DST-Net: Decomposed Spatio-Temporal Network for 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.

Time series forecasting is traditionally dominated by sequence-based architectures such as recurrent neural networks and attention mechanisms, which process all time steps uniformly and often incur substantial computational cost. However, real-world temporal signals typically exhibit heterogeneous structure, where informative patterns are sparsely distributed and interspersed with redundant observations. This work introduces SPaRSe-TIME, a structured and computationally efficient framework that models time series through a decomposition into three complementary components: saliency, memory, and trend. The proposed approach reformulates temporal modeling as a projection onto informative subspaces, where saliency acts as a data-dependent sparsification operator, memory captures dominant low-rank temporal patterns, and trend encodes low-frequency dynamics. These components are integrated through a lightweight, adaptive mapping that enables simplified, selective, and interpretable temporal reasoning. Extensive experiments on diverse real-world datasets demonstrate that SPaRSe-TIME achieves competitive predictive performance compared to recurrent and attention-based architectures, while significantly reducing computational complexity. The model is particularly effective in structured time series with clear temporal components and provides explicit interpretability through component-wise contributions. Furthermore, analysis reveals both the strengths and limitations of decomposition-based modeling, highlighting challenges in highly stochastic and complex multivariate settings. Overall, SPaRSe-TIME offers a principled alternative to monolithic sequence models, bridging efficiency, interpretability, and performance, and providing a scalable framework for time series learning.

Probabilistic time series forecasting remains challenging, largely because modeling distinct trend and seasonal dynamics requires specialized approaches. Existing methods often fail to capture the unique inner properties of these components, lack interpretability, or suffer from heavy memory and runtime overhead. To address these limitations, we propose DecoVAE, a lightweight interpretable trend-seasonal VAE framework that explicitly decomposes time series into trend and seasonal components by applying domain-specific inductive biases. The trend stream enforces structural smoothness using a differential regularizer on the latent trajectory, analogous to the Hodrick-Prescott filter. Concurrently, the seasonal stream operates in the frequency domain via a complex Gaussian VAE, natively capturing the amplitude and phase of periodic patterns. Extensive evaluations across seven real-world benchmarks show that DecoVAE consistently outperforms strong baselines. It achieves reductions of up to 14.96% in CRPS and 23.30% in NMAE for short-term forecasting, and up to 52.68% and 26.51% for long-term horizons. Crucially, DecoVAE yields these accuracy gains while remaining highly efficient, reducing model weight by up to 93% and accelerating speed by up to 74% compared to the second-best method.