Neural Multivariate Grey Model and Its Applications

Abstract

For time series forecasting, multivariate grey models are excellent at handling incomplete or vague information. The GM(1, N) model represents this group of models and has been widely used in various fields. However, constructing a meaningful GM(1, N) model is challenging due to its more complex structure compared to the construction of the univariate grey model GM(1, 1). Typically, fitting and prediction errors of GM(1, N) are not ideal in practical applications, which limits the application of the model. This study presents the neural ordinary differential equation multivariate grey model (NMGM), a new multivariate grey model that aims to enhance the precision of multivariate grey models. NMGM employs a novel whitening equation with neural ordinary differential equations, showcasing higher predictive accuracy and broader applicability than previous models. It can more effectively learn features from various data samples. In experimental validation, our novel model is first used to predict China’s per capita energy consumption, and it performed best in both the test and validation sets, with mean absolute percentage errors (MAPEs) of 0.2537% and 0.7381%, respectively. The optimal results for the compared models are 0.5298% and 1.106%. Then, our model predicts China’s total renewable energy with lower mean absolute percentage errors (MAPEs) of 0.9566% and 0.7896% for the test and validation sets, respectively. The leading outcomes for the competing models are 1.0188% and 1.1493%. The outcomes demonstrate that this novel model exhibits a higher performance than other models.

Keywords

• GM(1, N)
• neural ordinary differential equations
• adjoint sensitivity algorithm
• energy prediction