Grey-informed neural network for time-series forecasting
Wanli Xie, Ruibin Zhao, Zhenguo Xu, Tingting Liang
TL;DR
The paper tackles time-series forecasting under limited data by embedding grey-system laws into neural networks to improve interpretability and data efficiency. It introduces the Grey-Informed Neural Network (GINN) with a dual loss $L^{ALL}(\theta)=L^{NN}(\theta)+\xi L^{GM}(\theta)$, and extends it to a fractional variant FGINN using truncated M-fractional operators to form the $tM$-fractional Grey Model framework. Empirical results on multiple datasets show that FGINN often yields superior accuracy (lower $MAPE$, $MSE$, $MAE$, $RMSE$) compared to GINN and classical baselines, especially in small-sample regimes. The approach blends neural network flexibility with grey-system determinism, offering interpretable and accurate forecasts for multivariate time series such as regional electricity consumption.
Abstract
Neural network models have shown outstanding performance and successful resolutions to complex problems in various fields. However, the majority of these models are viewed as black-box, requiring a significant amount of data for development. Consequently, in situations with limited data, constructing appropriate models becomes challenging due to the lack of transparency and scarcity of data. To tackle these challenges, this study suggests the implementation of a grey-informed neural network (GINN). The GINN ensures that the output of the neural network follows the differential equation model of the grey system, improving interpretability. Moreover, incorporating prior knowledge from grey system theory enables traditional neural networks to effectively handle small data samples. Our proposed model has been observed to uncover underlying patterns in the real world and produce reliable forecasts based on empirical data.