# Computational Acceleration of Topology Optimization Using Deep Learning
## 1 Introduction
### Related Works in ML
Another interesting approach of using ML was carried out by [PERSON] et al. [12]. They applied deep reinforcement learning to train an agent to design 2D topologies. Compared to other AI and ML methods, reinforcement learning does not need any training data, but relies on the agent that learns to complete a given task or set of tasks within the scope ofthe interactive environment by providing feedback to the performance of the agent. The reward function is multi-objective and it was built to mimic the multi-objective feature of the compliance minimization in TO. The progressive refinement, from 6 \(\times\) 6 up to 24 \(\times\) 24, was conducted using randomly selected loads and bounded elements to train the agent. Once trained, it was tested on other load cases, and compared with gradient-based TO optimizers. The results showed that there is a generalized performance capacity of such approach, therefore, it is promising for complex tasks of TO. [PERSON] et al. [13] also proposed a gradient-free method DNN-MFSE, which is a combination of deep neural networks (DNN), and a topology representation model-material-field series expansion (MFSE). The authors concluded that this method indicated better performance compared to other gradient-free methods. Another advantage of the proposed method is the ease of parallel computational implementation since it is a surrogate-based approach. Furthermore, the authors added that this method can be extended to multiphysics problems opening up great opportunities for future studies. Conditional generative adversarial networks (GANs) are also used to accelerate TO problems [14]. OptiGAN method was proposed by authors for TO of structures. It is a non-iterative method using conditional generative adversarial networks with high accuracy. The proposed method was tested with different datasets, and the average pixel-wise accuracy of the method was estimated to be 83.15%. The authors mentioned that it is a rudimentary phase, and more training needs to be conducted to diversify the spectrum. [PERSON] et al. [15] proposed ML-driven framework to accelerate TO. Running time here was reduced by using ML for the sensitivity estimation, thus eliminating FEA to do this procedure. The authors used two-resolution TO: coarse-resolution (for physical information) and fine-resolution (for geometric/topological information) meshes. The information for those two meshes was used as an input for the ML model that predicts the sensitivity, which was then used for a design variables update on the fine-resolution mesh. CNN was used in the ML. Different examples were used to test the proposed method to show its robustness once trained. Moreover, authors mentioned its potential for large-scale problems. [PERSON] et al. [16] developed surrogate models based on artificial neural networks (ANN) with the purpose of reducing the training time. Particularly, a portion of the training data for full-scale calculations was obtained from coarse-mesh based simulation results. In other words, the proposed ANN-based model, property network, maps the coarse field to corresponding fine field, thus reducing the training time for full-scale TO calculations. Cantilever and L-shaped beams were considered as the test problems. The authors showed comparative analysis for three cases in terms of training cost (i.e., time) with fixed 60 iterations of TO: (i) FEA-based TO, (ii) surrogate model-based TO with fine data and (iii) surrogate model-based TO with hybrid data (coarse and fine mesh based data). Thus, the results showed that the computational time of the latter case (iii) is nearly similar to the case of (i), indicating that the training time of the surrogate model-based TO with hybrid data is compatible with FEA-based TO, while its accuracy is close to the surrogate model-based TO with fine data. Furthermore, the authors further used the trained property network to complete 10 TOs, and the results showed that it is much faster than the conventional FEA-based TO.