Data-driven reduced order models (ROMs) are combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding into the continuous problem, a data-driven internal solution is produced. This internal solution is then used in the Lippmann-Schwinger equation, thus making further iterative updates unnecessary. We show numerical experiments for spectral domain domain data for which our inversion is far superior to the Born inversion and works as well as when the true internal solution is known.

翻译：数据驱动减序模型(ROMs)与Lippmann-Schwinger综合方程式(ROMs)相结合,以产生直接的非线性反位法。 ROM被视为Galerkin投影,由于Lanczos orthogalization而稀疏。嵌入持续的问题中,生成了数据驱动的内部解决方案。这个内部解决方案随后用于Lippmann-Schwinger方程式中,因此不需要进一步的迭接更新。我们展示了光谱域域数据的数字实验,而我们的反向数据远优于原版和工作,以及当真正的内部解决方案已知时。