Related papers: Kernel-based collocation methods for Zakai equatio…
Stability and convergence of a time-weighted discrete scheme with nonuniform time steps are established for linear reaction-subdiffusion equations. The Caupto derivative is approximated at an offset point by using linear and quadratic…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
In this paper, we develop a novel accelerated fixed-point-based framework using delayed inexact oracles to approximate a fixed point of a nonexpansive operator (or equivalently, a root of a co-coercive operator), a central problem in…
We introduce a distance between kernels based on the Wasserstein distances between their values, study its properties, and prove that it is a metric on an appropriately defined space of kernels. We also relate it to various modes of…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…
We prove convergence to equilibrium for a class of coagulation-fragmentation equations that do not satisfy a detailed balance condition. More precisely, we consider perturbations of constant rate kernels. Our result provides in particular…
Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods…
Standard video frame interpolation methods first estimate optical flow between input frames and then synthesize an intermediate frame guided by motion. Recent approaches merge these two steps into a single convolution process by convolving…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
We introduce a direct numerical treatment of nonlinear higher-index differential-algebraic equations by means of overdetermined polynomial least-squares collocation. The procedure is not much more computationally expensive than standard…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the…
Using a lemma of Davis on Gram matrices applied to the classical Orthogonal Polynomials to generate reproducing kernel interpolation over the classical domains for polynomials. These kernels have terms which are exact over the rational…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
In this article, we solve a deterministically generalized interpolation problem by a stochastic approach. We introduce a kernel-based probability measure on a Banach space by a covariance kernel which is defined on the dual space of the…
We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation…