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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.09480 |
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| _version_ | 1866917775636692992 |
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| author | Liu, Ziyang Chen, Fukai Chen, Junqing Qiu, Lingyun Shi, Zuoqiang |
| author_facet | Liu, Ziyang Chen, Fukai Chen, Junqing Qiu, Lingyun Shi, Zuoqiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09480 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neumann Series-based Neural Operator for Solving Inverse Medium Problem Liu, Ziyang Chen, Fukai Chen, Junqing Qiu, Lingyun Shi, Zuoqiang Mathematical Physics Machine Learning 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. |
| title | Neumann Series-based Neural Operator for Solving Inverse Medium Problem |
| topic | Mathematical Physics Machine Learning |
| url | https://arxiv.org/abs/2409.09480 |