Related papers: Reconstructing Blood Flow in Data-Poor Regimes: A …

Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…

Generating computational anatomical models of cerebrovascular networks is vital for improving clinical practice and understanding brain oxygen transport. This is achieved by extracting graph-based representations based on pre-mapping of…

In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…

One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…

The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

In this paper we present a novel method for efficient and effective 3D surface reconstruction in open scenes. Existing Neural Radiance Fields (NeRF) based works typically require extensive training and rendering time due to the adopted…

Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood…

This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…

We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike,…

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…

We propose a novel class of Gaussian processes (GPs) whose spectra have compact support, meaning that their sample trajectories are almost-surely band limited. As a complement to the growing literature on spectral design of covariance…

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…

Modelling robot dynamics accurately is essential for control, motion optimisation and safe human-robot collaboration. Given the complexity of modern robotic systems, dynamics modelling remains non-trivial, mostly in the presence of…

Accurate prediction of cerebral blood flow is essential for the diagnosis and treatment of cerebrovascular diseases. Traditional computational methods, however, often incur significant computational costs, limiting their practicality in…

The reconstruction of physically valid transport fields from subject-specific imaging data is a fundamental challenge in image-based computational modeling due to measurement noise, modeling uncertainties and discretization errors. Without…

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…

Deep kernel learning refers to a Gaussian process that incorporates neural networks to improve the modelling of complex functions. We present a method that makes this approach feasible for problems where the data consists of line integral…