Work considers the usage of StyleGAN architecture for the task of microstructure synthesis. The task is the following: given number of samples of structure we try to generate similar samples at the same time preserving its properties. Since the considered architecture is not able to produce samples of sizes larger than the training images, we propose to use image quilting to merge fixedsized samples. One of the key features of the considered architecture is that it uses multiple image resolutions. We also investigate the necessity of such an approach. arXiv:1909.07042v1 [eess.IV]

In this paper, we study an instance of the G-closure problem for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two isotropic materials. We focus on the case when one material is has zero stiffness i.e., single-material structures with voids. This problem is important, in particular, in the context of designing small-scale structures for metamaterials that can be manufactured using additive fabrication. A range of effective metamaterial properties can be obtained this way using a single base material.We demonstrate that two closely related simple parametric families based on the structure proposed by O. Sigmund in [26] attain good coverage of the space of isotropic properties satisfying Hashin-Shtrikman bounds. In particular, for positive Poisson's ratio, we demonstrate that Hashin-Shtrikman bound can be approximated arbitrarily well, within limits imposed by numerical approximation: a strong evidence that these bounds are achievable in this case. For negative Poisson's ratios, we numerically obtain a bound which we hypothesize to be close to optimal, at least for metamaterials with rotational symmetries of a regular triangle tiling.

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