## 1 Introduction  
In recent years, the development of LEO satellite networks has attracted more and more attention, and LEO network constellations are being actively built around the world, including OneWeb, Telsat and Starlink. Compared with the geosynchronous Earth orbit (GEO) satellite network system, the satellites in the LEO satellite communication system are located in low Earth orbit, resulting in lower levels of transmission latency, better channel conditions and higher transmission rates, which will greatly enhance the user experience. However, these satellites are always in high-speed motion relative to the ground, so the number of satellites deployed will be much larger than the number of GEO satellites if global coverage is required using LEO satellites. With the increase in the number of satellites and the high-speed movement of satellites, the LEO satellite network structure will also become extremely complex. In order to achieve low levels of latency and a high-throughput performance in the case of a complex network structure, an efficient routing algorithm for LEO satellite networks becomes very important. The complex LEO network structure poses great challenges for routing algorithms. The high-speed movement of satellites and the large number of satellites have led to the instability of satellite network topology and the inability to make accurate predictions in advance. There is not much current work on routing algorithms based on LEO satellite networks, as most studies focus on self-organizing networks. Ref. [1] has used a combination of graph neural networks and deep learning for LEO routing algorithms, but the graph neural network algorithm (GNN) does not take into account the computational complexity caused by the large number of nodes in the LEO satellite network and the changing topology when using algorithms. In LEO satellite networks, due to their large number of nodes, we need to consider how to perform distributed training on large graph data and need to be able to learn about nodes that have not appeared before. [PERSON] et al. [2] relies only on deep learning to consider the design of routing algorithms. However, they do not address the challenge of adapting to the dynamic topology of LEO satellite networks. Many scholars have studied routing algorithms for self-organized networks and refer to the routing algorithms for LEO satellite networks, but they do not consider the characteristics of LEO satellite nodes, potential unpredictable topological changes, and instances of limited computational resources. Most of them take into account the state of the nodes while finding the shortest paths. As in [3], only the congestion state of the nodes and the channel quality are considered using deep learning. Ref. [4] introduces a graph neural network for the design of a routing algorithm using deep learning, but its convergence method only considers the characteristics of wireless sensor network nodes. The literature does not consider that if the computing resources of the nodes are limited, it is difficult to complete the whole topology computation. Ref. [5] uses a deep learning approach to design routing algorithms for wireless self-organizing networks, mainly considering the effect of QoS. However, this study also fails to consider the effect of rapid topological changes. Ref. [6] applies a deep learning approach to the design of routing algorithms for ad hoc networks, mainly considering end-to-end delay. Again, this study does not consider the effect of rapid topological changes. In summary, it is necessary to design a routing algorithm that can use distributed training to reduce the number of training nodes and computational complexity and can continuously learn to optimize the paths for the node state and link state. The intelligent routing algorithm based on deep learning is an algorithm that utilizes deep learning techniques to make decisions on routing in a network.