Multiscale simulations are demanding in terms of computational resources. In the context of continuum micromechanics, the multiscale problem arises from the need of inferring macroscopic material parameters from the microscale. If the underlying microstructure is explicitly given by means of $\mu$CT-scans, convolutional neural networks can be used to learn the microstructure–property mapping, which is usually obtained from computational homogenization. The CNN approach provides a significant speedup, especially in the context of heterogeneous or functionally graded materials. Another application is uncertainty quantification, where many expansive evaluations are required. However, one bottleneck of this approach is the large number of training microstructures needed.

This work closes this gap by proposing a generative adversarial network tailored towards three-dimensional microstructure generation. The lightweight algorithm is able to learn the underlying properties of the material from a single $\mu$CT-scan without the need of explicit descriptors. During prediction time, the network can produce unique three-dimensional microstructures with the same properties of the original data in a fraction of seconds and at consistently high quality.

多尺度模拟对计算资源的要求很高。在连续微观力学的背景下，多尺度问题源于从微观尺度推断宏观材料参数的需要。如果通过以下方式明确给出底层微观结构$\mu$CT扫描、卷积神经网络可用于学习微结构-特性映射，这通常是通过计算均质化获得的。CNN 方法提供了显着的加速，特别是在异质或功能分级材料的情况下。另一个应用是不确定性量化，其中需要许多广泛的评估。然而，这种方法的一个瓶颈是需要大量的训练微结构。

这项工作通过提出针对 3D 微结构生成量身定制的生成对抗网络来弥补这一差距。轻量级算法能够从单个$\mu$无需显式描述符的 CT 扫描。在预测时间内，该网络可以在几秒钟内以始终如一的高质量生成具有与原始数据相同属性的独特 3D 微结构。