The unmanned aerial manipulator system, consisting of a multirotor UAV (unmanned aerial vehicle) and a manipulator, has attracted considerable interest from researchers. Nevertheless, the operation of a dual-arm manipulator poses a dynamic challenge, as the CoM (center of mass) of the system changes with manipulator movement, potentially impacting the multirotor UAV. Additionally, unmodeled effects, parameter uncertainties, and external disturbances can significantly degrade control performance, leading to unforeseen dangers. To tackle these issues, this paper proposes a nonlinear adaptive RISE (robust integral of the sign of the error) controller based on DNN (deep neural network). The first step involves establishing the kinematic and dynamic model of the dual-arm aerial manipulator. Subsequently, the adaptive RISE controller is proposed with a DNN feedforward term to effectively address both internal and external challenges. By employing Lyapunov techniques, the asymptotic convergence of the tracking error signals are guaranteed rigorously. Notably, this paper marks a pioneering effort by presenting the first DNN-based adaptive RISE controller design accompanied by a comprehensive stability analysis. To validate the practicality and robustness of the proposed control approach, several groups of actual hardware experiments are conducted. The results confirm the efficacy of the developed methodology in handling real-world scenarios, thereby offering valuable insights into the performance of the dual-arm aerial manipulator system.