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In this contribution, we propose a general framework to inversely designing mesostructures using structure-property linkages. Typically, large datasets are necessary. Experiments alone are prohibitively expensive. Therefore, computational
augmentation is employed to allow for data-driven approaches even in this data scarce regime. In an iterative procedure (1) mesostructures are characterized by descriptors, (2) effective properties are derived from numerical simulations, (3) structureproperty linkages are set up using a Gaussian process, (4) descriptors of new candidate mesostructures are proposed by Bayesian optimization and (5) mesostructures are reconstructed. Steps 2 through 5 are repeated until a desired convergence criterion is reached, e.g., the uncertainty of the structure-property linkage is decreased or a mesostructured with preferable properties is found. This framework is applied and presented at the example of spinodoid structures. Augmenting a small initial data set by in silico reconstructed spinodoid structures and their simulated effective properties allows for deriving improved structure-property linkages and, thus, finding potentially optimal structures or predicting properties.