Multi-Scale Spectral Recurrent Network Based on Random Fourier Features for Wind Speed Forecasting

Accurate wind speed forecasting is critical for reliable wind-power integration, yet it remains challenging due to the strongly non-stationary and inherently multi-scale nature of atmospheric processes. While deep learning models—such as LSTM, GRU, and Transformer architectures—achieve competitive short- and medium-term performance, they frequently suffer from spectral bias, hyperparameter sensitivity, and reduced generalization under heterogeneous operating regimes. To address these limitations, we propose a multi-scale spectral–recurrent framework, termed RFF-RNN, which integrates multi-band Random Fourier Feature (RFF) encodings with parameterizable recurrent backbones. A key innovation of our approach is the deliberate relaxation of strict shift-invariance constraints; by jointly optimizing spectral frequencies, phase biases, and bandwidth scales alongside the neural weights, the framework dynamically shapes a fully data-driven spectral embedding. To ensure robust adaptation, we employ a two-stage optimization strategy combining gradient-based inner-loop learning with outer-loop Bayesian hyperparameter tuning. Extensive evaluations on a controlled synthetic benchmark and six geographically diverse real-world wind datasets (spanning the USA, China, and the Netherlands) demonstrate the superiority of the proposed framework. Statistical validation via the Friedman test confirms that RFF-enhanced models—particularly RFF-GRU and RFF-LSTM—systematically outperform standard recurrent networks and state-of-the-art Transformer architectures (Autoformer and FEDformer). The proposed approach yields significantly lower error metrics (MAE and RMSE) and higher explained variance (R2), while exhibiting remarkable resilience against error accumulation at extended forecasting horizons.