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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

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Numerical Analysis · Mathematics 2025-01-28 Qi Wang , Yuan Mi , Haoyun Wang , Yi Zhang , Ruizhi Chengze , Hongsheng Liu , Ji-Rong Wen , Hao Sun

Rapid developments in advanced sensing and imaging have significantly enhanced information visibility, opening opportunities for predictive modeling of complex dynamic systems. However, sensing signals acquired from such complex systems are…

Machine Learning · Statistics 2025-05-02 Xizhuo Zhang , Bing Yao

The last decade has seen an explosion in data sources available for the monitoring and prediction of environmental phenomena. While several inferential methods have been developed that make predictions on the underlying process by combining…

Methodology · Statistics 2023-03-06 Eun-Hye Yoo , Andrew Zammit-Mangion , Michael G. Chipeta

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

Machine Learning · Statistics 2021-02-17 Hao Xu , Haibin Chang , Dongxiao Zhang

Accurate and interpretable air pollution forecasting is crucial for public health, but most models face a trade-off between performance and interpretability. This study proposes a physics-guided, interpretable-by-design spatiotemporal…

Machine Learning · Computer Science 2026-01-23 Zhiguo Zhang , Xiaoliang Ma , Daniel Schlesinger

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Machine Learning · Statistics 2026-01-09 James Rice

This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…

Computational Engineering, Finance, and Science · Computer Science 2020-06-09 Raymond Leung

Accurately predicting spatio-temporal network traffic is essential for dynamically managing computing resources in modern communication systems and minimizing energy consumption. Although spatio-temporal traffic prediction has received…

Machine Learning · Computer Science 2026-03-24 Xintong Wang , Haihan Nan , Ruidong Li , Huaming Wu

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific…

This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…

Quantitative Methods · Quantitative Biology 2025-01-22 Nathalie Wehlitz , Mohsen Sadeghi , Alberto Montefusco , Christof Schütte , Grigorios A. Pavliotis , Stefanie Winkelmann

Spatio-temporal problems exist in many areas of knowledge and disciplines ranging from biology to engineering and physics. However, solution strategies based on classical statistical techniques often fall short due to the large number of…

Applications · Statistics 2017-06-15 Emil B. Iversen , Rune Juhl , Jan K. Møller , Jan Kleissl , Henrik Madsen , Juan M. Morales

The machine learning methods for data-driven identification of partial differential equations (PDEs) are typically defined for a given number of spatial dimensions and a choice of coordinates the data have been collected in. This dependence…

Machine Learning · Computer Science 2025-10-07 Trung V. Phan , George A. Kevrekidis , Soledad Villar , Yannis G. Kevrekidis , Juan M. Bello-Rivas

Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…

Fluid Dynamics · Physics 2017-09-12 A. Rupe , J. P. Crutchfield , K. Kashinath , Prabhat

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Machine Learning · Computer Science 2025-02-14 Alessandro Longhi , Danny Lathouwers , Zoltán Perkó

Medical vision-language pre-training methods mainly leverage the correspondence between paired medical images and radiological reports. Although multi-view spatial images and temporal sequences of image-report pairs are available in…

Artificial Intelligence · Computer Science 2024-05-31 Jinxia Yang , Bing Su , Wayne Xin Zhao , Ji-Rong Wen

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack…

Machine Learning · Computer Science 2026-05-25 Jinglin Li , Jun Tan , QI Fang , Ning Gui

Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and…

Applications · Statistics 2014-11-19 Yang Liu , Philip Kokic

Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g.,…

Machine Learning · Statistics 2022-06-07 Christopher K. Wikle , Andrew Zammit-Mangion

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…

Numerical Analysis · Mathematics 2021-04-26 Stefanos Nikolopoulos , Ioannis Kalogeris , Vissarion Papadopoulos