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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.01722 |
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| _version_ | 1866909579449729024 |
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| author | Brevis, Ignacio Muga, Ignacio Pardo, David Rodriguez, Oscar van der Zee, Kristoffer G. |
| author_facet | Brevis, Ignacio Muga, Ignacio Pardo, David Rodriguez, Oscar van der Zee, Kristoffer G. |
| contents | The efficient approximation of parametric PDEs is of tremendous importance in science and engineering. In this paper, we show how one can train Galerkin discretizations to efficiently learn quantities of interest of solutions to a parametric PDE. The central component in our approach is an efficient neural-network-weighted Minimal-Residual formulation, which, after training, provides Galerkin-based approximations in standard discrete spaces that have accurate quantities of interest, regardless of the coarseness of the discrete space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01722 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach Brevis, Ignacio Muga, Ignacio Pardo, David Rodriguez, Oscar van der Zee, Kristoffer G. Numerical Analysis 65N30 The efficient approximation of parametric PDEs is of tremendous importance in science and engineering. In this paper, we show how one can train Galerkin discretizations to efficiently learn quantities of interest of solutions to a parametric PDE. The central component in our approach is an efficient neural-network-weighted Minimal-Residual formulation, which, after training, provides Galerkin-based approximations in standard discrete spaces that have accurate quantities of interest, regardless of the coarseness of the discrete space. |
| title | Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2304.01722 |