Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach
In this paper, an adaptive mix training physics-informed neural networks (A-MTPINNs) model is proposed to study the high-order rogue waves of the famous Gardner equation (GE). Through a series of numerical experiments, we can conclude that this A-MTPINNs model can not only recover the dynamic behavi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-02-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724000688 |
| _version_ | 1797306951827193856 |
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| author | Shi-fei Sun Shi-fang Tian Biao Li |
| author_facet | Shi-fei Sun Shi-fang Tian Biao Li |
| author_sort | Shi-fei Sun |
| collection | DOAJ |
| description | In this paper, an adaptive mix training physics-informed neural networks (A-MTPINNs) model is proposed to study the high-order rogue waves of the famous Gardner equation (GE). Through a series of numerical experiments, we can conclude that this A-MTPINNs model can not only recover the dynamic behavior of the high-order rogue waves of the GE well, but also can guarantee higher learning ability and prediction accuracy than the original PINNs model, and the prediction accuracy is improved by two orders of magnitude. By testing that the A-MTPINNs model can maintain high robustness under different noises for the data-driven solutions of the GE. Furthermore, this model also has good performance for the inverse problem of the Gardner equation by a data-driven discovery approach and also remains robust in noise experiments. |
| first_indexed | 2024-03-08T00:50:15Z |
| format | Article |
| id | doaj.art-b57f592ba3cc48b28bc6c2e70a45f76f |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-08T00:50:15Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-b57f592ba3cc48b28bc6c2e70a45f76f2024-02-15T05:23:50ZengElsevierResults in Physics2211-37972024-02-0157107386Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approachShi-fei Sun0Shi-fang Tian1Biao Li2School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, PR ChinaSchool of Mathematics and Statistics, Ningbo University, Ningbo, 315211, PR ChinaCorresponding author.; School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, PR ChinaIn this paper, an adaptive mix training physics-informed neural networks (A-MTPINNs) model is proposed to study the high-order rogue waves of the famous Gardner equation (GE). Through a series of numerical experiments, we can conclude that this A-MTPINNs model can not only recover the dynamic behavior of the high-order rogue waves of the GE well, but also can guarantee higher learning ability and prediction accuracy than the original PINNs model, and the prediction accuracy is improved by two orders of magnitude. By testing that the A-MTPINNs model can maintain high robustness under different noises for the data-driven solutions of the GE. Furthermore, this model also has good performance for the inverse problem of the Gardner equation by a data-driven discovery approach and also remains robust in noise experiments.http://www.sciencedirect.com/science/article/pii/S2211379724000688Physics-informed neural networksGardner equationAdaptive meshHigh order rogue wavesInverse problem |
| spellingShingle | Shi-fei Sun Shi-fang Tian Biao Li Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach Results in Physics Physics-informed neural networks Gardner equation Adaptive mesh High order rogue waves Inverse problem |
| title | Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach |
| title_full | Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach |
| title_fullStr | Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach |
| title_full_unstemmed | Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach |
| title_short | Data-driven high-order rogue waves and parameters discovery for Gardner equation using deep learning approach |
| title_sort | data driven high order rogue waves and parameters discovery for gardner equation using deep learning approach |
| topic | Physics-informed neural networks Gardner equation Adaptive mesh High order rogue waves Inverse problem |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724000688 |
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