电磁逆问题的降阶建模：层状介质基准测试
Reduced-order modeling for electromagnetic inverse problems: a layered medium benchmark
AI总结：
该研究针对层状介质逆问题，采用Goupillaud结构构建离散动力系统，提出基于ROM的目标函数，经5层介质数值实验验证其反演重构效果优于经典方法且竞争力稳定。
AI中文摘要：
我们研究层状介质逆问题的降阶建模，重点是从时域测量中恢复阻抗剖面。采用Goupillaud结构，我们将正问题构建为离散动力系统，并在降阶算子层面引入基于ROM的目标函数。通过对5层介质在多种结构化扰动下的数值实验，我们将该基于ROM的目标函数与经典数据失配项进行比较。结果表明，在无噪声场景及特定结构化扰动工况下，基于ROM的反演能提供更优的重构效果，且在所有考察案例中均与经典方法保持一致的竞争力。
英文摘要：
We study reduced-order modeling for inverse problems in layered media, focusing on the recovery of impedance profiles from time-domain measurements. Using the Goupillaud structure, we formulate the forward problem as a discrete dynamical system and introduce a ROM-based objective defined at the level of reduced operators. Through numerical experiments on a 5-layer medium under various structured perturbations, we compare the ROM-based objective with a classical data misfit. The results show that the ROM-based inversion provides a more favorable reconstruction in the clean setting and in certain structured perturbation regimes, while remaining consistently competitive with the classical approach across all cases considered.
