# Heat Conduction Plate Layout Optimization Using Physics-Driven Convolutional Neural Networks
## 3 Methodology
### PSO Algorithm  
The particle swarm optimization (PSO) algorithm is inspired by groups of birds. The basic idea is to collaborate and share between individual birds in the group to find the optimal solution [51]. PSO has been selected in this research, which is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. PSO is a new evolutionary algorithm developed in recent years. Similar to the simulated annealing algorithm, PSO starts from a random solution and finds the optimal solution through iteration. It also evaluates the quality of the solution through fitness but has simpler rules than the genetic algorithm. PSO does not have the \"crossover\" and \"mutation\" operations of the genetic algorithm. It finds the global optimum by following the current searched optimum value. The algorithm of PSO is easy to implement, has high precision, and has fast convergence. It is also a parallel algorithm, that is, a a neural network algorithm with great potential. The PSO algorithm was proposed because of its intuitive background, simplicity, easy implementation, and wide adaptability to different types of functions. The PSO algorithm has good performance in many fields, such as power systems, biological information, logistics planning, etc. At present, the standard particle swarm algorithm is very mature and has standard test functions in many different dimensions, ranging from accuracy (deviation from the optimal solution), success rate (probability of computing to the optimal solution), computational speed, stability (mean, median, variance), etc. The algorithms were tested and achieved good results [52; 53; 54]. The feasibility of this method has been proved in many scientific and industrial fields [55; 56; 57; 58; 59; 60; 61]. PSO requires a solution space conventionally achieved by discrete methods by optimizing the algorithms. There are multiple boundary conditions and multiple inputs when considering complex optimization goals. The effort of accompanying numerical simulations is usually prohibitive [62]. The particle swarm optimization (PSO) algorithm is an emerging optimization technology whose ideas originate from artificial life and evolutionary computing theory. Particle swarm optimization completes the optimization by the particles following the best solution found by themselves and the best solution of the entire swarm. Compared with other evolutionary algorithms, this algorithm is simple and easy to implement, has few adjustable parameters, has stronger global optimization ability, and has been widely studied and applied [63; 64]. Similar to the simulated annealing algorithm, PSO starts from a random solution and finds the optimal solution through iteration. It also evaluates the quality of the solution through fitness but has simpler rules than the genetic algorithm. PSO does not have the \"crossover\" and \"mutation\" operations of the genetic algorithm. It finds the global optimum by following the currently searched optimum value. In this paper, the PD-CNN surrogate model calculates the solutions inside the domain effectively. Given a precise layout and boundary condition, the model can directly output the corresponding temperature distribution, significantly reducing the computational workload. The PD-CNN replaces the numerical analysis tool by constructing a high-precision model and has achieved a compromise between calculation accuracy and computational cost, thereby improving the optimization's efficiency. It is straightforward to guide the numerical algorithm to solve the optimization problem in a limited time. The PSO process is shown in Figure 3. As introduced above, the birds involve placing several simple things called particles. Each particle evaluates the fitness at its present location in the space of a problem or function. By combining some aspect of the history of the swarm's fitness values with those of one or more swarm members, each particle can determine its movement through the parameter space.