Related papers: Asymptotically compatible reproducing kernel collo…
In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
This paper proposes a consensus-based distributed nonlinear filter with kernel mean embedding (KME). This fills with gap of posterior density approximation with KME for distributed nonlinear dynamic systems. To approximate the posterior…
This article is concerned with solving the time fractional Vakhnenko Parkes equation using the reproducing kernels. Reproducing kernel theory, the normal basis, some important Hilbert spaces, homogenization of constraints, and the…
In this paper, we consider a free boundary problem with a nonlocal diffusion kernel function $k(x)$. Due to the long distance exchange effect of nonlocal diffusion, the free boundary can expand discontinuously, which makes the problem…
Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…
We prove that conditional diffusion models whose reverse kernels are finite Gaussian mixtures with ReLU-network logits can approximate suitably regular target distributions arbitrarily well in context-averaged conditional KL divergence, up…
In this paper we design and analyze an explicit partitioned procedure for a 2D dynamic local-to-nonlocal (LtN) coupling problem, based on a new nonlocal Robin-type transmission condition. The nonlocal subproblem is modeled by the nonlocal…
Kernel ridge regression (KRR) is a fundamental computational tool, appearing in problems that range from computational chemistry to health analytics, with a particular interest due to its starring role in Gaussian process regression.…
A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied.…
The concept of dispatchable region is useful in quantifying how much renewable generation power the system can handle. In this paper, we aim to provide an improved dispatchable region approximation method in distribution networks. First,…
The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…
The conditioning of implicit Runge-Kutta (RK) integration for linear finite element approximation of diffusion equations on general anisotropic meshes is investigated. Bounds are established for the condition number of the resulting linear…
Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…
We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate…
Multiple kernel clustering (MKC) is committed to achieving optimal information fusion from a set of base kernels. Constructing precise and local kernel matrices is proved to be of vital significance in applications since the unreliable…
In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a…
There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being…