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Kernels representing limiting cases of neural network architectures have recently gained popularity. However, the application and performance of these new kernels compared to existing options, such as the Matern kernel, is not well studied.…

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…

Gaussian process (GP) models have been used in a wide range of battery applications, in which different kernels were manually selected with considerable expertise. However, to capture complex relationships in the ever-growing amount of…

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…

Gaussian process (GP) priors are non-parametric generative models with appealing modelling properties for Bayesian inference: they can model non-linear relationships through noisy observations, have closed-form expressions for training and…

High-dimensional optimization is a critical challenge for operating large-scale scientific facilities. We apply a physics-informed Gaussian process (GP) optimizer to tune a complex system by conducting efficient global search. Typical GP…

Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can…

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…

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…

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…

Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

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…

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…

Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…

Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a…

In many areas of the observational and experimental sciences data is scarce. Data observation in high-energy astrophysics is disrupted by celestial occlusions and limited telescope time while data derived from laboratory experiments in…

Many inferential tasks involve fitting models to observed data and predicting outcomes at new covariate values, requiring interpolation or extrapolation. Conventional methods select a single best-fitting model, discarding fits that were…

Earth observation (EO) by airborne and satellite remote sensing and in-situ observations play a fundamental role in monitoring our planet. In the last decade, machine learning and Gaussian processes (GPs) in particular has attained…