Related papers: Uncertainty Quantification for Maxwell's Eigenprob…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
We associate a sequence of variational eigenvalues to any Radon measure on a compact Riemannian manifold. For particular choices of measures, we recover the Laplace, Steklov and other classical eigenvalue problems. In the first part of the…
Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displacement field is governed by Cauchy's equation of motion, i.e.,…
We study time harmonic acoustic scattering on large deviation rough random scatterers. Therein, the roughness of the scatterers is caused by a low Sobolev regularity in the covariance function of their deformation field. The motivation for…
In this paper, we are concerned with the quantification of uncertainties that arise from intra-day oscillations in the demand for natural gas transported through large-scale networks. The short-term transient dynamics of the gas flow is…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…
We consider the computational challenges associated with uncertainty quantification involved in parameter estimation such as seismic slowness and hydraulic transmissivity fields. The reconstruction of these parameters can be mathematically…
This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the…
In this paper, we take a fresh look at using spectral analysis for assessing locking phenomena in finite element formulations. We propose to "measure" locking by comparing the difference between eigenvalue and mode error curves computed on…
Microwave cavities for a Sikivie-type axion search are subject to several constraints. In the fabrication and operation of such cavities, often used at frequencies where the resonator is highly overmoded, it is important to be able to…
This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an…
In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
Identifying and quantifying $\gamma$-emitting radionuclides, considering spectral deformation from $\gamma$-interactions in radioactive source surroundings, present a significant challenge in $\gamma$-ray spectrometry. In that context, a…
Perturbation theory is a kind of estimation method based on theorem of Taylor expansion, and is useful to investigate electromagnetic solutions of small changes. By considering a sharp boundary as a limit of smoothed systems, previous study…
We have developed a method to measure the electric field standing wave distributions in a microwave resonator using a scanned perturbation technique. Fast and reliable solutions to the Helmholtz equation (and to the Schrodinger equation for…
We investigate the well-posedness and long-time behavior of a general continuum neural field model with Gaussian noise on possibly unbounded domains. In particular, we give conditions for the existence of invariant probability measures by…
The advent of next-generation radio interferometers like the Square Kilometer Array promises to revolutionise our radio astronomy observational capabilities. The unprecedented volume of data these devices generate requires fast and accurate…
Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…