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The reduced Lippmann-Schwinger-Lanczos (LSL) algorithm, initially designed for two-dimensional (2D) inverse problems within the diffusion domain in the context of reduced-order modeling (ROM) (Baker et al., Regularized reduced order Lippmann-Schwinger-Lanczos method for inverse scattering problems in the frequency domain (submitted). arXiv:2311.16367v1) and later adapted to one-dimensional (1D) inverse scattering in the wave domain (Abilgazy and Zaslavsky, Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrödinger equation in the resonance frequency domain. Extended abstracts of IPMS 2024 conference (accepted)), is extended in this work to address 2D Schrödinger inverse problems. Numerical experiments demonstrate that the required frequency sampling rate for 2D wave problems is substantially lower than for the 1D case, attributed to the inherently overdetermined nature of the 2D inverse problem. This finding suggests potential efficiency gains for solving high-dimensional wave-based inverse problems using reduced sampling strategies.

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Reduced Order Lippmann-Schwinger-Lanczos Inverse Scattering Method

  • 会议论文

  • 发表日期：

    2025年

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  • Justin Baker,
  • Elena Cherkaev,
  • Vladimir Druskin,
  • Shari Moskow,
  • Mikhail Zaslavsky

摘要

The reduced Lippmann-Schwinger-Lanczos (LSL) algorithm, initially designed for two-dimensional (2D) inverse problems within the diffusion domain in the context of reduced-order modeling (ROM) (Baker et al., Regularized reduced order Lippmann-Schwinger-Lanczos method for inverse scattering problems in the frequency domain (submitted). arXiv:2311.16367v1) and later adapted to one-dimensional (1D) inverse scattering in the wave domain (Abilgazy and Zaslavsky, Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrödinger equation in the resonance frequency domain. Extended abstracts of IPMS 2024 conference (accepted)), is extended in this work to address 2D Schrödinger inverse problems. Numerical experiments demonstrate that the required frequency sampling rate for 2D wave problems is substantially lower than for the 1D case, attributed to the inherently overdetermined nature of the 2D inverse problem. This finding suggests potential efficiency gains for solving high-dimensional wave-based inverse problems using reduced sampling strategies.