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In this paper, we extend the ROM-based approach for inverse scattering withNeumann boundary conditions, introduced by Druskin at. al. (Inverse Problems37, 2021), to the 1D Schr{\"o}dinger equation with impedance (Robin) boundaryconditions. We also propose a novel data-assimilation (DA) inversion methodbased on the ROM approach, thereby avoiding the need for aLanczos-orthogonalization (LO) step. Furthermore, we present a detailednumerical study and comparison of the accuracy and stability of the DA and LOmethods.

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