Ziyang Liu, Fukai Chen, Junqing Chen, Lingyun Qiu, Zuoqiang Shi
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Neumann Series-based Neural Operator for Solving Inverse Medium Problem
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.