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This paper addresses the issue of onboard inference for AI-based routing algorithms in dynamic LEO (Low Earth Orbit) satellite networks. In dynamic LEO networks, it is essential to maintain communication performance across varying topologies while considering link disconnections and overcoming computational constraints for real-time inference on embedded boards. This paper proposes a GPU-based inference acceleration method to reduce the computation time required for real-time onboard inference of a Dueling DQN (Deep Q-Network)-based routing algorithm in dynamic LEO satellite networks. The approach is composed of memory management, low-level operations, and efficient indexing methods, which collectively enhance computational efficiency. As a result, the proposed method achieves approximately 2.4 times faster inference compared to conventional CPU-based approaches. Additionally, the kernel performance analysis reveals that the proposed method reaches 10% of the peak computational performance and 20% of the peak memory performance. This demonstrates the compatibility of the proposed method for integration with additional applications in the multitasking systems of LEO satellites. [ABSTRACT FROM AUTHOR]