用尼曼级数构建神经算子，高效求解复杂反散射问题
Neumann Series-based Neural Operator for Solving Inverse Medium Problem
- 将尼曼级数嵌入神经网络，处理多参数输入
- 计算速度提升，对噪声和参数变化有强鲁棒性
- 适合需要高泛化能力的物理反问题研究者
反介质问题本质上是病态且非线性的，计算挑战巨大。本文提出一种新方法，在神经网络框架中引入尼曼级数结构，有效处理多参数输入。实验表明，该方法不仅显著加速计算，还大幅提升泛化性能，即使面对不同散射特性与含噪数据也表现稳健。所提框架的强鲁棒性与可适应性为各类散射问题提供了关键方法论支持，推动了传统复杂逆问题求解的可扩展性进展。
原文摘要 · Abstract (English)
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.
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