The rapid development of numerical methods enhanced by neural networks has greatly advanced the research field of simulations under extreme conditions. The incredible success of deep-learning methods has demonstrated significant potentials for challenging problems with traditional methods. Plasma dynamics in cross-field E×B configurations in a hall thruster is characterized by its strong multi-physics coupling and inherent multi-scale property. Its simulation poses a significant challenge to conventional numerical methods. We present an augmented particle-in-cell method based on gated attention neural network to enhance the simulation of the plasma transport in hall thrusters. In this work, we firstly demonstrate and discuss the preparation progress of high-fidelity dataset over a range of simulation conditions. Subsequently, the training parameter settings of our neural network are elaborated and we present and discuss the results of trained model in test dataset. Then we apply this method to simulate the sophisticated, multi-physics, multi-scale transport processes of low temperature plasma within hall thruster. Specifically, 2D axial-azimuthal particle-in-cell benchmark for low-temperature partially magnetized plasmas is performed to evaluate the efficiency, accuracy and complexity of our approach against conventional methods. The analysis implies the advantages of our proposed method and highlights the remarkable ability of neural-networks-enhanced numerical methods to address the challenges of multi-scale simulations.