相关论文: Efficient entropy stable Gauss collocation methods

Algorithms for computing the classical Gaussian quadrature rules (Gauss--Jacobi, Gauss--Laguerre, and Gauss--Hermite) are presented, based on globally convergent fourth-order iterative methods combined with asymptotic approximations, which…

We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain. This inclusion serves to mitigate outer boundary effects and, in the future, will…

Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…

Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass…

3D Gaussian Splatting (3DGS) has emerged as a leading technique for novel view synthesis, demonstrating exceptional rendering efficiency. \replaced[]{Well-reconstructed surfaces can be characterized by low configurational entropy, where…

This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…

Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…

Gaussian and Laplacian entropy models are proved effective in learned point cloud attribute compression, as they assist in arithmetic coding of latents. However, we demonstrate through experiments that there is still unutilized information…

Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…

In this paper, we present a block-oriented scheme for adaptive mesh refinement based on summation-by-parts (SBP) finite difference methods and simultaneous-approximation-term (SAT) interface treatment. Since the order of accuracy at SBP-SAT…

Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…

Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…

In this paper some methods to use the empirical bootstrap approach for stochastic gradient descent (SGD) to minimize the empirical risk over a separable Hilbert space are investigated from the view point of algorithmic stability and…

Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…

A high-order well-balanced scheme for the Euler equations with gravitation is presented. The scheme is able to preserve a spatially high-order accurate discrete representation of a large class of hydrostatic equilibria. It is based on a…

This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing…

Advances in information technology have led to extremely large datasets that are often kept in different storage centers. Existing statistical methods must be adapted to overcome the resulting computational obstacles while retaining…

We study the Small Ball Probabilities (SBPs) of Gaussian rough paths. While many works on rough paths study the Large Deviations Principles (LDPs) for stochastic processes driven by Gaussian rough paths, it is a noticeable gap in the…

Subcell limiting strategies for discontinuous Galerkin spectral element methods do not provably satisfy a semi-discrete cell entropy inequality. In this work, we introduce an extension to the subcell and monolithic convex limiting…