While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials’ community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources and their quantification and integration in the inversion process are essential in meeting the materials design objectives. The first contribution of this paper is a flexible, fully probabilistic formulation of materials’ optimization problems that accounts for the uncertainty in the process-structure and structure-property linkages and enables the identification of optimal, high-dimensional, process parameters. We employ a probabilistic, data-driven surrogate for the structure-property link which expedites computations and enables handling of non-differential objectives. We couple this with a problem-tailored active learning strategy, i.e., a self-supervised selection of training data, which significantly improves accuracy while reducing the number of expensive model simulations. We demonstrate its efficacy in optimizing the mechanical and thermal properties of two-phase, random media but envision that its applicability encompasses a wide variety of microstructure-sensitive design problems.
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