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Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension,…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…
Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the…
Simulating non-wetting fluid invasion in volumetric images of porous materials is of broad interest in applications as diverse as electrochemical devices and CO2 sequestration. Among available methods, image-based algorithms offer much…
We present Neural Kernel Fields: a novel method for reconstructing implicit 3D shapes based on a learned kernel ridge regression. Our technique achieves state-of-the-art results when reconstructing 3D objects and large scenes from sparse…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
Reactive flows are important part of numerous technical and environmental processes. Often monitoring the flow and species concentrations within the domain is not possible or is expensive, in contrast, outlet concentration is…
One-dimensional adaptive Fourier decomposition, abbreviated as 1-D AFD, or AFD, is an adaptive representation of a physically realizable signal into a linear combination of parameterized Szeg\"o and higher order Szeg\"o kernels of the…
We analyze the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data…
Generative models which use explicit density modeling (e.g., variational autoencoders, flow-based generative models) involve finding a mapping from a known distribution, e.g. Gaussian, to the unknown input distribution. This often requires…
Porous media are ubiquitous in both nature and engineering applications, thus their modelling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of such medium, obtaining its…
We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of…
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…
Compressive sampling (CoSa) has provided many methods for signal recovery of signals compressible with respect to an orthonormal basis. However, modern applications have sparked the emergence of approaches for signals not sparse in an…
We propose an active 3D mapping method for depth sensors, which allow individual control of depth-measuring rays, such as the newly emerging solid-state lidars. The method simultaneously (i) learns to reconstruct a dense 3D occupancy map…
Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, methods for drag prediction rely on experiments or numerical simulations which are costly and time-consuming. Data-driven…
Kernel based approximation offers versatile tools for high-dimensional approximation, which can especially be leveraged for surrogate modeling. For this purpose, both "knot insertion" and "knot removal" approaches aim at choosing a suitable…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…