Inverse scattering for Schrödinger equation in the frequency domain via data-driven reduced order modeling
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915603391971328 |
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| author | Tataris, Andreas van Leeuwen, Tristan Mamonov, Alexander V. |
| author_facet | Tataris, Andreas van Leeuwen, Tristan Mamonov, Alexander V. |
| contents | In this paper we develop a numerical method for solving an inverse scattering problem of estimating the scattering potential in a Schrödinger equation from frequency domain measurements based on reduced order models (ROM). The ROM is a projection of Schrödinger operator onto a subspace spanned by its solution snapshots at certain wavenumbers. Provided the measurements are performed at these wavenumbers, the ROM can be constructed in a data-driven manner from the measurements on a surface surrounding the scatterers. Once the ROM is computed, the scattering potential can be estimated using non-linear optimization that minimizes the ROM misfit. Such an approach typically outperforms the conventional methods based on data misfit minimization. We develop two variants of ROM-based algorithms for inverse scattering and test them on a synthetic example in two spatial dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse scattering for Schrödinger equation in the frequency domain via data-driven reduced order modeling Tataris, Andreas van Leeuwen, Tristan Mamonov, Alexander V. Numerical Analysis 65M32, 41A20 In this paper we develop a numerical method for solving an inverse scattering problem of estimating the scattering potential in a Schrödinger equation from frequency domain measurements based on reduced order models (ROM). The ROM is a projection of Schrödinger operator onto a subspace spanned by its solution snapshots at certain wavenumbers. Provided the measurements are performed at these wavenumbers, the ROM can be constructed in a data-driven manner from the measurements on a surface surrounding the scatterers. Once the ROM is computed, the scattering potential can be estimated using non-linear optimization that minimizes the ROM misfit. Such an approach typically outperforms the conventional methods based on data misfit minimization. We develop two variants of ROM-based algorithms for inverse scattering and test them on a synthetic example in two spatial dimensions. |
| title | Inverse scattering for Schrödinger equation in the frequency domain via data-driven reduced order modeling |
| topic | Numerical Analysis 65M32, 41A20 |
| url | https://arxiv.org/abs/2503.11034 |