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Active learning of Gaussian process (GP) surrogates has been useful for optimizing experimental designs for physical/computer simulation experiments, and for steering data acquisition schemes in machine learning. In this paper, we develop a…

Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…

Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…

This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…

We develop a general framework for piecewise deterministic Markov process (PDMP) samplers that enables efficient Bayesian inference in non-linear inverse problems with expensive likelihoods. The key ingredient is a surrogate-assisted…

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…

Stochastic simulations such as large-scale, spatiotemporal, age-structured epidemic models are computationally expensive at fine-grained resolution. While deep surrogate models can speed up the simulations, doing so for stochastic…

The Linear Parameter-Varying (LPV) framework enables the construction of surrogate models of complex nonlinear and high-dimensional systems, facilitating efficient stability and performance analysis together with controller design. Despite…

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

Simulations of optical quantum systems are essential for the development of quantum technologies. However, these simulations are often computationally intensive, especially when repeated evaluations are required for data fitting, parameter…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

Gaussian processes (GPs) are powerful non-parametric function estimators. However, their applications are largely limited by the expensive computational cost of the inference procedures. Existing stochastic or distributed synchronous…

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…

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 complex and computationally expensive nature of landscape evolution models pose significant challenges in the inference and optimisation of unknown parameters. Bayesian inference provides a methodology for estimation and uncertainty…

We propose automated augmented conjugate inference, a new inference method for non-conjugate Gaussian processes (GP) models. Our method automatically constructs an auxiliary variable augmentation that renders the GP model conditionally…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…