In this paper, we investigate an effective energy management in a UAV -assisted Metaverse synchronization system. The UAV s perform the data collection for a virtual service provider (VSP) for the synchronization between the physical objects and digital twins (DTs). The UAVs buy energy resources from an energy service provider (ESP). The key issue is to motivate both the ESP and the UAV s to participate in the energy trading market. For this, we design a deep learning (DL)-based auction scheme that maximizes the revenue of the ESP while guaranteeing individual rationality (IR) and incentive compatibility (IC). We provide numerical results to demonstrate the improvement of the DL-based auction scheme compared to the baseline scheme in terms of revenue, IC, and IR.