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We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
This paper presents a real-time capable algorithm for the learning of Gaussian Processes (GP) for submodels. It extends an existing recursive Gaussian Process (RGP) algorithm which requires a measurable output. In many applications,…
This paper introduces a new periodic fractional autoregressive process (PFAR) driven by fractional Gaussian noise (fGn) to model time series of precipitation evapotranspiration. Compared with the similar model in [\emph{Water Resources…
Short-term forecasting of solar photovoltaic energy (PV) production is important for powerplant management. Ideally these forecasts are equipped with error bars, so that downstream decisions can account for uncertainty. To produce…
Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…
Let $P$ be a linear differential operator over $\mathcal{D} \subset \mathbb{R}^d$ and $U = (U_x)_{x \in \mathcal{D}}$ a second order stochastic process. In the first part of this article, we prove a new necessary and sufficient condition…
The accurate prediction of precipitation is important to allow for reliable warnings of flood or drought risk in a changing climate. However, to make trust-worthy predictions of precipitation, at a local scale, is one of the most difficult…
The incomplete sampling of data in complex polarization measurements from radio telescopes negatively affects both the rotation measure (RM) transfer function and the Faraday depth spectra derived from these data. Such gaps in polarization…
Climate projections using data driven machine learning models acting as emulators, is one of the prevailing areas of research to enable policy makers make informed decisions. Use of machine learning emulators as surrogates for…
Improving the accuracy of soil moisture estimation is required for advancing irrigation scheduling and water conservation efforts. Central to this task are soil hydraulic parameters, which govern moisture dynamics but are rarely known…
While the generalized Langevin equation (GLE) is a powerful tool to understand the behavior of complex dissipative systems, driving by external fields renders standard GLE construction workflows invalid. Filtering approaches that separate…
The residential electrical energy scheduling of solar Photovoltaics (PV) is an important research area of the modern green buildings. On the demand side, factors such as building load, and the renewable PV energy resources are integrated…
Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including…
Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…
Accurate prediction of effluent temperature in recharge basins is essential for optimizing the Soil Aquifer Treatment (SAT) process, as temperature directly influences water viscosity and infiltration rates. This study develops and…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…
Time series forecasting is a growing domain with diverse applications. However, changes of the system behavior over time due to internal or external influences are challenging. Therefore, predictions of a previously learned fore-casting…
Gaussian processes regression is applied to augment experimental data of transfer-path analysis (TPA) by known information about the underlying physical properties of the system under investigation. The approach can be used as an…
Using very long baseline interferometry (VLBI) observations at (sub)millimeter wavelengths, the Event Horizon Telescope (EHT) currently achieves the finest angular resolution of any astronomical facility, necessary for imaging the…