Related papers: On optimality and bounds for internal solutions ge…
We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a nontrapping obstacle, with boundary data coming from plane-wave incidence, by the solution of the corresponding boundary value problem where the…
We deal with the problem of estimating the volume of inclusions using a finite number of boundary measurements in electrical impedance tomography. We derive upper and lower bounds on the volume fractions of inclusions, or more generally two…
We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that…
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann boundary condition posed on general irregular domains. The DDM…
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…
One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
We construct a unique global-in-time solution to the two species Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition, which can be viewed as one of the ideal scattering boundary model. The construction…
Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…
The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
Pulsar Timing Array (PTA) searches for nHz gravitational-wave backgrounds (GWBs) typically model time-correlated noise by assuming a diagonal covariance in Fourier space, neglecting inter-frequency correlations introduced by the finite…
This paper introduces a novel method to estimate distance fields from noisy point clouds using Gaussian Process (GP) regression. Distance fields, or distance functions, gained popularity for applications like point cloud registration,…
An efficient method is proposed for numerical solutions of nonlinear Schr\"{o}dinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation,…
We propose an algorithm to approximate solutions of global optimization problems in Sobolev spaces that follows the spirit of Consensus-based algorithms in finite dimensions. The main ingredient are Gaussian processes. In fact, we exploit…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
We study the inverse problem of determining uniquely and stably quasilinear terms appearing in an elliptic equation from boundary excitations and measurements associated with the solutions of the corresponding equation. More precisely, we…
We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains are…