With the advancement of cloud-edge-local computing, Unmanned Aerial Vehicles (UAVs), as flexible mobile nodes, offer novel solutions for dynamic network deployment. However, existing research on UAV networks faces substantial challenges in accurately predicting link dynamics and efficiently managing traffic loads, particularly in highly distributed and rapidly changing environments. These limitations result in inefficient resource allocation and suboptimal network performance. To address these challenges, this paper proposes a UAV-based cloud-edge-local network resource elastic scheduling architecture, which integrates the Graph-Autoencoder–GAN-LSTM (GA–GLU) algorithm for accurate link prediction and the FlowBender-Enhanced Reinforcement Learning for Load Balancing (FERL-LB) algorithm for dynamic traffic load balancing. GA–GLU accurately predicts dynamic changes in UAV network topologies, enabling adaptive and efficient scheduling of network resources. FERL-LB leverages these predictions to optimize traffic load balancing within the architecture, enhancing both performance and resource utilization. To validate the effectiveness of GA–GLU, comparisons are made with classical methods such as CN and Katz, as well as modern approaches like Node2vec and GAE–LSTM, which are commonly used for link prediction. Experimental results demonstrate that GA–GLU consistently outperforms these competitors in metrics such as AUC, MAP, and error rate. The integration of GA–GLU and FERL-LB within the proposed architecture significantly improves network performance in highly dynamic environments.