DRM Revisited: A Complete Error Analysis
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929418608312320 |
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| author | Jiao, Yuling Li, Ruoxuan Wu, Peiying Yang, Jerry Zhijian Zhang, Pingwen |
| author_facet | Jiao, Yuling Li, Ruoxuan Wu, Peiying Yang, Jerry Zhijian Zhang, Pingwen |
| contents | In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09032 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DRM Revisited: A Complete Error Analysis Jiao, Yuling Li, Ruoxuan Wu, Peiying Yang, Jerry Zhijian Zhang, Pingwen Numerical Analysis Machine Learning In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision? |
| title | DRM Revisited: A Complete Error Analysis |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2407.09032 |