标题： 基于Neumann级数的神经算子用于解决反问题 显示英文标题

标题： Neumann Series-based Neural Operator for Solving Inverse Medium Problem

摘要： 反介质问题本质上是病态且非线性的，带来了显著的计算挑战。 本研究通过在神经网络框架中整合一个Neumann级数结构，提出了一种新方法，以有效处理多参数输入。 实验表明，我们的方法不仅加速了计算，而且显著提高了泛化性能，即使在变化的散射特性和噪声数据下也是如此。 我们框架的鲁棒性和适应性提供了关键的见解和方法，扩展了其在广泛散射问题中的适用性。 这些进展标志着该领域的重要进步，为传统复杂的反问题提供了一个可扩展的解决方案。 显示英文摘要

摘要： 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.