Multi-scale dual-source fusion network for long-term time series forecasting

DeRNN: Decomposed Recurrent Neural Network for Long-Term Time Series Forecasting

The Decomposed Recurrent Neural Network (DeRNN) is proposed, which decouples global trend modeling from local fluctuation extraction via an asymmetric dual-track architecture and exhibits superior robustness against noise and distribution shifts.

TFF-Former: A Time-Frequency Fusion Transformer for Multivariate Weather Time Series Forecasting

Multivariate weather time series forecasting is highly challenging due to the complex coexistence of short-term dynamic fluctuations and long-term periodic patterns. Existing models predominantly focus on the time domain, lacking explicit mechanisms to capture frequency priors, or rely on complex spatial reconstructions that struggle with long-range temporal dependencies. To address these limitations, we propose the Time-Frequency Fusion Transformer (TFF-Former), a novel dual-branch architecture. Specifically, the time-domain branch utilizes a Transformer encoder to extract local dynamics and variable dependencies, while the frequency-domain branch employs the real Fast Fourier Transform (rFFT) combined with a parallel Transformer encoder to explicitly model multi-scale periodic structures from amplitude spectra. The representations from both domains are subsequently concatenated to achieve feature complementarity. Experiments on the Jena Climate dataset demonstrate that TFF-Former achieves state-of-the-art performance, outperforming strong baselines including TimesNet and PatchTST across MAE, MSE, RMSE, and SMAPE metrics. Ablation studies further validate that the time-frequency fusion mechanism significantly surpasses single-domain modeling.

HyBDM: Multi-Scale Hybrid Experts for Time Series Forecasting with Bidirectional Dependency Modeling

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.

AdaDyTS: Dynamic Multi-Scale Spectral Decoupling and Time-Variant Inference for Time Series Forecasting

Time series forecasting is fundamental to intelligent decision-making systems, enabling proactive planning and resource optimization across diverse application domains. However, the inherent complexity of real-world time series—including multi-scale temporal patterns, heterogeneous variable dependencies, and dynamic non-stationarity—poses significant challenges for existing forecasting models. Current approaches often suffer from high-frequency information attenuation in frequency-domain modeling, inadequate characterization of scale heterogeneity across variables, and limited capability to capture time-varying dynamics. To address these challenges, this paper introduces AdaDyTS, a unified knowledge-driven forecasting framework that synergistically integrates three complementary mechanisms: multi-scale frequency-domain interpolation decoupling via the Cascaded Spectral Residual Extractor (CSRE), dynamic morphological perception via the Dynamic Morphological Perception Unit (DMP-U), and time-variant state-space inference via the Time-Variant State-Space Module (TV-SS). CSRE separates low-frequency trends from high-frequency residuals through coarse-to-fine layer-wise self-reconstruction, preserving transient information that static filters typically attenuate. DMP-U employs deformable convolution guided by multi-expert attention to adaptively adjust receptive fields, enabling fine-grained modeling of local fluctuations and nonlinear distortions. TV-SS relaxes the conventional time-invariant parameter assumption, dynamically modulating state transition parameters to capture both short-term variations and long-term dependencies. Under a unified evaluation protocol across 13 benchmark datasets, AdaDyTS achieves average improvements of 4.35\% in MSE and 4.31\% in MAE over the AMD backbone, consistently outperforming state-of-the-art methods across long-horizon forecasting scenarios. The proposed framework demonstrates the effectiveness of integrating domain-specific knowledge—including spectral analysis, morphological feature extraction, and dynamic system modeling—within a unified deep learning architecture for enhanced predictive performance.

NeuroFlexMLP: A Low Complexity MLP Architecture for Long-Term Time Series Forecasting

Forecasting time series over long horizons is essential for proactive decision-making in many systems. Recent research has focused on transformer-based architectures, which capture long-range dependencies in sequential data. However, several studies show that simpler linear models can outperform transformers by avoiding overfitting during training. In this context, we present NeuroFlexMLP, a deep learning model for multivariate time series forecasting tasks. NeuroFlexMLP's key distinct feature is the adaptability to the diverse complexity of real-world time series, which is achieved, from the architecture standpoint, by adding non-linear residual blocks to a first linear block. This architectural design simplifies hyperparameter optimization, leading to accurate forecasts for various time series data types regardless of the lookback or prediction horizons, outperforming state-of-the-art (SOTA) models on challenging real-world datasets. Its Multi-Layer Perceptron (MLP) design ensures high computational efficiency, making it scalable for longer input sequences than transformer-based models. We validate NeuroFlexMLP for the LEO satellite beam hopping use case, where its lightweight design enables on-board deployment, and on state-of-the art AI datasets. Across all these benchmarks, NeuroFlexMLP achieves competitive accuracy over state-of-the-art models while providing an adaptive architecture that significantly reduces computational overhead. On the LEO beam hopping task, it achieves up to 35.9% MSE reduction over Informer, which translates into up to 28% lower provisioning cost under asymmetric cost models that penalize under-allocation more heavily than over-allocation.

FTSformer: a financial-initiated multi-scale transformer with exogenous fusion for time series forecasting