A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology optimization using neural networks. Our approach focuses on inverse homogenization that seamlessly maintains compatibility across neighboring microstructure cells. Our approach consists of a topology neural network that optimizes the microstructure shape and distribution across the design domain as a continuous field. Each microstructure cell is optimized based on a specified elasticity tensor that also accommodates in-plane rotations. The neural network takes as input the local coordinates within a cell to represent the density distribution within a cell, as well as the global coordinates of each cell to design spatially varying microstructure cells. As such, our approach models an n-dimensional multi-scale optimization problem as a 2n-dimensional inverse homogenization problem using neural networks. During the inverse homogenization of each unit cell, we extend the boundary of each cell by scaling the input coordinates such that the boundaries of neighboring cells are combined. Inverse homogenization on the combined cell improves connectivity. We demonstrate our method through the design and optimization of graded multi-scale structures.

中文翻译：

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使用神经网络的多尺度拓扑优化

一个长期存在的挑战是设计细胞之间具有良好连接性的多尺度结构，同时优化每个细胞以达到接近理论性能极限。我们提出了一种使用神经网络进行直接多尺度拓扑优化的新方法。我们的方法侧重于逆均质化，无缝地保持相邻微结构单元之间的兼容性。我们的方法由拓扑神经网络组成，该网络可将整个设计域中的微观结构形状和分布优化为连续场。每个微结构单元都根据指定的弹性张量进行优化，该弹性张量也适应面内旋转。神经网络将单元内的局部坐标作为输入来表示单元内的密度分布，并以每个单元的全局坐标作为输入来设计空间变化的微结构单元。因此，我们的方法使用神经网络将 n 维多尺度优化问题建模为 2n 维逆均质化问题。在每个晶胞的逆均质化过程中，我们通过缩放输入坐标来扩展每个晶胞的边界，从而组合相邻晶胞的边界。组合电池上的反向均质化改善了连接性。我们通过分级多尺度结构的设计和优化来展示我们的方法。