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Effective properties of functional materials crucially depend on their 3D microstructure. In this paper, we investigate quantitative relationships between descriptors of two-phase microstructures, consisting of solid and pores and their mass transport properties. To that end, we generate a vast database comprising 90,000 microstructures drawn from nine different stochastic models, and compute their effective diffusivity and permeability as well as various microstructural descriptors. To the best of our knowledge, this is the largest and most diverse dataset created for studying the influence of 3D microstructure on mass transport. In particular, we establish microstructure-property relationships using analytical prediction formulas, artificial (fully-connected) neural networks, and convolutional neural networks. Again, to the best of our knowledge, this is the first time that these three statistical learning approaches are quantitatively compared on the same dataset. The diversity of the dataset increases the generality of the determined relationships, and its size is vital for robust training of convolutional neural networks. We make the 3D microstructures, their structural descriptors and effective properties, as well as the code used to study the relationships between them available open access.

Large-Scale Statistical Learning for Mass Transport Prediction in Porous Materials Using 90,000 Artificially Generated Microstructures