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The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism…

Machine Learning · Computer Science 2023-05-09 Riccardo Ughi , Eugenio Lomurno , Matteo Matteucci

Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with…

Machine Learning · Computer Science 2026-01-29 Wei Li

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 the complex landscape of multivariate time series forecasting, achieving both accuracy and interpretability remains a significant challenge. This paper introduces the Fuzzy Transformer (Fuzzformer), a novel recurrent neural network…

Artificial Intelligence · Computer Science 2025-10-02 Miha Ožbot , Igor Škrjanc , Vitomir Štruc

In this paper, we propose an interpretable LSTM recurrent neural network, i.e., multi-variable LSTM for time series with exogenous variables. Currently, widely used attention mechanism in recurrent neural networks mostly focuses on the…

Machine Learning · Computer Science 2018-04-17 Tian Guo , Tao Lin , Yao Lu

Autoregressive attention-based time series forecasting (TSF) has drawn increasing interest, with mechanisms like linear attention sometimes outperforming vanilla attention. However, deeper Transformer architectures frequently misalign with…

Machine Learning · Computer Science 2026-02-06 Jiecheng Lu , Shihao Yang

Multivariate long-term time series forecasting is of great application across many domains, such as energy consumption and weather forecasting. With the development of transformer-based methods, the performance of multivariate long-term…

Machine Learning · Computer Science 2023-05-29 Zheng Sun , Yi Wei , Wenxiao Jia , Long Yu

Multivariate time series forecasting has been widely used in various practical scenarios. Recently, Transformer-based models have shown significant potential in forecasting tasks due to the capture of long-range dependencies. However,…

Machine Learning · Computer Science 2023-02-10 Zhe Li , Zhongwen Rao , Lujia Pan , Zenglin Xu

We present a conformal prediction method for time series using the Transformer architecture to capture long-memory and long-range dependencies. Specifically, we use the Transformer decoder as a conditional quantile estimator to predict the…

Machine Learning · Computer Science 2024-06-11 Junghwan Lee , Chen Xu , Yao Xie

In many scientific problems such as video surveillance, modern genomics, and finance, data are often collected from diverse measurements across time that exhibit time-dependent heterogeneous properties. Thus, it is important to not only…

Machine Learning · Statistics 2022-10-10 Lin Qiu , Vernon M. Chinchilli , Lin Lin

This study proposes a unified forecasting framework for high-dimensional multi-task time series to meet the prediction demands of cloud native backend systems operating under highly dynamic loads, coupled metrics, and parallel tasks. The…

Machine Learning · Computer Science 2025-12-25 Zixiao Huang , Jixiao Yang , Sijia Li , Chi Zhang , Jinyu Chen , Chengda Xu

An output feedback model predictive control (MPC) framework with adaptive tubes is proposed for linear time-invariant systems subject to parametric and additive uncertainties. An adaptive observer provides point estimates of the system…

Systems and Control · Electrical Eng. & Systems 2026-05-25 Anchita Dey , Shubhendu Bhasin

Spatial-temporal data modeling aims to mine the underlying spatial relationships and temporal dependencies of objects in a system. However, most existing methods focus on the modeling of spatial-temporal data in a single mode, lacking the…

Machine Learning · Computer Science 2023-08-23 Zihang Liu , Le Yu , Tongyu Zhu , Leiei Sun

Transformer-based models have greatly pushed the boundaries of time series forecasting recently. Existing methods typically encode time series data into $\textit{patches}$ using one or a fixed set of patch lengths. This, however, could…

Machine Learning · Computer Science 2024-02-09 Linfeng Du , Ji Xin , Alex Labach , Saba Zuberi , Maksims Volkovs , Rahul G. Krishnan

Time series forecasting is essential for many practical applications, with the adoption of transformer-based models on the rise due to their impressive performance in NLP and CV. Transformers' key feature, the attention mechanism,…

Machine Learning · Computer Science 2024-02-09 PeiSong Niu , Tian Zhou , Xue Wang , Liang Sun , Rong Jin

Machine learning is permeating every conceivable domain to promote data-driven decision support. The focus is often on advanced black-box models due to their assumed performance advantages, whereas interpretable models are often associated…

Machine Learning · Computer Science 2024-09-24 Sven Kruschel , Nico Hambauer , Sven Weinzierl , Sandra Zilker , Mathias Kraus , Patrick Zschech

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…

Optimization and Control · Mathematics 2021-11-18 Joseph E. Gaudio , Anuradha M. Annaswamy , Eugene Lavretsky , Michael A. Bolender

Data-driven convective parameterization aims to accurately represent convective adjustments to large-scale forcings in a computationally economic manner. While previous studies have demonstrated success using various model architectures,…

Atmospheric and Oceanic Physics · Physics 2025-06-02 Qiyu Song , Zhiming Kuang

In the era of information explosion, spatio-temporal data mining serves as a critical part of urban management. Considering the various fields demanding attention, e.g., traffic state, human activity, and social event, predicting multiple…

Artificial Intelligence · Computer Science 2023-09-19 Zijian Zhang , Xiangyu Zhao , Qidong Liu , Chunxu Zhang , Qian Ma , Wanyu Wang , Hongwei Zhao , Yiqi Wang , Zitao Liu

Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…

Methodology · Statistics 2017-11-15 Elynn Yi Chen , Qiwei Yao , Rong Chen