Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy
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...
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MDPI AG
2024-09-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/17/9/415 |
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| author | Stefano Berrone Moreno Pintore |
| author_facet | Stefano Berrone Moreno Pintore |
| author_sort | Stefano Berrone |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-4cb36f7d718e421da90c098e1eece1a6 |
| institution | OA Journals |
| issn | 1999-4893 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-4cb36f7d718e421da90c098e1eece1a62025-08-20T01:56:10ZengMDPI AGAlgorithms1999-48932024-09-0117941510.3390/a17090415Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training StrategyStefano Berrone0Moreno Pintore1Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, ItalyMEGAVOLT Team, Inria, 48 Rue Barrault, 75013 Paris, FranceIn 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.https://www.mdpi.com/1999-4893/17/9/415VPINNmeshfreePhysics-Informed Neural Networkserror estimatorpatches |
| spellingShingle | Stefano Berrone Moreno Pintore Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy Algorithms VPINN meshfree Physics-Informed Neural Networks error estimator patches |
| title | Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy |
| title_full | Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy |
| title_fullStr | Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy |
| title_full_unstemmed | Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy |
| title_short | Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): An Adaptive Training Strategy |
| title_sort | meshfree variational physics informed neural networks mf vpinn an adaptive training strategy |
| topic | VPINN meshfree Physics-Informed Neural Networks error estimator patches |
| url | https://www.mdpi.com/1999-4893/17/9/415 |
| work_keys_str_mv | AT stefanoberrone meshfreevariationalphysicsinformedneuralnetworksmfvpinnanadaptivetrainingstrategy AT morenopintore meshfreevariationalphysicsinformedneuralnetworksmfvpinnanadaptivetrainingstrategy |