An Efficient and Sparse Kernelized Gray RVFL Network for Energy Forecasting

Reliable energy forecasting is essential for the planning and dispatch of power and fuel systems; however, energy series are often short and exhibit pronounced nonlinearity. To tackle this small sample setting, we propose a gray random vector functional link (GRVFL) framework and further derive a kernelized variant (KGRVFL). In GRVFL, an RVFL network is integrated into gray system modeling, and the parameters are learned via sparsity-regularized regression, enabling stable and reproducible training without backpropagation or evolutionary optimization. Hyperparameters are tuned using Bayesian optimization driven by a Top-k mean absolute percentage error (Top-k MAPE) criterion to improve robustness. To further promote compactness, we introduce a fractional ratio-type Fr-ℓ1 penalty and solve the resulting problem efficiently using a fractional coordinate descent (FCD) algorithm. The proposed methods are assessed on six real-world energy datasets using eight evaluation metrics. Comparisons with nine gray model baselines and six machine learning forecasters demonstrate that the sparse KGRVFL (SKGRVFL) achieves higher predictive accuracy and improved training stability under small sample conditions.