## 1 Introduction  
Space telescopes are developing toward deep space exploration and maneuver to change orbit, with increasing demands on imaging quality, however, they experience changing and complex thermal environments [1, 2]. The temperature of a telescope directly affects its imaging quality, and a reliable thermal design remains the basis for ensuring the stable operation of the telescope [3]. The thermal design of telescopes involves the iterative optimization of a large number of parameter combinations, which currently relies on the design experience of engineers and involves a process of repeated attempts. The process is time consuming and it is difficult to find an optimal solution. The development of methods that allow the rapid optimization of the thermal design parameters of telescopes has become an important issue [4], and techniques of parameter optimization have thus received much attention in recent years. Scholars have investigated the parameter optimization of space telescopes, but there have been few studies on the optimization of the thermal design parameters of space telescopes. As examples, [PERSON] et al. [5] optimized the design parameters of X-ray mirrors using a genetic algorithm (GA) and [PERSON] et al. [6] used the inverse of the effective temperature of a star for a given flux density obtained using a stochastic particle swarm optimization algorithm and angular parameters, and solved the problem where the bandpass density of the detector is determined and fixed during the operational phase. Popular parametric optimization methods such as particle swarm algorithms [7, 8] and genetic algorithms [9, 10] reveal a better optimization speed and performance than the iterative trial-and-error approach that relies on the engineer. Among these methods, a GA as a global optimization probabilistic algorithm is employed to find an optimal value on the basis of superiority and inferiority and adapts to arbitrary forms of objective functions and constraints. Therefore, GA shows great potential and advantages in the design of thermal parameters of future complex space telescopes. However, these optimization algorithms are combined with traditional physical models to conduct finite element iterative calculations after selecting parameter combinations, which is a time-consuming process of solving partial differential equations that greatly reduces the speed of parameter optimization. The technique of using a surrogate model has attracted attention in recent years for its ability to accelerate the parameter optimization iterations and ensure the accuracy of design at the same time. A surrogate model [11, 12, 13] is commonly used for optimization in engineering problems. When the actual problem (involving a high-precision model) is computationally intensive and difficult to solve, a simplified model that is less computationally intensive and fast to solve can be used in place of the original model to accelerate optimization. The surrogate models most commonly used are those of the kriging method [13], polynomial response surface method [14], and artificial neural network [15], which have various industrial applications, including the thermal design of spacecraft. A back-propagation (BP) neural network [16, 17] is a multilayer feedforward network that can express almost any nonlinear system and is widely used in various fields owing to its excellent fitting ability. As examples, [PERSON] et al. [18] established a three-component proxy ignition delay prediction model based on a BP neural network, which had a computational speed that was nearly 9 times that of the traditional ignition delay calculation, and [PERSON] et al. [19] proposed a surrogate model for computational fluid dynamics simulation based on a GA-BP neural network to predict the concentration of aerosols after diffusion, which solved the problem of the simulation not being achieved in real time when predicting the concentration of diffused gas.