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We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvec{\theta}^* + \myvec{\omega},$$ and $\myvec{X} \in…
We introduce Variational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes and associated connectivity structures from multivariate signals. VLMD addresses key limitations of existing Multivariate Mode…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
We present a least squares method for estimating parameters from measurements of event yields in the presence of background and crossfeed. We adopt a unified approach to incorporating the statistical and systematic uncertainties on the…
We present an alternative method for carrying out a principal-component analysis of Wilson coefficients in standard model effective field theory (SMEFT). The method is based on singular-value decomposition (SVD). The SVD method provides…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…
We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…
SLAM technology plays a crucial role in indoor mapping and localization. A common challenge in indoor environments is the "double-sided mapping issue", where closely positioned walls, doors, and other surfaces are mistakenly identified as a…
In this paper we propose and analyze a novel multilevel version of Stein variational gradient descent (SVGD). SVGD is a recent particle based variational inference method. For Bayesian inverse problems with computationally expensive…
Latest least squares regression (LSR) methods mainly try to learn slack regression targets to replace strict zero-one labels. However, the difference of intra-class targets can also be highlighted when enlarging the distance between…
We present MMLSv2, a dataset for landslide segmentation on Martian surfaces. MMLSv2 consists of multimodal imagery with seven bands: RGB, digital elevation model, slope, thermal inertia, and grayscale channels. MMLSv2 comprises 664 images…
The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid has been recently proposed as a regularization of the 3D Navier-Stokes equations for the purpose of direct numerical simulations. In this work we investigate its…
We present a hybrid Volume-of-Fluid (VoF) Phase-Field method for general soluble surfactant-laden interfacial flows. The scheme retains the VoF method for interface tracking and momentum solution, while a diffused Phase-Field serves as a…
In this work we present a novel bulk-surface virtual element method (BSVEM) for the numerical approximation of elliptic bulk-surface partial differential equations (BSPDEs) in three space dimensions. The BSVEM is based on the discretisation…
Landslide is a natural disaster that can easily threaten local ecology, people's lives and property. In this paper, we conduct modelling research on real unidirectional surface displacement data of recent landslides in the research area and…
In this paper, we develop a generalized hybrid method for both two-dimensional (2-D) and three-dimensional (3-D) surfactant dynamics. While the Navier-Stokes equations are solved by the Eulerian method, the surfactant transport is tracked…
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…
LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these…