Neumann Series-based Neural Operator for Solving Inverse Medium Problem

TL;DR

This paper presents a neural network approach incorporating Neumann series to efficiently solve the complex inverse medium problem, improving speed and robustness in scattering applications.

Contribution

It introduces a novel Neumann series-based neural operator that enhances computational efficiency and generalization for inverse medium problems.

Findings

Accelerates inverse medium problem computations

Improves robustness against noise and varying scattering properties

Extends applicability to diverse scattering scenarios

Abstract

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.