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Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…

Machine Learning · Computer Science 2020-08-26 Yuying Liu , J. Nathan Kutz , Steven L. Brunton

Time series forecasting is a significant problem in many applications, e.g., financial predictions and business optimization. Modern datasets can have multiple correlated time series, which are often generated with global (shared)…

Machine Learning · Computer Science 2021-11-10 Ling Chen , Weiqi Chen , Binqing Wu , Youdong Zhang , Bo Wen , Chenghu Yang

Measuring distance or similarity between time-series data is a fundamental aspect of many applications including classification, clustering, and ensembling/alignment. Existing measures may fail to capture similarities among local trends…

Machine Learning · Computer Science 2024-12-20 Ajitesh Srivastava

While most time series are non-stationary, it is inevitable for models to face the distribution shift issue in time series forecasting. Existing solutions manipulate statistical measures (usually mean and std.) to adjust time series…

Machine Learning · Computer Science 2024-07-02 Wei Fan , Kun Yi , Hangting Ye , Zhiyuan Ning , Qi Zhang , Ning An

Time series forecasting has witnessed significant progress with deep learning. While prevailing approaches enhance forecasting performance by modifying architectures or introducing novel enhancement strategies, they often fail to…

Machine Learning · Computer Science 2026-03-31 Haonan Yang , Jianchao Tang , Zhuo Li

Forecasting with multivariate time series, which aims to predict future values given previous and current several univariate time series data, has been studied for decades, with one example being ARIMA. Because it is difficult to measure…

Artificial Intelligence · Computer Science 2020-10-19 Youngjin Park , Deokjun Eom , Byoungki Seo , Jaesik Choi

Dynamic Time Warping (DTW) is an algorithm to align temporal sequences with possible local non-linear distortions, and has been widely applied to audio, video and graphics data alignments. DTW is essentially a point-to-point matching method…

Computer Vision and Pattern Recognition · Computer Science 2016-06-07 Jiaping Zhao , Laurent Itti

Within the field of complicated multivariate time series forecasting (TSF), popular techniques frequently rely on intricate deep learning architectures, ranging from transformer-based designs to recurrent neural networks. However, recent…

Machine Learning · Computer Science 2023-12-25 Aiyinsi Zuo , Haixi Zhang , Zirui Li , Ce Zheng

Deep probabilistic time series forecasting has gained attention for its ability to provide nonlinear approximation and valuable uncertainty quantification for decision-making. However, existing models often oversimplify the problem by…

Machine Learning · Statistics 2024-10-22 Vincent Zhihao Zheng , Seongjin Choi , Lijun Sun

Neural networks have become a powerful tool in pattern recognition and part of their success is due to generalization from using large datasets. However, unlike other domains, time series classification datasets are often small. In order to…

Machine Learning · Computer Science 2020-04-21 Brian Kenji Iwana , Seiichi Uchida

Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate…

Machine Learning · Computer Science 2026-05-26 Yijun Wang , Qiyuan Zhuang , Xiu-Shen Wei

Spatio-temporal time series are widely used in real-world applications, including traffic prediction and weather forecasting. They are sequences of observations over extensive periods and multiple locations, naturally represented as…

Machine Learning · Computer Science 2026-03-12 Taehyung Kwon , Yeonje Choi , Yeongho Kim , Kijung Shin

Long-term time series forecasting (LTSF) offers broad utility in practical settings like energy consumption and weather prediction. Accurately predicting long-term changes, however, is demanding due to the intricate temporal patterns and…

Machine Learning · Computer Science 2025-05-19 Boshi Gao , Qingjian Ni , Fanbo Ju , Yu Chen , Ziqi Zhao

Irregularly sampled time series forecasting, characterized by non-uniform intervals, is prevalent in practical applications. However, previous research have been focused on regular time series forecasting, typically relying on transformer…

Machine Learning · Computer Science 2024-10-01 Byunghyun Kim , Jae-Gil Lee

Numerous deep learning architectures have been developed to accommodate the diversity of time series datasets across different domains. In this article, we survey common encoder and decoder designs used in both one-step-ahead and…

Machine Learning · Statistics 2021-04-28 Bryan Lim , Stefan Zohren

Time series is a special type of sequence data, a sequence of real-valued random variables collected at even intervals of time. The real-world multivariate time series comes with noises and contains complicated local and global temporal…

Machine Learning · Computer Science 2023-11-21 Site Mo , Haoxin Wang , Bixiong Li , Songhai Fan , Yuankai Wu , Xianggen Liu

Predicting when and where events will occur in cities, like taxi pick-ups, crimes, and vehicle collisions, is a challenging and important problem with many applications in fields such as urban planning, transportation optimization and…

Machine Learning · Statistics 2019-06-24 Maya Okawa , Tomoharu Iwata , Takeshi Kurashima , Yusuke Tanaka , Hiroyuki Toda , Naonori Ueda

Real-world time series typically exhibit complex temporal variations, making the time series classification task notably challenging. Recent advancements have demonstrated the potential of multi-scale analysis approaches, which provide an…

Artificial Intelligence · Computer Science 2025-07-25 Zhipeng Liu , Peibo Duan , Binwu Wang , Xuan Tang , Qi Chu , Changsheng Zhang , Yongsheng Huang , Bin Zhang

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While L\'evy stable distributions offer a natural framework for…

Machine Learning · Computer Science 2026-05-15 Yang Yang , Du Yin , Hao Xue , Flora Salim

Multi-step forecasting (MSF) in time-series, the ability to make predictions multiple time steps into the future, is fundamental to almost all temporal domains. To make such forecasts, one must assume the recursive complexity of the…

Machine Learning · Computer Science 2024-02-14 Riku Green , Grant Stevens , Telmo de Menezes e Silva Filho , Zahraa Abdallah