## 1 Introduction  
The application of air-sea cross-domain communication networks has gained increasing prominence across military, civilian, and commercial domains. However, these networks face significant challenges due to their complex propagation environments, which involve both aerial and underwater media [1, 2]. Their vulnerability to various factors, including natural disasters and human-induced attacks, often leads to node failures, substantially compromising communication continuity and reliability. Consequently, investigating network damage recovery methods is crucial for enhancing the performance and reliability of air-sea cross-domain communication networks. Implementing adaptive network topology recovery following node failures is essential for maintaining the stable operation of these networks [3]. The network topology of air-sea cross-domain communication networks exhibits distinct characteristics compared to traditional networks, featuring multi-layered structures, long-distance connectivity, and time-varying properties. These unique attributes significantly increase the complexity of network recovery processes. Traditional fault tolerance and recovery approaches, which primarily address single or limited node failures through shortest-path algorithms [4, 5, 6, 7, 8], prove inadequate for handling multi-node failure scenarios. Such limitations often lead to network partitioning into disconnected subsets, substantially compromising communication reliability and data transmission efficiency [9]. Recentadvancements have introduced various network topology recovery strategies, including graph-theory-based shortest-path algorithms, swarm intelligence optimization techniques, and load-balancing mechanisms. While these methods aim to enhance network robustness through optimized structural configurations and path selection, they frequently demonstrate limited flexibility and efficiency when confronted with large-scale node failures or significant topology alterations [10; 11; 12]. This paper presents a novel approach for damage recovery in air-sea cross-domain communication networks under multi-node failure scenarios. Our proposed method integrates an improved Dijkstra algorithm with load-balancing mechanisms, incorporating link quality prediction and minimum communication cost principles to optimize both path selection and load distribution. This comprehensive approach not only restores network connectivity but also minimizes communication overhead. The methodology comprises two key phases. In the prediction phase, we use the whale optimization algorithm to optimize the gray prediction model, overcoming the poor adaptability of the original model when processing dynamically changing data. During the link selection phase, we design a path selection strategy that combines the improved Dijkstra algorithm and load balancing to avoid the overload of certain links, ensuring a more balanced load distribution across the network and enhancing network stability and recovery efficiency. Through comprehensive simulation analysis, we validate the effectiveness of the proposed algorithm, particularly by comparing its performance with traditional recovery strategies in two failure scenarios: random node failures and deliberate attacks. The results further demonstrate the superior performance of our algorithm in network recovery, particularly in scenarios involving large-scale node failures. The main contributions of this paper are summarized as follows:  
1. We propose a multi-node failure recovery method that integrates link quality prediction with minimum communication cost, leveraging an improved Dijkstra algorithm and load-balancing strategy to achieve more efficient network recovery. 2. Considering the characteristics of air-sea cross-domain communication networks, we develop an objective function that balances load distribution and communication cost and solve it using the whale optimization algorithm to optimize path selection and load allocation during the recovery process. 3.