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This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of…

Methodology · Statistics 2024-03-14 Guy P Nason , James L. Wei

In multivariate time series forecasting, the Transformer architecture encounters two significant challenges: effectively mining features from historical sequences and avoiding overfitting during the learning of temporal dependencies. To…

Machine Learning · Computer Science 2024-04-30 Han Zhou , Yuntian Chen

With the development of Internet of Things (IoT) systems, precise long-term forecasting method is requisite for decision makers to evaluate current statuses and formulate future policies. Currently, Transformer and MLP are two paradigms for…

Machine Learning · Computer Science 2023-12-12 Li Shen , Yuning Wei , Yangzhu Wang , Hongguang Li

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local…

Machine Learning · Computer Science 2026-01-06 Kuiye Ding , Fanda Fan , Chunyi Hou , Zheya Wang , Lei Wang , Zhengxin Yang , Jianfeng Zhan

Global Climate Models (GCMs) are critical for simulating large-scale climate dynamics, but their coarse spatial resolution limits their applicability in regional studies. Regional Climate Models (RCMs) address this limitation through…

Machine Learning · Computer Science 2026-02-17 Fabio Merizzi , Harilaos Loukos

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…

Machine Learning · Computer Science 2025-10-24 Haonan Yang , Jianchao Tang , Zhuo Li , Long Lan

Conservation Voltage Reduction (CVR) relies on the effective coordination of slow-acting devices, such as OLTCs and CBs, and fast-acting devices, such as SVGs and PV inverters, typically implemented through a hierarchical multi-stage…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Qintao Du , Ran Li , Weiyi Lv , Huan Zhou , Moduo Yu , Jianzhe Liu

Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have…

Machine Learning · Computer Science 2026-03-13 Rajdeep Pathak , Rahul Goswami , Madhurima Panja , Palash Ghosh , Tanujit Chakraborty

Multivariate Time Series (MTS) forecasting involves modeling temporal dependencies within historical records. Transformers have demonstrated remarkable performance in MTS forecasting due to their capability to capture long-term…

Machine Learning · Computer Science 2024-07-17 Yifan Zhang , Rui Wu , Sergiu M. Dascalu , Frederick C. Harris

Transformer has become one of the most popular architectures for multivariate time series (MTS) forecasting. Recent Transformer-based MTS models generally prefer channel-independent structures with the observation that channel independence…

Machine Learning · Computer Science 2024-03-06 Ce Chi , Xing Wang , Kexin Yang , Zhiyan Song , Di Jin , Lin Zhu , Chao Deng , Junlan Feng

In practical time series forecasting, covariates provide rich contextual information that can potentially enhance the forecast of target variables. Although some covariates extend into the future forecasting horizon (e.g., calendar events,…

Machine Learning · Computer Science 2025-08-07 Yosuke Yamaguchi , Issei Suemitsu , Wenpeng Wei

Multivariate time series forecasting is crucial for various applications, such as financial investment, energy management, weather forecasting, and traffic optimization. However, accurate forecasting is challenging due to two main factors.…

Machine Learning · Computer Science 2025-01-13 Xiangfei Qiu , Xingjian Wu , Yan Lin , Chenjuan Guo , Jilin Hu , Bin Yang

Scattering transforms achieve Lipschitz stability and translation invariance, but dense prediction tasks require preserving spatial structure lost in global averaging. We propose Phase-Aware Scattering Encoder-Decoder, which restores this…

Computer Vision and Pattern Recognition · Computer Science 2026-05-26 Ghassen Marrakchi , Basarab Matei

Accurate electricity consumption forecasting is essential for demand management and smart grid operations. This paper introduces a unified deep learning framework that integrates cyclical temporal encoding with hybrid LSTM-CNN architectures…

Machine Learning · Computer Science 2025-12-04 Salim Khazem , Houssam Kanso

In this paper, we present an end-to-end trainable unified multiscale encoder-decoder transformer that is focused on dense prediction tasks in video. The presented Multiscale Encoder-Decoder Video Transformer (MED-VT) uses multiscale…

Computer Vision and Pattern Recognition · Computer Science 2024-09-18 Rezaul Karim , He Zhao , Richard P. Wildes , Mennatullah Siam

Multivariate forecasting with Transformers faces a core scalability challenge: modeling cross-channel dependencies via attention compounds attention's quadratic sequence complexity with quadratic channel scaling, making full cross-channel…

Machine Learning · Computer Science 2026-05-12 Willa Potosnak , Nina Żukowska , Michał Wiliński , Dan Howarth , Ignacy Stępka , Mononito Goswami , Artur Dubrawski

Time series forecasting holds significant importance across various industries, including finance, transportation, energy, healthcare, and climate. Despite the widespread use of linear networks due to their low computational cost and…

Machine Learning · Computer Science 2025-05-02 Chengsen Wang , Qi Qi , Jingyu Wang , Haifeng Sun , Zirui Zhuang , Jianxin Liao

Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with…

Machine Learning · Computer Science 2024-09-17 Peng Chen , Yingying Zhang , Yunyao Cheng , Yang Shu , Yihang Wang , Qingsong Wen , Bin Yang , Chenjuan Guo

In multivariable time series (MTS) forecasting, existing state-of-the-art deep learning approaches tend to focus on autoregressive formulations and often overlook the potential of using exogenous variables in enhancing the prediction of the…

Machine Learning · Computer Science 2025-04-03 Yuxuan Shu , Vasileios Lampos

Time series forecasting is essential for a wide range of real-world applications. Recent studies have shown the superiority of Transformer in dealing with such problems, especially long sequence time series input(LSTI) and long sequence…

Machine Learning · Computer Science 2022-02-15 Li Shen , Yangzhu Wang