BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm
Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequenc...
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| Autor*in: |
Zhu, Zhicheng [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Enthalten in: Neural computing & applications - Springer London, 1993, 35(2023), 28 vom: 02. Aug., Seite 21093-21113 |
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volume:35 ; year:2023 ; number:28 ; day:02 ; month:08 ; pages:21093-21113 |
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| DOI / URN: |
10.1007/s00521-023-08876-4 |
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OLC2145282378 |
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| 520 | |a Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. | ||
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10.1007/s00521-023-08876-4 doi (DE-627)OLC2145282378 (DE-He213)s00521-023-08876-4-p DE-627 ger DE-627 rakwb eng 004 VZ Zhu, Zhicheng verfasserin aut BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. Physics informed neural network Gradient pathologies Coevolutionary algorithm Biased multiobjective optimization Hao, Jia aut Huang, Jin aut Huang, Biao aut Enthalten in Neural computing & applications Springer London, 1993 35(2023), 28 vom: 02. Aug., Seite 21093-21113 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:35 year:2023 number:28 day:02 month:08 pages:21093-21113 https://doi.org/10.1007/s00521-023-08876-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_2018 GBV_ILN_4277 AR 35 2023 28 02 08 21093-21113 |
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10.1007/s00521-023-08876-4 doi (DE-627)OLC2145282378 (DE-He213)s00521-023-08876-4-p DE-627 ger DE-627 rakwb eng 004 VZ Zhu, Zhicheng verfasserin aut BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. Physics informed neural network Gradient pathologies Coevolutionary algorithm Biased multiobjective optimization Hao, Jia aut Huang, Jin aut Huang, Biao aut Enthalten in Neural computing & applications Springer London, 1993 35(2023), 28 vom: 02. Aug., Seite 21093-21113 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:35 year:2023 number:28 day:02 month:08 pages:21093-21113 https://doi.org/10.1007/s00521-023-08876-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_2018 GBV_ILN_4277 AR 35 2023 28 02 08 21093-21113 |
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10.1007/s00521-023-08876-4 doi (DE-627)OLC2145282378 (DE-He213)s00521-023-08876-4-p DE-627 ger DE-627 rakwb eng 004 VZ Zhu, Zhicheng verfasserin aut BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. Physics informed neural network Gradient pathologies Coevolutionary algorithm Biased multiobjective optimization Hao, Jia aut Huang, Jin aut Huang, Biao aut Enthalten in Neural computing & applications Springer London, 1993 35(2023), 28 vom: 02. Aug., Seite 21093-21113 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:35 year:2023 number:28 day:02 month:08 pages:21093-21113 https://doi.org/10.1007/s00521-023-08876-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_2018 GBV_ILN_4277 AR 35 2023 28 02 08 21093-21113 |
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10.1007/s00521-023-08876-4 doi (DE-627)OLC2145282378 (DE-He213)s00521-023-08876-4-p DE-627 ger DE-627 rakwb eng 004 VZ Zhu, Zhicheng verfasserin aut BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. Physics informed neural network Gradient pathologies Coevolutionary algorithm Biased multiobjective optimization Hao, Jia aut Huang, Jin aut Huang, Biao aut Enthalten in Neural computing & applications Springer London, 1993 35(2023), 28 vom: 02. Aug., Seite 21093-21113 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:35 year:2023 number:28 day:02 month:08 pages:21093-21113 https://doi.org/10.1007/s00521-023-08876-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_2018 GBV_ILN_4277 AR 35 2023 28 02 08 21093-21113 |
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10.1007/s00521-023-08876-4 doi (DE-627)OLC2145282378 (DE-He213)s00521-023-08876-4-p DE-627 ger DE-627 rakwb eng 004 VZ Zhu, Zhicheng verfasserin aut BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm 2023 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. Physics informed neural network Gradient pathologies Coevolutionary algorithm Biased multiobjective optimization Hao, Jia aut Huang, Jin aut Huang, Biao aut Enthalten in Neural computing & applications Springer London, 1993 35(2023), 28 vom: 02. Aug., Seite 21093-21113 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:35 year:2023 number:28 day:02 month:08 pages:21093-21113 https://doi.org/10.1007/s00521-023-08876-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_2018 GBV_ILN_4277 AR 35 2023 28 02 08 21093-21113 |
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BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm |
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BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm |
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Zhu, Zhicheng |
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Neural computing & applications |
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Zhu, Zhicheng Hao, Jia Huang, Jin Huang, Biao |
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10.1007/s00521-023-08876-4 |
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004 |
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bc-pinn: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm |
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BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm |
| abstract |
Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract Physics informed neural network (PINN) has become a promising method for solving partial differential equations (PDEs). The loss function of PINN is a weighted sum of multiple items. This makes it easy to fall into local optima, especially the gradient pathologies when solving high frequency problems. The value of penalty coefficients has a crucial impact on the prediction results. Therefore, a new PINN with adaptive penalty coefficients iteratively optimized by biased multiobjective coevolutionary algorithm (BC-PINN) is presented. In BC-PINN, a two-stage optimization mechanism is used to search for parameters of neural network and penalty coefficients respectively. This method involves constructing the fitness function of penalty coefficients based on the biased dominance ranking by data item and regularization item. Compared with the previous works of others, the accuracy of fitting the initial conditions and boundary conditions is considered to be given priority, which is more conducive to PINN converging to the particular solution of PDE. In addition, the set of penalty coefficients is divided into multiple populations to improve the optimization efficiency through coevolutionary algorithm. The empirical results show that: (1) Our method can improve the gradient pathologies and effectively capture the high-frequency features. (2) Compared to the original PINN, it reduces the MSE by 1–6 orders of magnitude in our benchmark functions. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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28 |
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BC-PINN: an adaptive physics informed neural network based on biased multiobjective coevolutionary algorithm |
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https://doi.org/10.1007/s00521-023-08876-4 |
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Hao, Jia Huang, Jin Huang, Biao |
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