The primary source of atmospheric neutrons is the interaction between cosmic rays and the Earth's atmosphere. The flux and dose of atmospheric neutrons are commonly utilized for radiation risk assessment in aviation personnel. To achieve real-time prediction of atmospheric neutron radiation, this paper adopts an empirical model of atmospheric neutron flux to randomly generate a data set. The data set is then used to train a backpropagation neural network (BPNN), establishing a non-linear mapping relationship between atmospheric neutron flux and variables such as solar modulation potential, kp index, OULU cosmic ray station detection data, latitude and longitude, and altitude. The result shows that the atmospheric neutron inversion model is capable of providing real-time responses in both the temporal and spatial domains. Error analysis is conducted using two balloon detection data. The inversion results are kept in the same order as the detection data.