# Novel Artificial Neural Network Aided Structural Topology Optimization
## 1 Introduction  
The importance of topology optimization includes improving network performance, cost reduction, and improving efficiency and performance. In network topology optimization, optimizing the physical connections of network nodes can reduce latency, improve bandwidth utilization, and enhance network reliability and fault tolerance. For example, using the minimum spanning tree method can reduce network latency and congestion, and improve the network's fault resilience. In 3D printing, topology optimization can reduce the amount of material used, thereby lowering production costs. In game modeling, a reasonable topology structure can make the model more natural and smoother in animation and deformation, reduce the number of faces in the model, and improve the running efficiency of the game. For example, by keeping quadrilaterals as the main feature, planning edge flow, and reducing unnecessary faces, the animation effect and rendering efficiency of the model can be improved. Topology optimization uses mathematical methods to find the optimal structural design that meets mechanical requirements while reducing material usage, achieving the goal of reducing the weight. For example, in 3D printing, topology optimization can reduce material usage, lower costs, and improve product performance. In network topology optimization, reasonable node deployment and link allocation can enhance the performance and reliability of the network. For example, using greedy algorithms and genetic algorithms can optimize the location selection of network nodes and link bandwidth allocation, improving network performance and efficiency. Topology optimization can adapt to constantly changing network environments and requirements. For example, innetwork topology optimization, genetic algorithms can cope with complex environmental changes by simulating mechanisms such as natural selection, crossover, and mutation. [PERSON] et al. presented an efficient method for optimizing damping system parameters using design sensitivity analysis to relate design changes to available variables [1]. Topics of topology optimization have received increasing attention from researchers lately. For example, [PERSON] et al. [1; 2; 3; 4] used structural topology optimization to design a post-tensioned prestressed concrete pedestrian bridge. They used 3D concrete printing technology to construct corresponding assembly components. However, the major challenge currently hindering the widespread application of topology optimization in industrial design is the high computational cost of large-scale structural topology optimization [5]. How to reduce the computational resource cost of structural topology optimization has been an important issue for engineers. One type of topology optimization method discretized the optimized design area into a series of design density units. This type of method, known as the density-based topology optimization method, mainly includes solid isotropic material with a penalization (SIMP) method [6; 7; 8]. The other most widely used method is the ESO method initially developed by [PERSON] and [PERSON] [9]. Subsequently, [PERSON] et al. [10] made improvements to the method via the addition of efficient units to the structure, while inefficient units were removed. Another optimization method constructed high-order functions in implicit or explicit form for the boundary. This kind of method includes the level-set method [11; 12; 13], the phase field method [14], the moving deformable components/voids method [15; 16; 17; 18], and the bubble method [19; 20]. In recent years, the field of machine learning, especially deep learning, has shown excellent capabilities in terms of feature recognition and the approximation of complex relationships [21; 22; 23; 24; 25]. From the perspective of function fitting, machine learning could be seen as a series of models. When an input-output mapping relationship was difficult to define explicitly, these frameworks provided multiple means of implementing function approximation [26].