The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomen…

In this work, we study the semi-classical limit of the Schr\"odinger equation with random inputs, and show that the semi-classical Schr\"odinger equa…

In this work we analyze the dimension-independent convergence property of an abstract sparse quadrature scheme for numerical integration of functions…

Oja's algorithm has been the cornerstone of streaming methods in Principal Component Analysis (PCA) since it was first proposed in 1982. However, Oja…

We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusio…

We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochori…

This work concerns the numerical solution of a coupled system of self-consistent reaction-drift-diffusion-Poisson equations that describes the macros…

Two-photon absorption photoacoustic tomography (TP-PAT) is a recent hybrid imaging modality that aims at reconstructing two-photon absorption propert…

Kalman filtering is a classic state estimation technique used widely in engineering applications such as statistical signal processing and control of…

Lyapunov exponents measure the average exponential growth rate of typical linear perturbations in a chaotic system, and the inverse of the largest ex…

The goal of a recommendation system is to predict the interest of a user in a given item by exploiting the existing set of ratings as well as certain…

In this work, we consider optimal control problems constrained by elliptic partial differential equations (PDEs) with lognormal random coefficients, …

An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamen…

Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usu…

In this paper, we propose an enriched Galerkin (EG) approximation for a two-phase pressure saturation system with capillary pressure in heterogeneous…

Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure inte…

We study image inverse problems with invertible generative priors, specifically normalizing flow models. Our formulation views the solution as the Ma…

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quanti…

We study the fractionation of two components between a well-mixed gas and a saturated convecting porous layer. Motivated by geological carbon dioxide…

Kernel matrices appear in machine learning and non-parametric statistics. Given $N$ points in $d$ dimensions and a kernel function that requires $\ma…

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