# Computational Acceleration of Topology Optimization Using Deep Learning
## 1 Introduction
### Related Works in ML  
These days, ML methods are being used in various ways to accelerate the running time of TO methods, and here we will review the latest works in this area. The reader should note that the works discussed below are the ones published within the last two years. The reader should refer to our work [4], Section 4.3, to obtain a summarized knowledge of ML-accelerated TO, which are earlier in time than the following works. [PERSON] et al. [8] used ML algorithms on so-called moving morphable component (MMC)-based topology optimization. In an MMC-based approach, TO relies on parameter tuning of topological description function (TDF), where the turning is usually carried out manually. To address the latter, an ML-based parameter tuning strategy was proposed, which considers an extra-trees (ET)-based image classifier and particle swarm optimization algorithm. The approach was tested on a cantilever and L-shaped beams and the results are satisfactory. [PERSON] et al. [9] developed a deep learning (DL) algorithm for the computational acceleration of TO using a convolutional neural network (CNN) with U-net architecture and recurrent neural network (RNN) with long-short term memory (LSTM) architecture. The trained algorithm was tested for the lightweighting of 2D and 3D cantilever-beam structures. The generated designs showed high accuracy based on a comparative analysis with FEM-based methods. [PERSON] et al. [10] introduced the following two frameworks for TO: density sequence (DS) prediction and coupled density and compliance sequence (CDCS) prediction. The first approach considers a sequential prediction model that allows the transformation of material densities without compliance. In the second method, the authors included intermediate compliance results with the results of improving the efficiency of the compliance predicting surrogate model. Both methods were compared with the baseline approach, so-called direct optimal density (DOD). In case of DS, there are two convolutional neural networks (CNN) are included in it to obtain the final prediction. On the other CDCS is based on three CNNs that iterate while predicting the final optimal topology. The authors demonstrated the better performance of their method by testing it on 2D and 3D structures and comparing the results with a direct density-based approach and SIMP methods. [PERSON] et al. [11] proposed a new method to predict the results of TO using initial stress learning and DL techniques. A stress matrix was used instead of load cases and boundary conditions. Moreover, the given method doesn't require repeated iteration and produces real-time results. The algorithm consists of three steps, the first step is the generation of data on the boundary conditions using SIMP (in particular, the main stress matrix at the first iteration, and the result of TO to use as a label); the second step is training the CNN model with the data obtained in step 1; the third step is to test the proposed method for different loading cases. The authors tested the proposed prediction method with the traditional TO method for several examples with a single load. It was observed that the two results are highly approximate. Another interesting approach of using ML was done by [PERSON] et al. [12] They investigated using reinforcement learning (RL) to automate the designing of 2D topologies. RL is a subset of ML that uses past experience to design an object by removing elements to satisfy compliance minimization objectives. The main advantage of using the RL method is that it does not rely on the pre-creation of the training dataset, to avoid such a time-consuming process. In this method, the algorithm is trained to solve the optimal control problem for the task by receiving feedback or rewards for its work. The algorithm was tested for different load cases, and results showed that it is well adapted to solve the TO problem. The authors showed that the proposed method can optimize 2D objects just as with traditional gradient-based TO methods.