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We propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents…
Deep neural networks are powerful tools for biomedical image segmentation. These models are often trained with heavy supervision, relying on pairs of images and corresponding voxel-level labels. However, obtaining segmentations of…
Image-based crack detection algorithms are increasingly in demand in infrastructure monitoring, as early detection of cracks is of paramount importance for timely maintenance planning. While deep learning has significantly advanced crack…
The path-following scheme in [Loisel and Maxwell, SIAM J. Matrix Anal. Appl., 39-4 (2018), pp. 1726-1749] is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current.…
A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…
This work presents a new approach to anomaly detection and localization in synthetic aperture radar imagery (SAR), expanding upon the existing patch distribution modeling framework (PaDiM). We introduce the adaptive cosine estimator (ACE)…
We investigate the computation of stable fracture paths in brittle thin films using one-dimensional damage models with an elastic foundation. The underlying variational formulation is non-convex, making the evolution path sensitive to…
With continuous progression of Moore's Law, integrated circuit (IC) device complexity is also increasing. Scanning Electron Microscope (SEM) image based extensive defect inspection and accurate metrology extraction are two main challenges…
The Morley finite element method (FEM) is attractive for semilinear problems with the biharmonic operator as a leading term in the stream function vorticity formulation of 2D Navier-Stokes problem and in the von K\'{a}rm\'{a}n equations.…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes,…
Deep neural networks achieve impressive performance but remain difficult to interpret and control. We present SALVE (Sparse Autoencoder-Latent Vector Editing), a unified "discover, validate, and control" framework that bridges mechanistic…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
Object tracking is one of the fundamental problems in visual recognition tasks and has achieved significant improvements in recent years. The achievements often come with the price of enormous hardware consumption and expensive labor effort…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
Emerging high-frequency accelerator technology in the terahertz regime is promising for the development of compact high-brightness accelerators and high resolution-power beam diagnostics. One resounding challenge when scaling to higher…
In recent years, unmanned aerial vehicles (UAVs) equipped with imaging sensors and automated processing algorithms have emerged as a promising tool to accelerate large-area surveys while reducing risk to human operators. Although…
The problem of the emergence of wave dispersion due to the heterogeneity of a transmission line (TL) is considered. An exactly solvable model helps to better understand the physical process of a signal passing through a non-uniform section…