# Computational Acceleration of Topology Optimization Using Deep Learning
## 7 Conclusions  
In the paper, we investigated the possibility of acceleration of standard SIMP approaches using deep learning methods. For this purpose, we tested and comparatively analysed three neural network models on the three different structured datasets introduced by [17, 18, 19]. The first experiment had a goal to examine the efficiency of boosting SIMP approach by applying Res-U-Net and using different data distributions and different depths of the model. According to the experiment results (Table 1), Res-U-Net gives better results than U-Net for higher iteration, which is considered as a benchmark for Dataset #1 [22]. Additionally, it is defined that increasing the depth of the model by more than three did not play a significant role in the obtained results of the correlation between accuracy and iteration. Moreover, the training model using uniform distribution also has not played a significant role in the accuracy of the resulting model. The target of the second experiment was to study a deep learning model that can be used as an alternative method to the existing technologies. Initially, there were six different physical parameters that are used for training purposes. In each experiment, some of them were eliminated for understanding their importance and effect on the final result. Von Mises stress, strain energy density, and volume fraction were selected as an initial dataset. Adding boundary conditions as an additional field increased the accuracy of the model. However, the usage of loads for the model slightly decreased the accuracy score. In the second experiment, we modified the input tensors of the dataset by separating boundary conditions (BC) into two feature matrixes in Dataset #2 and applied U-Net and Res-U-Net directly to the modified input data. According to the experiment, MAE = 0.0312 and MSE = 0.0215 are obtained for U-Net, MAE = 0.037 and MSE = 0.48 for Res-U-Net, which are higher than TopologyGAN accuracy presented in the work [24]. Furthermore, TopologyGAN is computationally heavier model than U-Net. According to experiments with Dataset #1, the proposed Res-U-Net model shows better results in terms of accuracy. But according to the studies with Dataset #2, our U-Net and Res-U-Net models are more effective in terms of timing since they take less than 1 min to train 1 epoch compared to the original TopologyGAN [18] model that takes approximately 15 min to train the 1 epoch. Accuracy results are almost the same in both models. In the third experiment, we applied CNN to the same Dataset#3 with modified input such as inputs of 2D objects of 6 elements {VF, U1:U5}, inputs of 3D objects consisting of 19 elements {VF, U1:18} and achieved 96.67% accuracy for 2D and 93.22% for 3D objects (Table 4). In Dataset #3 we used a CNN model, which is comparatively less complex than SILONET [19] in the original paper in terms of depth and model parameters. SILONET consists of two networks that use over 700 million parameters; however, our suggested model uses less than 800 thousand parameters in the training process. The relationship between the accuracy of the models and number of parameters are given in the Tables 5 and 6. Due to the shape of the images (40 \(\times\) 40) in Dataset #1, maximum depth size can be taken as four and it slightly affects the accuracy of the model. On the other hand, images from the Dataset #2 have a bigger shape (64 \(\times\) 128) which gives us possibilities to increase the depth of the model twice. Such an increase leads to a significant change in accuracy (83.6 vs. 90.07 and 84.32 vs. 89.61). Overall, we defined that Res-U-Net and U-Net are the more reliable and effective methods among deep learning approaches for the computational acceleration of topology optimization problems. Depending on the boundary condition, the number of elements, volume fraction, minimum radius, penalization, and filter number of iterations required to generate the optimized topology sample varies from tens to thousands of iterations by using SIMP model.