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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2406.19831 |
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| _version_ | 1866913507598925824 |
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| author | Berrone, Stefano Pintore, Moreno |
| author_facet | Berrone, Stefano Pintore, Moreno |
| contents | In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space, we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational-Physics-Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19831 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Meshfree Variational Physics Informed Neural Networks (MF-VPINN): an adaptive training strategy Berrone, Stefano Pintore, Moreno Numerical Analysis Optimization and Control 65N12, 65N15, 65N50, 68T05, 92B20 In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space, we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational-Physics-Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh. |
| title | Meshfree Variational Physics Informed Neural Networks (MF-VPINN): an adaptive training strategy |
| topic | Numerical Analysis Optimization and Control 65N12, 65N15, 65N50, 68T05, 92B20 |
| url | https://arxiv.org/abs/2406.19831 |