A data-driven approach to solving a 1D inverse scattering problem

In this paper, we extend a recently proposed approach for inverse scattering with Neumann boundary conditions [Druskin et al., Inverse Probl. 37, 075003 (2021)] to the 1D Schrödinger equation impedance (Robin) conditions. This method approaches in two steps: first, extract reduced order model (ROM) directly from data and, subsequently, potential ROM. We also propose novel data-assimilation (DA) inversion based on ROM approach, thereby avoiding need Lanczos-orthogonalization (LO) step. Furthermore, present detailed numerical study and A comparison of accuracy stability DA LO methods.