Related papers: A universal preprocessing algorithm of average ker…
In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new…
We calculate Gaussian averages of arbitrary exponentials of the matrix variable $X$ with the help of superintegrability, which provides explicit expressions for Schur averages. As in the simpler cases the answer is expressed in terms of…
A global approximation method of Nystr\"om type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first…
With the rise of big data sets, the popularity of kernel methods declined and neural networks took over again. The main problem with kernel methods is that the kernel matrix grows quadratically with the number of data points. Most attempts…
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The…
Global solutions to the multicomponent Smoluchowski coagulation equation are constructed for measure-valued initial data with minimal assumptions on the moments. The framework is based on an abstract formulation of the Arzel\`a-Ascoli…
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision…
The paper considers the numerical solution of nonlinear integral equations using the Newton-Kantorovich method with the mpmath library. High-precision quadrature of the kernel K(t, s, u) with respect to the variable s for fixed t increases…
Next generation radio-interferometers, like the Square Kilometre Array, will acquire tremendous amounts of data with the goal of improving the size and sensitivity of the reconstructed images by orders of magnitude. The efficient processing…
In this work, solvers and preconditioners based on Gauss-Seidel and Jacobi algorithms are explored for stochastic Galerkin discretization of partial differential equations (PDEs) with random input data. Gauss-Seidel and Jacobi algorithms…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…
We analyze the prior that a Deep Gaussian Process with polynomial kernels induces. We observe that, even for relatively small depths, averaging effects occur within such a Deep Gaussian Process and that the prior can be analyzed and…
A general scheme for divisive hierarchical clustering algorithms is proposed. It is made of three main steps : first a splitting procedure for the subdivision of clusters into two subclusters, second a local evaluation of the bipartitions…
This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical…
The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…
The processes of simultaneous coagulation and Ostwald ripening of particles in the concluding stage of phase transformation are considered. We solve the integro-differential system of Smoluchowski-type kinetic and mass balance equations…
We build upon Estrin et al. (2019) to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970, 1973b). Although Fletcher's approach has historically been considered…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…