Bayesian Frequency-Adaptive and Cross-Scale Neural Signal Modeling for Energy Systems

This article proposes a Bayesian signal modeling framework that uses recursive filtering and residual-stage refinement to separate dominant operating trends, fast variations, and stochastic disturbances. Sparse cross-scale attention and entropy-guided fusion integrate these components into an uncertainty-aware representation. On the weekly WTI crude oil price dataset, the model reduced mean-absolute error (MAE), root-mean-square error (RMSE), mean absolute percentage error (MAPE), and mean-squared error (MSE) by 56.6%, 57.3%, 56.8%, and 81.8%, respectively, compared with MLP. On daily WTI data, it achieved RMSE of 1.126 and MAPE of 1.236%. On a Halifax-based multivariate renewable dataset, it achieved a vector RMSE of 0.124 and prediction interval coverage probability (PICP) of 0.946. Compared with the strongest baseline in the weekly WTI experiment, TimesNet, the proposed model reduced RMSE from 1.506 to 1.209 and mse from 2.268 to 1.461, corresponding to 19.7% and 35.6% reductions, respectively. In the daily WTI and Halifax experiments, the model achieved high uncertainty reliability, with PICP values of 0.941 and 0.946, respectively, indicating that the predictive intervals closely matched the nominal confidence level. These results indicate stronger reliability for energy-market analysis and renewable-rich grid operation under uncertainty.