A Novel Neural-Augmented Grey System Approach with Its Applications in Carbon Emission Forecasting

Grey system models (GMs) have achieved considerable progress in recent decades, yet their effectiveness is often limited when dealing with nonlinear data. In contrast, machine learning (ML) models can capture complex nonlinear relationships but generally require large datasets and lack interpretability. To address these limitations, this paper proposes a novel neural grey system model that embeds a neural network into the traditional GM framework. This integration enhances the model’s nonlinear learning capacity while maintaining the grey model’s suitability for sparse and uncertain data. The model is optimized using the Adam algorithm, and hyperparameters are fine-tuned via GridSearch. To validate its effectiveness, we conduct carbon emission forecasting experiments for four countries, comparing the proposed model against eight benchmark models, including conventional GMs and ML-based approaches. Results demonstrate superior forecasting accuracy and generalization ability, confirming the proposed model’s potential for complex, nonlinear prediction tasks in environmental and energy domains.