This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a one-scale design on a fine mesh, we avoid solving the least square problems associated with traditional de-homogenization approaches and save time correspondingly. To train the neural network, a two-step custom loss function has been developed which ensures a periodic output field that follows the local lamination orientations. A key feature of the proposed method is that the training is carried out without any use of or reference to the underlying structural optimization problem, which renders the proposed method robust and insensitive wrt domain size, boundary conditions, and loading. A post-processing procedure utilizing a distance transform on the output field skeleton is used to project the desired lamination widths onto the output field while ensuring a predefined minimum length-scale and volume fraction. To demonstrate that the deep learning approach has excellent generalization properties, numerical examples are shown for several different load and boundary conditions. For an appropriate choice of parameters, the de-homogenized designs perform within 7–25% of the homogenization-based solution at a fraction of the computational cost. With several options for further improvements, the scheme may provide the basis for future interactive high-resolution topology optimization.

本文提出了一种基于深度学习的去均质化方法，用于结构顺应性最小化。通过使用卷积神经网络对从粗网格上的一组层压参数到细网格上的单尺度设计的映射进行参数化，我们避免了解决与传统去均匀化方法相关的最小二乘问题并相应地节省时间。为了训练神经网络，开发了一个两步自定义损失函数，以确保遵循局部层压方向的周期性输出场。所提出方法的一个关键特征是在不使用或参考潜在结构优化问题的情况下进行训练，这使得所提出的方法鲁棒且不敏感，并且对域大小、边界条件和载荷不敏感。在输出场骨架上利用距离变换的后处理程序用于将所需的层压宽度投影到输出场，同时确保预定义的最小长度尺度和体积分数。为了证明深度学习方法具有出色的泛化特性，给出了几种不同负载和边界条件的数值示例。对于适当的参数选择，脱均匀化设计以计算成本的一小部分在基于均质的基于均化的解决方案的7-25％内执行。通过进一步改进的几个选项，该方案可能为未来交互式高分辨率拓扑优化提供基础。