Topology optimization (TO) is a common technique used in free-form designs. However, conventional TO-based design approaches suffer from high computational cost due to the need for repetitive forward calculations and/or sensitivity analysis, which are typically done using high-dimensional simulations such as finite element analysis (FEA). In this work, artificial neural networks are used as efficient surrogate models for forward and sensitivity calculations in order to greatly accelerate the design process of topology optimization. To improve the accuracy of sensitivity analyses, dual-model artificial neural networks that are trained with both forward and sensitivity data are constructed and are integrated into the Solid Isotropic Material with Penalization (SIMP) method to replace the FEA. The performance of the accelerated SIMP method is demonstrated on two benchmark design problems namely minimum compliance design and metamaterial design. The efficiency gained in the problem with size of 64 × 64 is 137 times in forward calculation and 74 times in sensitivity analysis. In addition, effective data generation methods suitable for TO designs are investigated and developed, which lead to a great saving in training time. In both benchmark design problems, a design accuracy of 95% can be achieved with only around 2000 training data.

拓扑优化（TO）是自由格式设计中常用的技术。然而，由于需要重复的前向计算和/或灵敏度分析，传统的基于TO的设计方法遭受了高计算成本，这通常使用诸如有限元分析（FEA）的高维仿真来完成。在这项工作中，人工神经网络被用作前向和敏感性计算的有效替代模型，以极大地加快拓扑优化的设计过程。为了提高灵敏度分析的准确性，构建了使用前向和灵敏度数据训练的双模型人工神经网络，并将其集成到带有罚分法的固体各向同性材料（SIMP）中，以代替FEA。SIMP加速方法的性能在两个基准设计问题上得到了证明，即最小顺应性设计和超材料设计。在尺寸为64×64的问题中获得的效率在正向计算中为137倍，在灵敏度分析中为74倍。此外，研究和开发了适用于TO设计的有效数据生成方法，从而大大节省了培训时间。在这两个基准设计问题中，仅约2000个训练数据就可以达到95％的设计精度。研究并开发了适用于TO设计的有效数据生成方法，从而大大节省了培训时间。在这两个基准设计问题中，仅约2000个训练数据就可以达到95％的设计精度。研究并开发了适用于TO设计的有效数据生成方法，从而大大节省了培训时间。在这两个基准设计问题中，仅约2000个训练数据就可以达到95％的设计精度。