The convolutional neural network-based deep generative model (DGM) is a powerful tool for handling image datasets that opens up strategies for fast synthesis of optimum designs at unseen boundary conditions. Existing DGMs for design synthesis are typically based on O (10000) training data, which limits the engineering applications. This paper explores the feasibility of improving DGM data efficiency with O (100) training data through prior constraints. A two-stage data-efficient deep generative model (DE-DGM) is proposed which leverages the first-stage design synthesis from probabilistic proper orthogonal decomposition and the second-stage enhancement from encoder-decoder convolutional neural network. Four topology optimization cases have been adopted, including compliance minimization, heat conduction, airplane bearing bracket design, and three-dimensional machine tool column structure design. The proposed DE-DGMs could be trained with 100–200 data and synthesize the main features of the design at unseen boundary conditions. The overall computation cost of warm-start topology optimization leveraging DE-DGM predictions reduces to 36 %–58 % of the standard cases.

基于卷积神经网络的深度生成模型 (DGM) 是处理图像数据集的强大工具，它开辟了在看不见的边界条件下快速合成最佳设计的策略。现有的设计综合DGM通常基于O(10000)训练数据，这限制了工程应用。本文探讨了通过先验约束，用O(100)训练数据提高DGM数据效率的可行性。提出了一种两阶段数据高效深度生成模型（DE-DGM），该模型利用概率正确正交分解的第一阶段设计综合和编码器-解码器卷积神经网络的第二阶段增强。采用了四种拓扑优化案例，包括柔度最小化、热传导、飞机轴承支架设计、三维机床立柱结构设计。所提出的 DE-DGM 可以使用 100-200 个数据进行训练，并在未见过的边界条件下综合设计的主要特征。利用 DE-DGM 预测的热启动拓扑优化的总体计算成本降低至标准情况的 36%–58%。