Neumann Series-based Neural Operator for Solving Inverse Medium Problem
This work addresses computational challenges in inverse scattering problems, offering a scalable solution that is incremental in its integration of existing mathematical structures.
The paper tackles the ill-posed and nonlinear inverse medium problem by integrating a Neumann series structure into a neural network framework, resulting in accelerated computations and enhanced generalization performance with varying scattering properties and noisy data.
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively handle multiparameter inputs. Experiments demonstrate that our methodology not only accelerates computations but also significantly enhances generalization performance, even with varying scattering properties and noisy data. The robustness and adaptability of our framework provide crucial insights and methodologies, extending its applicability to a broad spectrum of scattering problems. These advancements mark a significant step forward in the field, offering a scalable solution to traditionally complex inverse problems.