A data-driven approach to solving a 1D inverse scattering problem
Numerical Analysis
2023-04-07 v1 Numerical Analysis
Mathematical Physics
math.MP
Abstract
In this paper, we extend the ROM-based approach for inverse scattering with Neumann boundary conditions, introduced by Druskin at. al. (Inverse Problems 37, 2021), to the 1D Schr{\"o}dinger equation with impedance (Robin) boundary conditions. We also propose a novel data-assimilation (DA) inversion method based on the ROM approach, thereby avoiding the need for a Lanczos-orthogonalization (LO) step. Furthermore, we present a detailed numerical study and comparison of the accuracy and stability of the DA and LO methods.
Cite
@article{arxiv.2304.02926,
title = {A data-driven approach to solving a 1D inverse scattering problem},
author = {Tristan van Leeuwen and Andreas Tataris},
journal= {arXiv preprint arXiv:2304.02926},
year = {2023}
}