In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering contexts. This work proposes a multi-stage machine learning strategy that aims to predict an optimal topology and the related stress fields of interest, either in 2D or 3D, without resorting to any iterative analysis and design process. The overall topology optimization is treated as regression task in a low-dimensional latent space, that encodes the variability of the target designs. First, a fully-connected model is employed to surrogate the functional link between the parametric input space characterizing the design problem and the latent space representation of the corresponding optimal topology. The decoder branch of an autoencoder is then exploited to reconstruct the desired optimal topology from its latent representation. The deep learning models are trained on a dataset generated through a standard method of topology optimization implementing the solid isotropic material with penalization, for varying boundary and loading conditions. The underlying hypothesis behind the proposed strategy is that optimal topologies share enough common patterns to be compressed into small latent space representations without significant information loss. Results relevant to a 2D Messerschmitt-B\"olkow-Blohm beam and a 3D bridge case demonstrate the capabilities of the proposed framework to provide accurate optimal topology predictions in a fraction of a second.

翻译：传统拓扑优化中，迭代更新设计域内材料分布所需的计算时间严重依赖于问题的复杂度或规模，这限制了其在真实工程场景中的应用。本文提出一种多阶段机器学习策略，旨在无需任何迭代分析与设计流程即可预测二维或三维问题中的最优拓扑结构及相关应力场。整体拓扑优化被处理为低维潜在空间中的回归任务，该空间编码了目标设计变量的变异性。首先，采用全连接模型拟合表征设计问题的参数化输入空间与对应最优拓扑潜在空间表示之间的函数映射关系。随后，利用自编码器的解码分支从潜在表示中重建期望的最优拓扑。深度学习模型通过标准拓扑优化方法（采用固体各向同性材料惩罚法）生成的数据集进行训练，该数据集包含不同边界条件与载荷工况。该策略的核心假设在于：最优拓扑共享足够的共同模式，可被压缩为小规模潜在空间表示且无明显信息损失。二维梅塞施密特-伯尔科-布洛姆梁与三维桥梁案例的结果表明，所提框架能在亚秒级时间内提供精确的最优拓扑预测。