FreAPNet: Learnable Amplitude–Phase Parameterization and Dual‐Path Frequency Learning for Multivariate Time Series Forecasting

ABSTRACT Multivariate time series forecasting remains challenging. Key hurdles include long‐range temporal dependencies, temporal misalignment, and complex cross‐variable interactions. This paper presents FreAPNet, a frequency‐domain forecasting framework built upon two complementary components. The first component is a learnable amplitude–phase parameterization. It separately models spectral magnitude and phase to refine periodic strength and temporal alignment. The second is a dual‐path frequency learning architecture, which captures both temporal‐frequency evolution and channel‐frequency coupling. Together, these designs provide a structured and physically meaningful representation. This representation overcomes the limitations of conventional time‐domain approaches. Extensive experiments on multiple benchmark datasets show that FreAPNet achieves state‐of‐the‐art or competitive accuracy in long‐horizon forecasting. Notably, the model maintains a lightweight size and favorable computational efficiency. Ablation results further reveal a clear contribution hierarchy: amplitude modeling provides the greatest performance gain, followed by phase refinement and dual‐path frequency modeling. These findings demonstrate the effectiveness of structured, learnable frequency‐domain modeling for multivariate time series forecasting.