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Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…
We consider the Kolmogorov-Sinai entropy for dilute gases of $N$ hard disks or spheres. This can be expanded in density as $h_{\mathrm{KS}} \propto n N [\ln n a^d+ B + O(n a^d)+O(1/N)]$, with $a$ the diameter of the sphere or disk, $n$ the…
Large-scale Fourier modes of the cosmic density field are of great value for learning about cosmology because of their well-understood relationship to fluctuations in the early universe. However, cosmic variance generally limits the…
Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography.…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
In a previous paper, we outlined a new Bayesian method for inferring the properties of extended gravitational lenses, given data in the form of resolved images. This method holds the most promise for optimally extracting information from…
Gravitational wave astronomy has placed strong constraints on fundamental physics, and there is every expectation that future observations will continue to do so. In this work we quantify this expectation for future binary merger…
Reconstructing the properties of the astrophysical population of binary compact objects in the universe is a key science goal of gravitational wave detectors. This goal is hindered by the finite strain, frequency sensitivity and observing…
We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor…
This work presents the simulation results of the radio science experiment onboard the proposed Heavy Metal mission to the M-type asteroid (216) Kleopatra. Earth-based radiometric measurements (range and range-rate), complemented by images…
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…
With the inception of gravitational wave astronomy, astrophysical studies using interferometric techniques have begun to probe previously unknown parts of the universe. In this work, we investigate the potential of a new interferometric…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…