A vital necessity when employing state-of-the-art deep neural networks (DNNs) for topology optimization is to predict near-optimal structures while satisfying pre-defined optimization constraints and objective function. Existing studies, on the other hand, suffer from the structural disconnections which result in unexpected errors in the objective and constraints. In this study, a two-stage network model is proposed using convolutional encoder-decoder networks that incorporate a new way of loss functions to reduce the number of structural disconnection cases as well as to reduce pixel-wise error to enhance the predictive performance of DNNs for topology optimization without any iteration. In the first stage, a single DNN model architecture is proposed and used in two parallel networks using two different loss functions for each called the mean square error (MSE) and mean absolute error (MAE). Once the priori information is generated from the first stage, it is instantly fed into the second stage, which acts as a rectifier network over the priori predictions. Finally, the second stage is trained using the binary cross-entropy (BCE) loss to provide the final predictions. The proposed two-stage network with the proposed loss functions is implemented for both two-dimensional (2D) and three-dimensional (3D) topology optimization datasets to observe its generalization ability. The validation results showed that the proposed two-stage framework could improve network prediction ability compared to a single network while significantly reducing compliance and volume fraction errors.

在采用最新的深度神经网络（DNN）进行拓扑优化时，至关重要的是要在满足预定义的优化约束和目标函数的同时预测接近最佳的结构。另一方面，现有研究存在结构上的脱节，从而导致目标和约束方面出现意想不到的错误。在这项研究中，提出了一种使用卷积编码器-解码器网络的两阶段网络模型，该模型结合了一种新的损失函数方式，以减少结构断开情况的数量以及减少像素误差，从而增强DNN的预测性能无需任何迭代即可进行拓扑优化。在第一阶段 提出了一个单一的DNN模型架构，并在两个并行网络中使用，两个并行网络使用两个不同的损耗函数，分别称为均方误差（MSE）和均值绝对误差（MAE）。从第一阶段生成先验信息后，立即将其馈入第二阶段，该阶段将充当先验预测上的整流器网络。最后，使用二进制交叉熵（BCE）损失训练第二阶段，以提供最终的预测。针对二维（2D）和三维（3D）拓扑优化数据集都实施了带有损失函数的提议两阶段网络，以观察其泛化能力。