## 1 Introduction  
The traction control of high-speed trains is a factor critical to ensuring their safety, punctuality, and reduced energy consumption. However, traditional traction control methods often make it challenging to achieve the optimal traction distribution in the face of complex dynamic characteristics and environmental conditions during the operation of high-speed trains. Especially in regards to the issue of energy consumption, drivers often need to make a difficult trade-off between traction and speed, resulting in an unnecessary waste of energy and reduced operating efficiency. Saving energy during the operation of trains is essentially an optimization control problem and has attracted the attention of many scholars. Control strategies based on dynamic models are more common than others, but such methods face challenges in accurately describing the dynamic characteristics of train operation [1]. Scholars have applied modern intelligent control methods to the field of train operational control; thus, a series of methods using deep learning have been developed. In terms of the driving strategy of high-speed railway trains, [PERSON] et al. optimized the genetic algorithm based on the speed limit, slope of the actual route, and the constraints of the vehicle. Although it has an obvious energy-saving effect, it has a high degree of computational complexity and strong data dependence, and it is difficult to adjust its parameters [2]. [PERSON] et al. proposed a high-speedrailway train track optimization model considering continuous train constraints but could not guarantee the global optimal solution [3]. [PERSON] et al. proposed a method based on mixed integer linear programming to optimize the trajectory of high-speed trains, but the process of transforming the problem into a mathematical model is more complicated [4]. Based on the Soft Actor Critic method, [PERSON] et al. proposed a method to optimize the train driving strategy, but it is sensitive to the initial strategy, which may cause the algorithm to fall into the local optimal solution or the convergence speed to be slow [5]. [PERSON] et al. transformed the inverse problem of training energy-saving control into a decision-making machine learning algorithm solved by a finite Markov process through deep reinforcement. They adopted the algorithm of the Soft Actor Critic method to determine the optimal driving strategy, but selecting the appropriate hyperparameters often requires a lot of experiments and tuning [6]. [PERSON] et al. proposed a real-time energy-saving optimization method of timetable based on an improved differential evolution algorithm and fast iteration method, but the effect of reducing energy consumption is not obvious [7]. [PERSON] et al. optimized the curve of energy saved during train operation by quadratic constraint linear programming, but it was limited to only the neutral zone system [8]. [PERSON] et al. proposed a new intelligent proportional-integral-differential controller to optimize the velocity trajectory. However, when there is integral saturation in the system, the performance of the controller will decrease [9]. A high-speed railway system usually contains complex nodes and edges, and the interaction and influence of these are complex to model by traditional methods. The GNN (graph neural network) can capture important information in the network through mechanisms such as convolution, attention addition, and information dissemination, thus providing more accurate energy consumption prediction and energy-saving optimization [10]. The VGAE developed from the variational auto-encoder (VAE) is a graph neural network that uses latent variable learning to approximate the Gaussian distribution and can effectively solve the link prediction problem [11; 12; 13]. Nowadays, an algorithm based on graph neural networks is mainly applied in the field of transportation to solve the problem of traffic flow prediction in urban traffic networks and is rarely applied to issues related to high-speed trains [14; 15; 16].