Related papers: Reduced Order Model Approach to Inverse Scattering
In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems…
Reduced-order models (ROMs) of turbulent flows based on Galerkin projection often require many degrees of freedom to resolve the dynamics of the turbulence, or simulation data to obtain an optimal modal basis. However, obtaining simulation…
The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…
Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…
This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering…
While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…
A seismic wavefield reconstruction framework based on compressed sensing using the data-driven reduced-order model (ROM) is proposed and its characteristics are investigated through numerical experiments. The data-driven ROM is generated…
We devise and analyze a reduced basis model order reduction (MOR) strategy for an abstract wave problem with vanishing initial conditions and a source term given by the product of a temporal Ricker wavelet and a spatial profile. Such wave…
We study an inverse source problem for the acoustic wave equation in a random waveguide. The goal is to estimate the source of waves from measurements of the acoustic pressure at a remote array of sensors. The waveguide effect is due to…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…
This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach…
Scattering is defined on compact manifolds with boundary which are equipped with an asymptotically hyperbolic metric, $g.$ A model form is established for such metrics close to the boundary. It is shown that the scattering matrix at energy…
In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of…