Learning on the correct class for domain inverse problems of gravimetry
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910364321447936 |
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| author | Chen, Yihang Li, Wenbin |
| author_facet | Chen, Yihang Li, Wenbin |
| contents | We consider end-to-end learning approaches for inverse problems of gravimetry. Due to ill-posedness of the inverse gravimetry, the reliability of learning approaches is questionable. To deal with this problem, we propose the strategy of learning on the correct class. The well-posedness theorems are employed when designing the neural-network architecture and constructing the training set. Given the density-contrast function as a priori information, the domain of mass can be uniquely determined under certain constrains, and the domain inverse problem is a correct class of the inverse gravimetry. Under this correct class, we design the neural network for learning by mimicking the level-set formulation for the inverse gravimetry. Numerical examples illustrate that the method is able to recover mass models with non-constant density contrast. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_07393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning on the correct class for domain inverse problems of gravimetry Chen, Yihang Li, Wenbin Geophysics Numerical Analysis We consider end-to-end learning approaches for inverse problems of gravimetry. Due to ill-posedness of the inverse gravimetry, the reliability of learning approaches is questionable. To deal with this problem, we propose the strategy of learning on the correct class. The well-posedness theorems are employed when designing the neural-network architecture and constructing the training set. Given the density-contrast function as a priori information, the domain of mass can be uniquely determined under certain constrains, and the domain inverse problem is a correct class of the inverse gravimetry. Under this correct class, we design the neural network for learning by mimicking the level-set formulation for the inverse gravimetry. Numerical examples illustrate that the method is able to recover mass models with non-constant density contrast. |
| title | Learning on the correct class for domain inverse problems of gravimetry |
| topic | Geophysics Numerical Analysis |
| url | https://arxiv.org/abs/2403.07393 |