A digital workflow for learning the reduced-order structure-property linkages for permeability of porous membranes

Quantitative relationships between the complex porous structure of a membrane (henceforth simply referred to as microstructure) and its effective permeability are critical for improving the performance of membranes used in filtration and separation applications. This paper presents a digital workflow for learning the porous structure-permeability linkages in membranes. The presented workflow establishes the desired linkages by bringing together recent advances in (i) digital generators for three-dimensional representative volume elements (3-D RVEs) reflecting a large and diverse set of porous structures, (ii) numerical approaches for reliable evaluation of permeability of 3D-RVEs, (iii) low dimensional representation of material internal structure using the framework of 2-point spatial correlations and principal component analyses, and (iv) Gaussian process (GP) regression with input-dependent noise (i.e., heteroscedasticity). It is seen that the digital workflow presented in this study can systematically identify the salient features of the 3-D membrane microstructure and train reduced-order heteroscedastic GP models on the data generated using digital microstructure generators and physics-based permeability simulations. It will be shown that the structure-property linkages are able to make high fidelity predictions and assessment of uncertainties for new porous membrane structures at minimal computational cost.