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In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for…
The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example of such fields are Whittle-Mat\'ern fields on bounded…
In this paper, we first propose a coupled numerical model of unsaturated flow in soils and plant root water uptake. The Richards equation and different formulations are used in the developed numerical model to describe infiltration in root…
Fractional Gaussian fields provide a rich class of spatial models and have a long history of applications in multiple branches of science. However, estimation and inference for fractional Gaussian fields present significant challenges. This…
Recent advancements in remote sensing technology have resulted in petabytes of data in raster format. This data is often processed in combination with high resolution vector data that represents, for example, city boundaries. One of the…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
Reconstructing the high-fidelity surface from multi-view images, especially sparse images, is a critical and practical task that has attracted widespread attention in recent years. However, existing methods are impeded by the memory…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
Simulating high-resolution Synthetic Aperture Radar (SAR) images in complex scenes has consistently presented a significant research challenge. The development of a microwave-domain surface scattering model and its reversibility are poised…
A function approximation method is developed that aims to approximate a function in a small neighborhood of a state that travels within a compact set. The development is based on the theory of universal reproducing kernel Hilbert spaces…
Sampling-based algorithms, such as Rapidly Exploring Random Trees (RRT) and its variants, have been used extensively for motion planning. Control barrier functions (CBFs) have been recently proposed to synthesize controllers for…
Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…
Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of…
Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set)…
This paper presents a comprehensive experimental validation of a recently developed Ray Deflection Function (RDF) approach, which offers a new framework for modeling surface roughness effects in optical systems. Through detailed geometrical…
Conditional Random Fields (CRF) have been widely used in a variety of computer vision tasks. Conventional CRFs typically define edges on neighboring image pixels, resulting in a sparse graph such that efficient inference can be performed.…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
Common to many analysis pipelines in lattice gauge theory and the broader scientific discipline is the need to fit a semi-parametric model to data. We propose a fit method that utilizes a radial basis function network to approximate the…