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Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to…

Machine Learning · Computer Science 2023-10-18 Gerald Woo , Chenghao Liu , Doyen Sahoo , Akshat Kumar , Steven Hoi

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Numerical Analysis · Mathematics 2022-01-11 Yihao Hu , Tong Zhao , Shixin Xu , Zhiliang Xu , Lizhen Lin

Temporal data, notably time series and spatio-temporal data, are prevalent in real-world applications. They capture dynamic system measurements and are produced in vast quantities by both physical and virtual sensors. Analyzing these data…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

Methodology · Statistics 2025-07-01 Ziyuan Chen , Shunxing Yan , Fang Yao

Multivariate long-term time series forecasting (LTSF) supports critical applications such as traffic-flow management, solar-power scheduling, and electricity-transformer monitoring. The existing LTSF paradigms follow a three-stage pipeline…

Machine Learning · Computer Science 2026-02-03 Hyekyung Yoon , Minhyuk Lee , Imseung Park , Myungjoo Kang

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

Machine Learning · Statistics 2023-03-07 Sebastian Kaltenbach , Phaedon-Stelios Koutsourelakis , Petros Koumoutsakos

Large pre-trained models have been vital in recent advancements in domains like language and vision, making model training for individual downstream tasks more efficient and provide superior performance. However, tackling time-series…

Machine Learning · Computer Science 2024-12-06 Harshavardhan Kamarthi , B. Aditya Prakash

Time series AI is crucial for analyzing dynamic web content, driving a surge of pre-trained large models known for their strong knowledge encoding and transfer capabilities across diverse tasks. However, given their energy-intensive…

Machine Learning · Computer Science 2025-11-03 ChengAo Shen , Ziming Zhao , Hanghang Tong , Dongjin Song , Dongsheng Luo , Qingsong Wen , Jingchao Ni

Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…

Methodology · Statistics 2025-08-19 Andrea Arnold

Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex…

Machine Learning · Computer Science 2024-08-14 Zibo Liu , Zhe Jiang , Shigang Chen

Spatio-temporal forecasting is crucial in transportation, logistics, and supply chain management. However, current methods struggle with large, complex datasets. We propose a dynamic, multi-modal approach that integrates the strengths of…

Machine Learning · Computer Science 2024-08-27 Sagar Srinivas Sakhinana , Geethan Sannidhi , Chidaksh Ravuru , Venkataramana Runkana

Diffusion models have recently emerged as powerful frameworks for generating high-quality images. While recent studies have explored their application to time series forecasting, these approaches face significant challenges in cross-modal…

Computer Vision and Pattern Recognition · Computer Science 2025-02-24 Weilin Ruan , Siru Zhong , Haomin Wen , Yuxuan Liang

Time series forecasting in specialized domains is often constrained by limited data availability, where conventional models typically require large-scale datasets to effectively capture underlying temporal dynamics. To tackle this few-shot…

Machine Learning · Computer Science 2026-02-03 Haonan Shi , Dehua Shuai , Liming Wang , Xiyang Liu , Long Tian

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

Numerical Analysis · Mathematics 2021-04-21 Cheng Chang , Liu Liu , Tieyong Zeng

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…

Machine Learning · Computer Science 2025-02-03 Macheng Shen , Chen Cheng

Time series forecasting (TSF) has long been a crucial task in both industry and daily life. Most classical statistical models may have certain limitations when applied to practical scenarios in fields such as energy, healthcare, traffic,…

Machine Learning · Computer Science 2025-03-14 Xiangjie Kong , Zhenghao Chen , Weiyao Liu , Kaili Ning , Lechao Zhang , Syauqie Muhammad Marier , Yichen Liu , Yuhao Chen , Feng Xia

Multivariate Time Series Forecasting (MTSF) has long been a key research focus. Traditionally, these studies assume a fixed number of variables, but in real-world applications, Cyber-Physical Systems often expand as new sensors are…

Machine Learning · Computer Science 2025-06-03 Minbo Ma , Kai Tang , Huan Li , Fei Teng , Dalin Zhang , Tianrui Li

Multivariate time series forecasting has long received significant attention in real-world applications, such as energy consumption and traffic prediction. While recent methods demonstrate good forecasting abilities, they have three…

Machine Learning · Computer Science 2022-11-24 Ming Jin , Yu Zheng , Yuan-Fang Li , Siheng Chen , Bin Yang , Shirui Pan

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

Machine Learning · Computer Science 2025-12-01 Eduardo Soares , Emilio Vital Brazil , Victor Shirasuna , Breno W. S. R. de Carvalho , Cristiano Malossi

While exogenous variables have a major impact on performance improvement in time series analysis, inter-series correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of…

Machine Learning · Computer Science 2023-09-26 Penglei Gao , Xi Yang , Rui Zhang , Ping Guo , John Y. Goulermas , Kaizhu Huang