Wireless communication systems face challenges in meeting the demand for higher data rates and reliable connectivity in complex environments. Stacked intelligent metasurfaces (SIMs) have emerged as a promising technology for advanced wave-domain signal processing, where mobile SIMs can outperform fixed counterparts. In this paper, we propose a novel unmanned aerial vehicle (UAV)-mounted SIM (UAV-SIM) assisted communication system within low-altitude economy (LAE) networks, where UAVs act as both cache-enabled base stations and mobile SIM carriers to enhance uplink transmissions. To maximize network capacity, we formulate a UAV-SIM-based joint optimization problem (USBJOP) that integrates user association, UAV-SIM three-dimensional positioning, and multi-layer SIM phase shift design. Due to the non-convexity and NP-hardness of USBJOP, we decompose it into three subproblems, which are the association between UAV-SIMs and users optimization problem (AUUOP), the UAV location optimization problem (ULOP), and the UAV-SIM phase shifts optimization problem (USPSOP). Then, we solve them through an alternating optimization strategy. Specifically, AUUOP and ULOP are transformed into convex forms solvable via the CVX tool, while USPSOP is addressed by a generative artificial intelligence (GAI)-based hybrid optimization algorithm. Simulation results show that the proposed approach achieves approximately 1.5 times higher network capacity compared with suboptimal schemes, effectively mitigates multi-user interference with increasing SIM layers and meta-atoms, and reduces runtime by 10\% while maintaining solution quality, thereby demonstrating its practicality for real-world deployments.
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