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Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we…

Machine Learning · Statistics 2026-02-24 Kurt Butler , Guanchao Feng , Tong Chen , Petar Djuric

Due to its state-of-the-art estimation performance complemented by rigorous and non-conservative uncertainty bounds, Gaussian process regression is a popular tool for enhancing dynamical system models and coping with their inaccuracies.…

Systems and Control · Electrical Eng. & Systems 2025-02-05 Anna Scampicchio , Elena Arcari , Amon Lahr , Melanie N. Zeilinger

We propose a nonlinear ocean forecasting technique based on a combination of genetic algorithms and empirical orthogonal function (EOF) analysis. The method is used to forecast the space-time variability of the sea surface temperature (SST)…

Accurate analysis of global oceanographic data, such as temperature and salinity profiles from the Argo program, requires geostatistical models capable of capturing complex spatial dependencies. This study introduces Gaussian and…

Methodology · Statistics 2025-06-04 Damilya Saduakhas , David Bolin , Xiaotian Jin , Alexandre B. Simas , Jonas Wallin

Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…

Machine Learning · Computer Science 2021-12-16 Yuya Yoshikawa , Tomoharu Iwata

The world ocean plays a key role in redistributing heat in the climate system and hence in regulating Earth's climate. Yet statistical analysis of ocean heat transport suffers from partially incomplete large-scale data intertwined with…

Applications · Statistics 2022-07-19 Beomjo Park , Mikael Kuusela , Donata Giglio , Alison Gray

The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governing equations to determine output quantities of interest. In…

Optimization and Control · Mathematics 2015-11-05 Tobin Isaac , Noemi Petra , Georg Stadler , Omar Ghattas

The reserve of crude oil in the Arctic area is abundant. Ice melting is making it possible to have intermediate access to the Arctic crude oil and its transportation. A novel compositional data's grey model is proposed in this paper to…

Applications · Statistics 2020-11-04 Pan Qilong , Yin Jieru , Xiao Xinping

The present work is aimed to examine the potential of advanced machine learning strategies to predict the monthly rainfall (precipitation) for the Indus Basin, using climatological variables such as air temperature, geo-potential height,…

Signal Processing · Electrical Eng. & Systems 2019-01-27 Hamidreza Ghasemi Damavandi , Reepal Shah

In applications of climate information, coarse-resolution climate projections commonly need to be downscaled to a finer grid. One challenge of this requirement is the modeling of sub-grid variability and the spatial and temporal dependence…

The state of the art for physical hazard prediction from weather and climate requires expensive km-scale numerical simulations driven by coarser resolution global inputs. Here, a generative diffusion architecture is explored for downscaling…

Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…

Methodology · Statistics 2025-10-02 Alexis Romero , Kyle Cranmer , Daniel Whiteson

Heteroscedastic Gaussian process regression, based on the concept of chained Gaussian processes, is used to build surrogates to predict site-specific loads on an offshore wind turbine. Stochasticity in the inflow turbulence and irregular…

Applications · Statistics 2022-06-15 Deepali Singh , Richard P. Dwight , Kasper Laugesen , Laurent Beaudet , Axelle Viré

Weather forecasting requires not only accuracy but also the ability to perform probabilistic prediction. However, deterministic weather forecasting methods do not support probabilistic predictions, and conversely, probabilistic models tend…

Computer Vision and Pattern Recognition · Computer Science 2023-12-06 Donggeun Yoon , Minseok Seo , Doyi Kim , Yeji Choi , Donghyeon Cho

We consider multi-task regression models where the observations are assumed to be a linear combination of several latent node functions and weight functions, which are both drawn from Gaussian process priors. Driven by the problem of…

Machine Learning · Statistics 2018-12-05 Astrid Dahl , Edwin V. Bonilla

Utilizing the information in observations of a complex system to make accurate predictions through a quantitative model when observations are completed at time $T$, requires an accurate estimate of the full state of the model at time $T$.…

Chaotic Dynamics · Physics 2014-05-13 Zhe An , Daniel Rey , Henry D. I. Abarbanel

In this paper, we propose a new method to forecast the drift of objects in near coastal ocean on a period of several weeks. The proposed approach consists in estimating the probability of events linked to the drift using Monte Carlo…

Numerical Analysis · Mathematics 2007-05-23 Pierre Ailliot , Emmanuel Frenod , Valerie Monbet

A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…

Data Analysis, Statistics and Probability · Physics 2019-09-10 Christopher G. Albert

Global medium-range weather forecasting is critical to decision-making across many social and economic domains. Traditional numerical weather prediction uses increased compute resources to improve forecast accuracy, but cannot directly use…

As urbanization and climate change progress, urban heat island effects are becoming more frequent and severe. To formulate effective mitigation plans, cities require detailed air temperature data. However, predictive analytics methods based…

Computer Vision and Pattern Recognition · Computer Science 2025-09-23 David Kreismann
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