Being able to design, e.g., the microstructure of a material to achieve a desired behavior is a key enabler for innovation. To achieve this goal, knowledge about the influence of the local material structure on the mechanical properties of the material, e.g. measured in terms of stiffness, strength or ductility, must be acquired. Ideally, experiments and simulation results are combined to build structure-property linkages. The key challenge is then to invert this knowledge to find a material structure for a desired set of material properties. This process is known as inverse design.

While surely inverse design is challenging, even the forward prediction of SP linkages using multiscale simulations of complex microstructures is still a demanding task. The difficulties lie in (i) describing the features of the local material structure, (ii) reconstructing plausible 3D statistically representative volume elements (SVEs), e. g., from 2D slices like microscopy images, (iii) modeling the complex and non-linear effective constitutive response and (iv) using it in an efficient multiscale scheme.

In this contribution, we present recently developed methods that aim at addressing these issues and it is shown how to integrate them in an efficient workflow. Descriptors are employed to characterize complex microstructures. Examples of such descriptors are volume fraction, generalized spatial n-point correlations or Gram matrices of pre-trained convolutional neural networks. Corresponding SVEs are generated using differentiable microstructure characterization and reconstruction (DMCR). An advantage of DMCR over similarly efficient reconstruction algorithms is that it allows to prescribe generic high-dimensional microstructure descriptors as long as they are differentiable. The reconstructed structures are then used for numerical simulation and effective properties are obtained from homogenization techniques. Together with the descriptors of the local material structure, SP linkages are set up.

As engineering data, including the SP linkages, are generally costly to generate, inverse design has to cope with scarce data. We therefore employ a Bayesian optimization approach and it is shown that significantly less data are needed in comparison to classical sampling procedures and alternative inverse design methods which is due to the iterative data augmentation. The approach is demonstrated for spinodoid metamaterials. In future work, the active learning augmentation loop could be applied to a broader range of materials.