Gradient-free optimizers allow for tackling problems regardless of the smoothness or differentiability of their objective function, but they require many more iterations to converge when compared to gradient-based algorithms. This has made them unviable for topology optimization due to the high computational cost per iteration and high dimensionality of these problems. We propose a pre-trained neural reparameterization strategy that leads to at least one order of magnitude decrease in iteration count when optimizing the designs in latent space, as opposed to the conventional approach without latent reparameterization. We demonstrate this via extensive computational experiments in- and out-of-distribution with the training data. Although gradient-based topology optimization is still more efficient for differentiable problems, such as compliance optimization of structures, we believe this work will open up a new path for problems where gradient information is not readily available (e.g. fracture).

翻译：无梯度优化器能够处理目标函数非光滑或不可微的问题，但与基于梯度的算法相比，其收敛所需的迭代次数要多得多。由于拓扑优化问题每次迭代的计算成本高且维度高，这一特性使得无梯度优化器在该领域难以应用。我们提出了一种预训练神经重参数化策略，与传统的无潜变量重参数化方法相比，在潜空间中优化设计时，迭代次数至少降低一个数量级。我们通过大量计算实验（包括与训练数据分布内和分布外的场景）证明了这一效果。尽管对于可微问题（如结构柔度优化），基于梯度的拓扑优化仍然更为高效，但我们相信，这项工作将为梯度信息不易获取的问题（如断裂问题）开辟新路径。