PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917685539897344 |
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| author | Gao, Jiexing Zakharian, Yurii |
| author_facet | Gao, Jiexing Zakharian, Yurii |
| contents | In the paper, we describe in operator form classes of PDEs that admit PINN's error estimation. Also, for $L^p$ spaces, we obtain a Bramble-Hilbert type lemma that is a tool for PINN's residuals bounding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11915 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces Gao, Jiexing Zakharian, Yurii Functional Analysis Machine Learning Numerical Analysis In the paper, we describe in operator form classes of PDEs that admit PINN's error estimation. Also, for $L^p$ spaces, we obtain a Bramble-Hilbert type lemma that is a tool for PINN's residuals bounding. |
| title | PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces |
| topic | Functional Analysis Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2305.11915 |