The objective and accurate prediction of carbon dioxide emissions holds great significance for improving governmental energy policies and plans. Therefore, starting from an evolutionary system of carbon emissions, this paper studies the evolution of the system, establishes a grey model of the system, and expands the modeling structure of this model. The modeling mechanism of the classical feedforward neural network model is organically combined with the function of the external influencing factors of carbon emissions, and the grey model of the carbon emission dynamic system is established with a neural network. Then, the properties of the model are studied, the parameters of the model are optimized, and the modeling steps are obtained. Finally, the validity of the model is analyzed by using the carbon emissions of Beijing from 2009 to 2018. The results of the four cases show that the simulation and prediction errors of the new model are all less than 10%, and case 1 shows the best results of 1.56% and 2.07%, respectively, which are used to predict the carbon dioxide emissions in the next 5 years in Beijing. The prediction results are in accordance with the actual trend, which indicates the effectiveness and feasibility of the model.

Carbon dioxide emissions have received widespread attention and have become one of the most important research topics in the world. The objective and accurate prediction of carbon dioxide emissions holds great significance for improving government energy policies and plans. Therefore, starting from an evolutionary system of carbon emissions, this paper studies the evolution of the system, establishes a grey model of the evolutionary dynamic system of carbon emissions, and expands the modelling structure of the grey model. The modelling mechanism of the neural network model is organically combined with the function of the external influencing factors of carbon emissions, and the carbon emission dynamic system's grey model with a neural network is established, which expands the modelling object of the neural network method. Then, the properties of the model are studied, the parameters of the model are optimized, and the modelling steps of the model are obtained. Finally, the validity of the new model is analysed by using the carbon emissions of Beijing from 2009 to 2018. Four different modelling objects show that the new model has good simulation and prediction accuracy. Furthermore, we choose the best one to predict carbon dioxide emissions over the next five years. The results show that the existing measures taken by Beijing for carbon dioxide emissions are effective and have controlled the increase in carbon emissions to a certain extent. However, it is necessary to continue to strictly control carbon emissions and further improve the measures to achieve the goal of a continuous reduction in carbon emissions.