Length scale control is imposed in topology optimization (TO) to make designs amenable to manufacturing and other functional requirements. Broadly, there are two types of length-scale control in TO: \emph {exact} and \emph {approximate}. While the former is desirable, its implementation can be difficult, and is computationally expensive. Approximate length scale control is therefore preferred, and is often sufficient for early stages of design. In this paper we propose an approximate length scale control strategy for TO, by extending a recently proposed density-based TO formulation using neural networks (TOuNN). Specifically, we enhance TOuNN with a Fourier space projection, to control the minimum and/or maximum length scales. The proposed method does not involve additional constraints, and the sensitivity computations are automated by expressing the computations in an end-end differentiable fashion using the neural net's library. The proposed method is illustrated through several numerical experiments for single and multi-material designs.

中文翻译：

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使用傅立叶增强神经网络的拓扑优化中的长度尺度控制

拓扑优化 (TO) 中施加了长度比例控制，以使设计符合制造和其他功能要求。从广义上讲，TO 中有两种类型的长度尺度控制：\emph {exact} 和 \emph {approximate}。虽然前者是可取的，但它的实现可能很困难，并且计算成本很高。因此，近似长度比例控制是首选，并且通常对于设计的早期阶段就足够了。在本文中，我们通过使用神经网络 (TOuNN) 扩展最近提出的基于密度的 TO 公式，为 TO 提出了一种近似长度尺度控制策略。具体来说，我们使用傅立叶空间投影增强 TOuNN，以控制最小和/或最大长度尺度。所提出的方法不涉及额外的约束，并且通过使用神经网络的库以端到端可微分的方式表达计算，灵敏度计算是自动化的。通过针对单一和多材料设计的几个数值实验来说明所提出的方法。