相关论文: Partial Gromov-Wasserstein Metric

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying…

We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…

Over a complete Riemannian manifold of finite dimension, Greene and Wu introduced a convolution, known as Greene-Wu (GW) convolution. In this paper, we study properties of the GW convolution and apply it to non-Euclidean machine learning…

This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…

The examination of parity symmetry in gravitational interactions has drawn increasing attention. Although Einstein's General Relativity is parity-conserved, numerous theories of parity-violating (PV) gravity in different frameworks have…

Gravitational Waves (GWs) have been detected in the $\sim$100 Hz and nHz bands, but most of the gravitational spectrum remains unobserved. A variety of detector concepts have been proposed to expand the range of observable frequencies. In…

The search for new materials, based on computational screening, relies on methods that accurately predict, in an automatic manner, total energy, atomic-scale geometries, and other fundamental characteristics of materials. Many…

Gravitational Waves (GWs) from the early universe and unresolved astrophysical sources are expected to create a stochastic GW background (SGWB). The GW radiometer algorithm is well suited to probe such a background using data from ground…

Dynamic Time Warping (DTW) and Geometric Edit Distance (GED) are basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequences of points in some metric space $(X,…

The first law of geography is a cornerstone of spatial analysis, emphasizing that nearby and related locations tend to be more similar, however, defining what constitutes "near" and "related" remains challenging, as different phenomena…

A weak Galerkin (WG) method is introduced and numerically tested for the Helmholtz equation. This method is flexible by using discontinuous piecewise polynomials and retains the mass conservation property. At the same time, the WG finite…

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

In object detection, a well-defined similarity metric can significantly enhance model performance. Currently, the IoU-based similarity metric is the most commonly preferred choice for detectors. However, detectors using IoU as a similarity…

We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…

We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…

The novel idea of weak Galerkin (WG) finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives can be approximated by polynomials with various degrees.…

In this paper we introduce a notion of the Gromov-Hausdorff distance with boundary, denoted by $d_{GHB}$, to construct a framework of convergence of noncomplete metric spaces. We show that a class of bounded $A$-uniform spaces with diameter…

The simulation of high-dimensional problems with manageable computational resource represents a long-standing challenge. In a series of our recent work [25, 17, 18, 24], a class of sparse grid DG methods has been formulated for solving…

Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions,…

The collection of gravitational waves (GWs) that are either too weak or too numerous to be individually resolved is commonly referred to as the gravitational-wave background (GWB). A confident detection and model-driven characterization of…