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We consider the inverse problem of reconstructing an effective model for aprototypical diffusion process in strongly heterogeneous media based on coarsemeasurements. The approach is motivated by quasi-local numerical effectiveforward models that are provably reliable beyond periodicity assumptions andscale separation. The goal of this work is to show that an identification ofthe matrix representation related to these effective models is possible. On theone hand, this provides a reasonable surrogate in cases where a directreconstruction is unfeasible due to a mismatch between the coarse data scaleand the microscopic quantities to be reconstructed. On the other hand, theapproach allows us to investigate the requirement for a certain non-locality inthe context of numerical homogenization. Algorithmic aspects of the inversionprocedure and its performance are illustrated in a series of numericalexperiments.

Reconstruction of quasi-local numerical effective models from low-resolution measurements