The engineering design process often entails optimizing the underlying geometry while simultaneously selecting a suitable material. For a certain class of simple problems, the two are separable where, for example, one can first select an optimal material, and then optimize the geometry. However, in general, the two are not separable. Furthermore, the discrete nature of material selection is not compatible with gradient-based geometry optimization, making simultaneous optimization challenging. In this paper, we propose the use of variational autoencoders (VAE) for simultaneous optimization. First, a data-driven VAE is used to project the discrete material database onto a continuous and differentiable latent space. This is then coupled with a fully-connected neural network, embedded with a finite-element solver, to simultaneously optimize the material and geometry. The neural-network's built-in gradient optimizer and back-propagation are exploited during optimization. The proposed framework is demonstrated using trusses, where an optimal material needs to be chosen from a database, while simultaneously optimizing the cross-sectional areas of the truss members. Several numerical examples illustrate the efficacy of the proposed framework. The Python code used in these experiments is available at github.com/UW-ERSL/MaTruss

翻译：工程设计过程往往需要优化基础几何,同时选择合适的材料。 对于某类简单的问题, 两者是可分离的, 例如, 前者可以先选择最佳材料, 然后再优化几何。 然而, 一般而言, 两者是不可分离的。 此外, 材料选择的离散性质与基于梯度的几何优化不兼容, 使得同步优化具有挑战性。 在本文中, 我们提议使用可变自动读数器( VAE) 来同时优化同步优化。 首先, 数据驱动VAE 用来将离散材料数据库投射到连续和可差异的潜在空间。 然后, 与一个完全连接的神经网络相配合, 并嵌入一个固定元素求解解的网络, 以同时优化材料和几何测量。 在优化过程中, 神经网络的内建梯度优化器和反向调节器是不相匹配的。 在数据库中选择最佳材料, 同时优化三角体成员的交叉区域。 几个数字示例说明了所使用的框架的磁体/ 。