Neural Ordinary Differential Grey Model and Its Applications

Abstract Due to the efficiency of grey models in predicting the time series of small samples, grey system theory has been well studied since it was first proposed and has now become an important method for small sample prediction. Inspired by the neural ordinary differential equations (NODE), this paper proposes a novel grey forecasting model called the neural ordinary differential grey model (NODGM). The NODGM model includes a novel whitening equation that allows the prediction model to be learned through a training procedure. Therefore, compared with other models whose structures and terms need to be artificially predefined based on the laws of real samples, the NODGM model has a wider application range and can learn the characteristics of different data samples. Then, to obtain a model with better prediction performance, we apply NODE to train the model. Finally, the predicting sequence is obtained by using the Runge-Kutta method to solve the model. In the experiments, we apply NODGM model to two energy samples and then contrast the experimental results with the results of some classical grey models to validate the effectiveness of NODGM model. The comparison results from predicting China’s annual crude oil consumption and forecasting oilfield production in northern China show that the prediction accuracies achieved by NODGM model are 28% and 8% higher, respectively, than those achieved by the state-of-the-art grey forecasting models.