Multi-scale dual-stream architecture for long-term time series forecasting

doi:10.3785/j.issn.1008-973X.2026.08.016

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (8): 1770-1781 DOI: 10.3785/j.issn.1008-973X.2026.08.016

Multi-scale dual-stream architecture for long-term time series forecasting

Meijia WANG1(

),Fan ZHANG1,2,*(

),Hua WANG3,Mingli ZHANG4,Caiming ZHANG5

1. School of Computer Science and Technology, Shandong Technology and Business University, Yantai 264005, China
2. Shandong Provincial Higher Education Institutions Future Health Intelligent Medical Industry Engineering Research Center, Yantai 264005, China
3. School of Computer and Artificial Intelligence, Ludong University, Yantai 264025, China
4. McGill Centre for Integrative Neuroscience, Montreal Neurological Institute, McGill University, Montreal, H3A 2B4, Canada
5. School of Software, Shandong University, Jinan 250100, China

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Abstract

A dual-stream framework named Patchflow was proposed to address the limited ability to capture multi-scale dynamic and insufficient nonlinear modeling capability in long-term time series forecasting. A multi-scale segmentation strategy was employed to partition long-term time series into local segments of different granularities, enabling accurate simultaneous modeling of local and global temporal dynamics while enhancing adaptability to multi-frequency patterns. A Chebyshev polynomial-based approximate convolution operator was further introduced to capture inter-segment correlations from a geometric perspective, improving the modeling accuracy of non-stationary sequences. Based on the trend modeling branch, a structured prior was introduced to extract complex temporal dependencies. Experiments on multiple public datasets showed that Patchflow consistently outperformed state-of-the-art methods, with particularly notable improvements on sequences with strong seasonality and long-term trends.

Key words： time series forecasting dual-stream architecture multi-scale segmentation non-stationary sequences Chebyshev polynomials

Received: 24 June 2025 Published: 16 July 2026

CLC:

TP 393

Fund: 国家自然科学基金联合基金资助项目（U24A20219）；国家自然科学基金资助项目（62272281）；泰山学者专项基金资助项目（tsqn202306274）；山东省高等学校青创科技支持计划（2023KJ212）.

Corresponding Authors: Fan ZHANG E-mail: 2024410048@sdtbu.edu.cn;zhangfan@sdtbu.edu.cn

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Cite this article:

Meijia WANG,Fan ZHANG,Hua WANG,Mingli ZHANG,Caiming ZHANG. Multi-scale dual-stream architecture for long-term time series forecasting. Journal of ZheJiang University (Engineering Science), 2026, 60(8): 1770-1781.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.08.016 OR https://www.zjujournals.com/eng/Y2026/V60/I8/1770

面向长期时间序列预测的多尺度双流架构

针对长期时间序列预测中多尺度动态捕捉不足与非线性建模能力有限的问题，提出名为Patchflow的双流架构. 设计多尺度分割策略，将长期时间序列划分为不同粒度的局部片段，精准同步建模局部与全局时序动态，提升对多频率特征的自适应能力. 引入切比雪夫多项式构建的近似卷积算子，从几何视角刻画片段间相关性，有效增强非平稳序列的建模精度. 在趋势建模的基础上，引入结构化先验以提取复杂时序依赖. 实验结果表明，相较同类方法，Patchflow在多个公开数据集上的预测精度均显著提升，在强季节性与长期趋势性序列上的表现尤为突出.

关键词： 时间序列预测, 双流结构, 多尺度分割, 非平稳序列, 切比雪夫多项式

Fig.1 Proposed multi-scale dual-stream architecture

Fig.2 Chebyshev polynomial layer

Fig.3 Local-global convolution module

Tab.1 Statistical data of public datasets for benchmarking

Tab.2 Long-term forecasting results of different models on multiple standard multivariate time series datasets (MSE)

Tab.3 Long-term forecasting results of different models on multiple standard multivariate time series datasets (MAE)

Tab.4 Module ablation results of proposed multi-scale dual-stream architecture

Tab.5 Experimental results of introducing Chebyshev polynomial layer into strong baseline

Fig.4 Comparison of fitting effects for multi-layer perceptrons and Chebyshev polynomial layers

Fig.5 Comparison of input and output features for Chebyshev polynomial layer

Fig.6 Parameter sensitivity analysis of convolutional kernels on ETT dataset

Fig.7 Parameter sensitivity analysis of embedded dimensions on Weather dataset

Tab.6 Model complexity analysis

Tab.7 Performance evaluation of lightweight models

Tab.8 Model pruning experiment results

Tab.9 Comparison of time series interpolation performance across different models

Fig.8 Robustness test results of model under anomalous perturbation

Fig.9 Global scaling factor visualization

Fig.10 Comparison of prediction performance between patch-scale and multi-scale fusion schemes across different datasets

Fig.11 Comparison of predictions and ground truth for two models on Electricity and Weather datasets

Fig.12 Comparison of predictions and ground truth for two models on ETTh1 and ETTm1 datasets


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