PESD-TSF: A Period-Aware and Explicit Structured Decomposition Framework for Long-Term Time Series Forecasting

Deep forecasting models often suffer from attenuated periodic perception and entangled trend–noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability, disrupts intrinsic dynamic coordination among variables, hindering the modeling of cross-variable consistency in multivariate time series. To address these issues, we propose PESD-TSF, a physics-inspired structured decomposition framework for long-term time series forecasting that jointly emphasizes interpretability and predictive accuracy. PESD-TSF introduces three key designs. First, a Multiplicative Periodic Gating mechanism incorporates continuous-time priors to dynamically modulate signal amplitudes, preserving periodic structures across deep layers. Second, a multi-scale structured encoder integrates detrended attention with hierarchical sampling to explicitly decouple long-term trends from high-frequency variations while retaining fine-grained temporal semantics. Third, to recover disrupted inter-variable dependencies, we propose Cross-Scale Collaborative Attention (CSCA) together with an RLC regularization scheme, which reconstructs global inter-variable topology in deep feature spaces and enforces physically consistent collaboration through orthogonality and consistency constraints. Extensive experiments on benchmark datasets from multiple domains demonstrate that PESD-TSF consistently achieves state-of-the-art performance, with particularly strong gains on multivariate forecasting tasks involving complex inter-variable coupling, highlighting its superior structural modeling capability and generalization.

Many important systems change over time. Traffic roads become crowded or clear, electricity use rises and falls during the day, and environmental measurements change with weather and human activity. To plan ahead, we need computer models that can predict these future changes from past records. This is hard because the data usually contain several things at once: regular patterns, sudden changes, and links between different measurements. Our work introduces PESD-TSF, a method that helps a forecasting model look at these parts more separately. Instead of treating the whole signal as one complicated curve, it learns repeated patterns, short-term changes, and relationships between variables together. This makes the model better at predicting the future and also easier to understand. Across several public forecasting datasets, PESD-TSF gives accurate long-term predictions. It may help applications such as traffic planning, energy management, and environmental monitoring, where reliable forecasts are useful for making better decisions.