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Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to…

Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring…

Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…

Recently, 3D Gaussian Splatting has emerged as a promising approach for modeling 3D scenes using mixtures of Gaussians. The predominant optimization method for these models relies on backpropagating gradients through a differentiable…

Finite element model updating utilizing frequency response functions as inputs is an important procedure in structural analysis, design and control. This paper presents a highly efficient framework that is built upon Gaussian process…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Deep Gaussian processes (DGP) have appealing Bayesian properties, can handle variable-sized data, and learn deep features. Their limitation is that they do not scale well with the size of the data. Existing approaches address this using a…

Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…

Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…

Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…

The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility…

Gaussian processes are flexible, probabilistic, non-parametric models widely used in machine learning and statistics. However, their scalability to large data sets is limited by computational constraints. To overcome these challenges, we…

Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…

Gaussian Processes (GPs) offer an attractive method for regression over small, structured and correlated datasets. However, their deployment is hindered by computational costs and limited guidelines on how to apply GPs beyond simple…