Related papers: A hybrid data driven-physics constrained Gaussian …

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…

A majority of experimental disciplines face the challenge of exploring large and high-dimensional parameter spaces in search of new scientific discoveries. Materials science is no exception; the wide variety of synthesis, processing, and…

Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by…

Forward Osmosis (FO) is a promising low-energy membrane separation technology, but challenges in accurately modelling its water flux (Jw) persist due to complex internal mass transfer phenomena. Traditional mechanistic models struggle with…

Gaussian Process (GP) models are popular tools in uncertainty quantification (UQ) because they purport to furnish functional uncertainty estimates that can be used to represent model uncertainty. It is often difficult to state with…

Combining Gaussian processes with the expressive power of deep neural networks is commonly done nowadays through deep kernel learning (DKL). Unfortunately, due to the kernel optimization process, this often results in losing their Bayesian…

In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…

Lost circulation remains a major and costly challenge in drilling operations, often resulting in wellbore instability, stuck pipe, and extended non-productive time. Accurate prediction of fluid loss is therefore essential for improving…

Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…

In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…

This paper presents a new hybrid model for predicting German electricity prices. The algorithm is based on a combination of Gaussian Process Regression (GPR) and Support Vector Regression (SVR). Although GPR is a competent model for…

Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…

Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their…

Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of…

In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of…

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…