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Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed…

Applications · Statistics 2016-05-25 Stefan Siegert , Philip G. Sansom , Robin Williams

While numerical weather prediction (NWP) models are essential for forecasting thunderstorms hours in advance, NWP uncertainty, which increases with lead time, limits the predictability of thunderstorm occurrence. This study investigates how…

Atmospheric and Oceanic Physics · Physics 2025-02-20 Kianusch Vahid Yousefnia , Tobias Bölle , Christoph Metzl

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…

Computational Engineering, Finance, and Science · Computer Science 2023-06-06 Abhinav Gupta , Pierre F. J. Lermusiaux

Data-driven weather models have recently achieved state-of-the-art performance, yet progress has plateaued in recent years. This paper introduces a Mixture of Experts (MoWE) approach as a novel paradigm to overcome these limitations, not by…

While machine learning-based weather prediction (MLWP) has achieved significant advancements, research on assimilating real observations or ensemble forecasts within MLWP models remains limited. We introduce ClimaX-LETKF, the first purely…

Machine Learning · Computer Science 2025-12-17 Akira Takeshima , Kenta Shiraishi , Atsushi Okazaki , Tadashi Tsuyuki , Shunji Kotsuki

In modern computer experiment applications, one often encounters the situation where various models of a physical system are considered, each implemented as a simulator on a computer. An important question in such a setting is determining…

Methodology · Statistics 2023-05-08 John C. Yannotty , Thomas J. Santner , Richard J. Furnstahl , Matthew T. Pratola

Deep Ensembles are a simple, reliable, and effective method of improving both the predictive performance and uncertainty estimates of deep learning approaches. However, they are widely criticised as being computationally expensive, due to…

Machine Learning · Computer Science 2023-10-10 Guoxuan Xia , Christos-Savvas Bouganis

A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…

Methodology · Statistics 2026-04-28 Matteo Amestoy , R. Vermeulen , Mark A. van de Wiel , Wessel N. van Wieringen

Short-term load forecasting for AI data centers presents new challenges because it is computing-driven, with heterogeneous job arrivals, sizes, and durations exhibiting bursty, non-stationary dynamics. Compared with traditional load types,…

Systems and Control · Electrical Eng. & Systems 2026-05-01 Ziying Wang , Ying Zhang , Lei Wang , Yuzhang Lin

We introduce a score-filter-enhanced data assimilation framework designed to reduce predictive uncertainty in machine learning (ML) models for data-driven dynamical system forecasting. Machine learning serves as an efficient numerical model…

Dynamical Systems · Mathematics 2026-03-17 Jingqiao Tang , Ryan Bausback , Feng Bao , Guannan Zhang , Phuoc-Toan Huynh

Anomaly Detection in multivariate time series is a major problem in many fields. Due to their nature, anomalies sparsely occur in real data, thus making the task of anomaly detection a challenging problem for classification algorithms to…

Machine Learning · Computer Science 2023-08-08 Anastasios Iliopoulos , John Violos , Christos Diou , Iraklis Varlamis

Accurately quantifying uncertainty in predictions and projections arising from irreducible internal climate variability is critical for informed decision making. Such uncertainty is typically assessed using ensembles produced with physics…

Machine Learning · Computer Science 2026-02-09 Parsa Gooya , Reinel Sospedra-Alfonso , Johannes Exenberger

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

Machine Learning · Computer Science 2025-03-12 Christof Schötz , Alistair White , Maximilian Gelbrecht , Niklas Boers

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models…

Machine Learning · Computer Science 2024-08-12 Xiaohui Zhong , Lei Chen , Hao Li , Jun Liu , Xu Fan , Jie Feng , Kan Dai , Jing-Jia Luo , Jie Wu , Bo Lu

Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for…

Methodology · Statistics 2026-02-24 Yonggwan Shin , Yire Shin , Jeong-Soo Park

Time series forecasting is a challenging problem particularly when a time series expresses multiple seasonality, nonlinear trend and varying variance. In this work, to forecast complex time series, we propose ensemble learning which is…

Machine Learning · Computer Science 2022-03-03 Grzegorz Dudek

Science-based simulation tools such as Finite Element (FE) models are routinely used in scientific and engineering applications. While their success is strongly dependent on our understanding of underlying governing physical laws, they…

Machine Learning · Computer Science 2021-03-31 Navid Zobeiry , Anoush Poursartip

This research introduces a novel methodology for optimizing Bayesian Neural Networks (BNNs) by synergistically integrating them with traditional machine learning algorithms such as Random Forests (RF), Gradient Boosting (GB), and Support…

Machine Learning · Computer Science 2023-10-10 Peiwen Tan

We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…

Machine Learning · Statistics 2023-10-24 Veit David Wild , Sahra Ghalebikesabi , Dino Sejdinovic , Jeremias Knoblauch

Meteorological ensembles are a collection of scenarios for future weather delivered by a meteorological center. Such ensembles form the main source of valuable information for probabilistic forecasting which aims at producing a predictive…

Applications · Statistics 2019-03-07 Marie Courbariaux , Pierre Barbillon , Luc Perreault , Éric Parent