2023-06-01
A data-driven approach to solving a 1D inverse scattering problem
Publication
Publication
AIP Advances , Volume 13 p. 065310:1- 065310:9
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 with impedance (Robin) boundary conditions. This method approaches inverse scattering in two steps: first, to extract a reduced order model (ROM) directly from the data and, subsequently, to extract the scattering potential from the ROM. 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 A comparison of the accuracy and stability of the DA and LO methods.
| Additional Metadata | |
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| doi.org/10.1063/5.0154182 | |
| AIP Advances | |
| Organisation | Computational Imaging |
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van Leeuwen, T., & Tataris, A. (2023). A data-driven approach to solving a 1D inverse scattering problem. AIP Advances, 13, 065310:1–065310:9. doi:10.1063/5.0154182 |
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