minification , statistical physics , mathematical optimization , data mining , mathematics , theoretical computer science , physics , artificial intelligence , geometry , discrete mathematics , quantum mechanics , politics , political science , law
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.