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The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…

Computational Physics · Physics 2007-05-23 Weinan E , Bjorn Engquist

Collecting multiple longitudinal measurements and time-to-event outcomes is a common practice in clinical and epidemiological studies, often focusing on exploring associations between them. Joint modeling is the standard analytical tool for…

Methodology · Statistics 2024-12-10 Taban Baghfalaki , Reza Hashemi , Catherine Helmer , Helene Jacqmin-Gadda

Large Language Models (LLMs) offer the potential for automatic time series analysis and reporting, which is a critical task across many domains, spanning healthcare, finance, climate, energy, and many more. In this paper, we propose a…

Computation and Language · Computer Science 2024-10-10 Elizabeth Fons , Rachneet Kaur , Soham Palande , Zhen Zeng , Tucker Balch , Manuela Veloso , Svitlana Vyetrenko

Time series forecasting plays a pivotal role in a wide range of applications, including weather prediction, healthcare, structural health monitoring, predictive maintenance, energy systems, and financial markets. While models such as LSTM,…

Machine Learning · Computer Science 2026-04-03 Qianying Cao , Shanqing Liu , Alan John Varghese , Jerome Darbon , Michael Triantafyllou , George Em Karniadakis

Groundwater level prediction is an applied time series forecasting task with important social impacts to optimize water management as well as preventing some natural disasters: for instance, floods or severe droughts. Machine learning…

Machine Learning · Computer Science 2022-09-29 Michael Franklin Mbouopda , Thomas Guyet , Nicolas Labroche , Abel Henriot

Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models. Capturing patterns both within and between temporal and multivariate components is crucial for reliable…

Machine Learning · Computer Science 2025-11-21 Maurice Kraus , Felix Divo , Devendra Singh Dhami , Kristian Kersting

Spatio-temporal forecasting in various domains, like traffic prediction and weather forecasting, is a challenging endeavor, primarily due to the difficulties in modeling propagation dynamics and capturing high-dimensional interactions among…

Machine Learning · Computer Science 2024-05-29 Xiaobei Zou , Luolin Xiong , Yang Tang , Jürgen Kurths

This paper addresses a common problem with hierarchical time series. Time series analysis demands the series for a model to be the sum of multiple series at corresponding sub-levels. Hierarchical Time Series presents a two-fold problem.…

Applications · Statistics 2022-12-27 Seema Sangari , Xinyan Zhang

Amounts of historical data collected increase and business intelligence applicability with automatic forecasting of time series are in high demand. While no single time series modeling method is universal to all types of dynamics,…

Machine Learning · Statistics 2022-04-18 Evaldas Vaiciukynas , Paulius Danenas , Vilius Kontrimas , Rimantas Butleris

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale…

Statistics Theory · Mathematics 2009-11-11 G. A. Pavliotis , A. M. Stuart

The non-stationary nature of real-world Multivariate Time Series (MTS) data presents forecasting models with a formidable challenge of the time-variant distribution of time series, referred to as distribution shift. Existing studies on the…

Machine Learning · Computer Science 2024-07-19 Hui He , Qi Zhang , Kun Yi , Xiaojun Xue , Shoujin Wang , Liang Hu , Longbing Cao

We study adaptive pooling under predictive heterogeneity in high-dimensional multivariate time series forecasting, where global models improve statistical efficiency but may fail to capture heterogeneous predictive structure, while naive…

Methodology · Statistics 2026-04-16 Ziling Ma , Ángel López Oriona , Hernando Ombao , Ying Sun

Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model…

Hardware Architecture · Computer Science 2017-05-16 Bing Li , Ning Chen , Manuel Schmidt , Walter Schneider , Ulf Schlichtmann

Time series forecasting remains a challenging task, particularly in the context of complex multiscale temporal patterns. This study presents LLM-Mixer, a framework that improves forecasting accuracy through the combination of multiscale…

Occupancy models involve both the probability a site is occupied and the probability occupancy is detected. The homogeneous occupancy model, where the occupancy and detection probabilities are the same at each site, admits an orthogonal…

Methodology · Statistics 2018-08-10 N. Karavarsamis , R. M. Huggins

Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a…

Social and Information Networks · Computer Science 2024-09-17 Yifan Huang , Clayton Barham , Eric Page , PK Douglas

Improvement of time series forecasting accuracy through combining multiple models is an important as well as a dynamic area of research. As a result, various forecasts combination methods have been developed in literature. However, most of…

Artificial Intelligence · Computer Science 2013-02-28 Ratnadip Adhikari , R. K. Agrawal

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS)…

Machine Learning · Computer Science 2023-10-10 Fan Zhou , Chen Pan , Lintao Ma , Yu Liu , Shiyu Wang , James Zhang , Xinxin Zhu , Xuanwei Hu , Yunhua Hu , Yangfei Zheng , Lei Lei , Yun Hu

Spatiotemporal forecasting is critical in applications such as traffic prediction, climate modeling, and environmental monitoring. However, the prevalence of missing data in real-world sensor networks significantly complicates this task. In…

Machine Learning · Computer Science 2025-01-20 Muhammad Bilal , Luis Carretero Lopez

Time series methods are of fundamental importance in virtually any field of science that deals with temporally structured data. Recently, there has been a surge of deterministic transformer models with time series-specific architectural…

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