Low Probability of Detection (LPD) communication aims to obscure the presence of radio frequency (RF) signals to evade surveillance. In the context of mobile surveillance utilizing unmanned aerial vehicles (UAVs), achieving LPD communication presents significant challenges due to the UAVs' rapid and continuous movements, which are characterized by unknown nonlinear dynamics. Therefore, accurately predicting future locations of UAVs is essential for enabling real-time LPD communication. In this paper, we introduce a novel framework termed predictive covert communication, aimed at minimizing detectability in terrestrial ad-hoc networks under multi-UAV surveillance. Our data-driven method synergistically integrates graph neural networks (GNN) with Koopman theory to model the complex interactions within a multi-UAV network and facilitating long-term predictions by linearizing the dynamics, even with limited historical data. Extensive simulation results substantiate that the predicted trajectories using our method result in at least 63%-75% lower probability of detection when compared to well-known state-of-the-art baseline approaches, showing promise in enabling low-latency covert operations in practical scenarios.

Deep Reinforcement Learning (DRL) is widely used to optimize the performance of multi-UAV networks. However, the training of DRL relies on the frequent interactions between the UAVs and the environment, which consumes lots of energy due to the flying and communication of UAVs in practical experiments. Inspired by the growing digital twin (DT) technology, which can simulate the performance of algorithms in the digital space constructed by coping features of the physical space, the DT is introduced to reduce the costs of practical training, e.g., energy and hardware purchases. Different from previous DT-assisted works with an assumption of perfect reflecting real physics by virtual digital, we consider an imperfect DT model with deviations for assisting the training of multi-UAV networks. Remarkably, to trade off the training cost, DT construction cost, and the impact of deviations of DT on training, the natural and virtually generated UAV mixing deployment method is proposed. Two cascade neural networks (NN) are used to optimize the joint number of virtually generated UAVs, the DT construction cost, and the performance of multi-UAV networks. These two NNs are trained by unsupervised and reinforcement learning, both low-cost label-free training methods. Simulation results show the training cost can significantly decrease while guaranteeing the training performance. This implies that an efficient decision can be made with imperfect DTs in multi-UAV networks.