Related papers: Sparse Gaussian processes for solving nonlinear PD…

Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such…

Gaussian processes (GPs) offer appealing properties but are costly to train at scale. Sparse variational GP (SVGP) approximations reduce cost yet still rely on Cholesky decompositions of kernel matrices, ill-suited to low-precision,…

Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both…

Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…

Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent…

We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement…

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…

In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Radial basis functions have become a popular tool for approximation and solution of partial differential equations (PDEs). The recently proposed multilevel sparse interpolation with kernels (MuSIK) algorithm proposed in \cite{Georgoulis}…

This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…

Partial differential equations (PDEs) are widely used for the description of physical and engineering phenomena. Some key parameters involved in PDEs, which represent certain physical properties with important scientific interpretations,…