  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
such 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 novel active learning strategy, i.e. a self-supervised
collection of data, which significantly improves accuracy while requiring small
amounts of training data. We demonstrate its efficacy in optimizing the
mechanical and thermal properties of two-phase, random media but envision its
applicability encompasses a wide variety of microstructure-sensitive design
problems.
