Inverse design of anisotropic spinodoid materials with prescribed diffusivity

The three-dimensional microstructure of functional materials determines its effective properties, like the mass transport properties of a porous material. Hence, it is desirable to be able to tune the properties by tuning the microstructure accordingly. In this work, we study a class of spinodoid i.e. spinodal decomposition-like structures with tunable anisotropy, based on Gaussian random fields. These are realistic yet computationally efficient models for bicontinuous porous materials. We use a convolutional neural network for predicting effective diffusivity in all three directions. We demonstrate that by incorporating the predictions of the neural network in an approximate Bayesian computation framework for inverse problems, we can in a computationally efficient manner design microstructures with prescribed diffusivity in all three directions.