# Novel Artificial Neural Network Aided Structural Topology Optimization
## 1 Introduction
The deep learning field, located at the center of the flourishing development of Artificial Intelligence (AI), was based on artificial neural networks. AI performance was shown to be superior to human beings in many fields such as image recognition [27; 28]. Thus, how to use the diverse deep neural network techniques to improve structural topology optimization has been one of the most important issues in the scientific field. The application of machine-learning-based techniques into structural topology optimization mainly focused on reducing the computational costs of finite element analyses. One of the most well-known methods was used to train artificial neural networks to predict the final structural shape. The computational costs of topology optimization iterations were considerably decreased. Several neural networks, such as convolutional neural networks (CNNs), generative adversarial networks (GANs), and moving morphable component-based (MMC) frameworks, have been well developed [29; 30]. In addition, neural networks have been extensively used in metaheuristics, which should be appreciated [31; 32; 33; 34]. Multi-objective optimization has also been extensively studied [35; 36; 37]. To increase the efficiency of the machine learning models, it is necessary to limit the size of the training dataset and number of elements. Many researchers avoided the full connection layer with a fixed number of input parameters. For example, [PERSON] et al. [38] designed a large grid domain to ensure the flexibility of input data. The size of data input into a surrogate-based model could range from 4000 to 26,000 [39]. The other issue with the surrogate-based approach regards how to prevent disconnection in the optimized structure. [PERSON] et al. [40] generated volume fractions between 0.2 and 0.8 for two-dimensional structures with specific boundary conditions under randomly distributed loading. [PERSON] and [PERSON] [41] increased the number of training data while disconnection still existed. [PERSON] et al. [21] found that discontinuity in the structure might result from a high mean average error (MAE) in the training model. Mechanical response information has been added to the loss function to prevent disconnection [42; 43]. In the solid mechanics area, physics-informed neural networks (PINNs) [44] and deep operator networks (DeepONets) [45] are two well-developed techniques that have impressed many researchers in recent years. PINN added physical information constraints of partial differential equations to the loss function of the network training process. DeepONet, on the other hand, used neural networks for nonlinear mapping in different vector spaces. To reduce the computational cost of finite element analyses, researchers [46; 47; 48; 49; 50] have been enlightened by some conventional topology optimization acceleration methods, such as Deep Belief Network (DBN) [51; 52]. For instance, [PERSON] et al. [53; 54] used Deep Belief Network (DBN) to predict the unit density change throughout the entire iteration process. However, in most studies, using deep neural networks was not sufficiently accurate for topology optimization, mainly because it was required to perform finite element analyses of the full-scale structure at each iteration. Thus, it is necessary to improve the efficiency of finite element computation as well as the convergence of iterations during optimization. This study developed a novel partitioned deep learning algorithm to enhance structural topology optimization. The method decomposed a full-scale structure into several partitions at a coarse scale. The partition-based architecture was adopted to train the neural networks at both coarse and fine scales to reduce the computational costs of finite element analyses during topology optimization. Novel neural networks were used to optimize various types of structures of different meshes, partition numbers, and parameters. In addition, patterns of sensitivity maps were analyzed with various visualization tools to assess structural performance with high accuracy.