Related papers: Mesh density functions based on local bandwidth ap…
Moving mesh methods are designed to redistribute a mesh in a regular way. This applied problem can be considered to overlap with the problem of finding a diffeomorphic mapping between density measures. In applications, an off-the-shelf grid…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
Practical applications of kernel methods often use variable bandwidth kernels, also known as self-tuning kernels, however much of the current theory of kernel based techniques is only applicable to fixed bandwidth kernels. In this paper, we…
We study adaptive mesh selection for the solution of systems of initial value problems. The goal is a rigorous theoretical analysis of potential advantages of adaption. For an optimal method in the sense of the speed of convergence, we…
It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same…
We apply a range of density-functional-theory-based methods capable of describing van der Waals interactions to weakly bonded layered solids in order to investigate their accuracy for extended systems. The methods under investigation are…
We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of a space-time signal designed to well-approximate solutions to partial differential…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to…
We consider mesh functions which are discrete convex in the sense that their central second order directional derivatives are positive. Analogous to the case of a uniformly bounded sequence of convex functions, we prove that the uniform…
While elastic metasurfaces offer a remarkable and very effective approach to the subwalength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. This work introduces…
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…
Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…
In this paper a numerical meshless method for solving the radiative transfer equations in a slab medium with an isotropic scattering is considered. The method is based on radial basis functions to approximate the solution of an…
We propose a new method for the construction of layer-adapted meshes for singularly perturbed differential equations (SPDEs), based on mesh partial differential equations (MPDEs) that incorporate \emph{a posteriori} solution information.…
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in $H^1$-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular…
Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…