MFDNet: Adaptive Multi‐scale Frequency Decomposition Network for Long‐term Time Series Forecasting

Abstract

Long‐term time series forecasting (LTSF) plays a crucial role in practical applications such as power dispatching, financial market analysis, and climate prediction. To tackle core challenges in LTSF, including the difficulty of capturing nonlinear patterns and insufficient multi‐scale feature extraction, we propose a novel Multi‐scale Frequency Domain Decomposition Network (MFDNet). The proposed model features a hierarchical frequency‐domain processing architecture driven by three key innovations. First, a reversible instance normalization (RevIN) layer is introduced to mitigate distribution shifts in non‐stationary data, thereby enhancing model generalization. Second, a differentiable wavelet decomposition module with learnable, orthogonality‐constrained filters is designed to explicitly separate trend and seasonal components, where symmetric boundary extension is adopted to avoid the discontinuities that zero padding would introduce at the two ends of the observation window. Third, an attention‐guided adaptive frequency selection mechanism dynamically emphasizes critical frequency components across multiple scales and temporal contexts. Experimental results on seven benchmark datasets across four domains demonstrate that MFDNet significantly outperforms or matches state‐of‐the‐art methods. For instance, on the ETTm2 dataset, MFDNet reduces the Mean Squared Error (MSE) by 17.8%$$ 17.8\% $$ compared to SparseTSF, and on the Traffic dataset, the average MSE decreases by 11.3%$$ 11.3\% $$ compared to iTransformer, highlighting the model's predictive accuracy and robustness.