Data-driven reduced homogenization for transient diffusion problems with emergent history effects

In this paper, we propose a data-driven reduced homogenization technique to capture diffusional phenomena in heterogeneous materials which reveal, on macroscopic level, history-dependent non-Fickian behavior. The adopted enriched-continuum formulation, the transient effects are due underlying microstructure is represented by enrichment-variables that obtained model reduction at micro-scale. minimizes distance between points lying data-set and associated with state of material. excellent pointers for selection correct part problems time-dependent material state. Proof-of-principle simulations carried out linear exhibiting relaxed separation scales. Information from micro-scale unit-cell used determine approximate values metric coefficients function. proposed also performs adequately case noisy data-sets. Finally, possible extensions non-linear behavior discussed.