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Spherically embedded spatial data are spatially indexed observations whose values naturally reside on or can be equivalently mapped to the unit sphere. Such data are increasingly ubiquitous in fields ranging from geochemistry to demography.…
Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…
Generalising deep models to new data from new centres (termed here domains) remains a challenge. This is largely attributed to shifts in data statistics (domain shifts) between source and unseen domains. Recently, gradient-based…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
Reconstructing 3D scenes with high fidelity and efficiency remains a central pursuit in computer vision and graphics. Recent advances in 3D Gaussian Splatting (3DGS) enable photorealistic rendering with Gaussian primitives, yet the modeling…
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…
We propose a template-driven triangulation framework that embeds raster- or segmentation-derived boundaries into a regular triangular grid for stable PDE discretization on image-derived domains. Unlike constrained Delaunay triangulation…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with…
The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of…
A variational coarse-graining framework for heterogeneous media is developed that allows for a seamless transition from the traditional static scenario to a arbitrary loading conditions, including inertia effects and body forces. The…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
Global variations in terrain appearance raise a major challenge for satellite image analysis, leading to poor model performance when training on locations that differ from those encountered at test time. This remains true even with recent…
Capturing the structure of a data-generating process by means of appropriate inductive biases can help in learning models that generalize well and are robust to changes in the input distribution. While methods that harness spatial and…