Time Series Forecasting (TSF) faces persistent challenges in modeling intricate temporal dependencies across different scales. Despite recent advances leveraging different decomposition operations and novel architectures based on CNN, MLP or Transformer, existing methods still struggle with static decomposition strategies, fragmented dependency modeling, and inflexible fusion mechanisms, limiting their ability to model intricate temporal dependencies. To explicitly solve the mentioned three problems respectively, we propose a novel Dynamic Multi-Scale Coordination Framework (DMSC) with Multi-Scale Patch Decomposition block (EMPD), Triad Interaction Block (TIB) and Adaptive Scale Routing MoE block (ASR-MoE). Specifically, EMPD is designed as a built-in component to dynamically segment sequences into hierarchical patches with exponentially scaled granularities, eliminating predefined scale constraints through input-adaptive patch adjustment. TIB then jointly models intra-patch, inter-patch, and cross-variable dependencies within each layer's decomposed representations. EMPD and TIB are jointly integrated into layers forming a multi-layer progressive cascade architecture, where coarse-grained representations from earlier layers adaptively guide fine-grained feature extraction in subsequent layers via gated pathways. And ASR-MoE dynamically fuses multi-scale predictions by leveraging specialized global and local experts with temporal-aware weighting. Comprehensive experiments on thirteen real-world benchmarks demonstrate that DMSC consistently maintains state-of-the-art (SOTA) performance and superior computational efficiency for TSF tasks. Code is available at https://github.com/1327679995/DMSC.
Time series forecasting (TSF) is vital to many applications, yet existing models often struggle to capture the heterogeneous long-range global patterns and short-range local variations in multivariate time series. While some approaches partially model these dependencies, they often do not jointly exploit temporal and feature-wise information. To address this challenge, we propose HyBDM, a multi-scale hybrid model that decomposes temporal dynamics into global patterns and local variations, which are modeled by two specialized experts. The Global Patterns Expert employs an enhanced BiConv-Mamba module that integrates bidirectional convolutions, an M-SSM layer, a forgetting mechanism, and a GDD-MLP module for cross-channel modeling. The Local Variations Expert uses a Local Window Transformer (LWT) to perform efficient locality-aware attention with reduced computational complexity. In addition, a Multi-Scale Patcher and a Long-Short Router enable multi-resolution representations and adaptive fusion of the two experts. Experiments on six benchmark datasets show that HyBDM outperforms state-of-the-art methods in both forecasting accuracy and computational efficiency, demonstrating its effectiveness in bridging global-local dependencies for multivariate TSF.
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 serves as an essential tool for many real-world applications, supporting tasks such as resource optimization and decision-making. Despite significant architectural advancements, most modern models still treat forecasting task as a fixed mapping from history to target horizons. This induces temporal decoupling across future time points and limits the model's ability to adapt to the evolving context as forecasting progresses. In this work, we present LeapTS, a novel framework that reformulates time series forecasting as a dynamic scheduling process over the prediction horizon. Specifically, LeapTS organizes the forecasting process into multi-level decisions using: (1) the hierarchical controller to dynamically select the optimal prediction scale and advancement length at each step, and (2) continuous-time state evolution driven by neural controlled differential equations. Within this process, the controlled update mechanism explicitly couples the irregular temporal dynamics with discrete scheduling feedback. Extensive evaluations on both real-world and synthetic datasets demonstrate that LeapTS improves overall forecasting performance by at least 7.4% while achieving a 2.6× to 5.3× inference speedup over representative Transformer-based models. Furthermore, by explicitly tracing the scheduling trajectories, we reveal how the model autonomously adapts its forecasting behavior to capture non-stationary dynamics.