Related papers: Tensor Basis Gaussian Process Models of Hyperelast…

Skin tension plays a pivotal role in clinical settings, it affects scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension or its natural pre-stretch. This…

In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

We present a new polynomial-free prolongation scheme for Adaptive Mesh Refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based…

In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…

Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…

We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic…

Multi-output Gaussian process regression has become an important tool in uncertainty quantification, for building emulators of computationally expensive simulators, and other areas such as multi-task machine learning. We present a holistic…

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

Hyperelastic materials models are well established to describe the non-linear stress-strain relations of elastomers. In this paper, a polyurethane adhesive is considered as an exemplary material and subjected to tensile, compressive and…

We study posterior contraction rates for a class of deep Gaussian process priors applied to the nonparametric regression problem under a general composition assumption on the regression function. It is shown that the contraction rates can…

Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…

Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…

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…

Physical modeling of robotic system behavior is the foundation for controlling many robotic mechanisms to a satisfactory degree. Mechanisms are also typically designed in a way that good model accuracy can be achieved with relatively simple…

Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…

The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster…