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

2026-05-14

AI Summary

This work addresses key limitations in deep time series forecasting models, which often suffer from degraded periodicity awareness, entangled trend and noise components, and disrupted dynamic inter-variable relationships due to the channel independence assumption when network depth increases. To overcome these issues, the authors propose a structured decomposition framework that preserves deep periodic structures through multiplicative periodic gating, explicitly disentangles trends from high-frequency components via multi-scale decoupled encoding, and captures global topological dependencies among variables using cross-scale collaborative attention (CSCA) enhanced with RLC regularization—incorporating orthogonality and physics-informed consistency constraints. The method achieves state-of-the-art performance across multiple benchmark datasets, demonstrating substantial accuracy gains in complex, tightly coupled multivariate long-term forecasting scenarios and confirming its superior structural modeling capacity and generalization ability.

Abstract

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.

Problem

• periodic perception
• trend-noise entanglement
• channel-independent paradigm
• inter-variable dependencies
• multivariate time series forecasting

Innovation

• Multiplicative Periodic Gating
• Structured Decomposition
• Cross-Scale Collaborative Attention
• Detrended Attention
• RLC Regularization