TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929265677697024 |
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| author | Chen, Yanlai Ji, Yajie Narayan, Akil Xu, Zhenli |
| author_facet | Chen, Yanlai Ji, Yajie Narayan, Akil Xu, Zhenli |
| contents | We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs framework. Building on the recent development of the GPT-PINN that is a network-of-networks design achieving snapshot-based model reduction, we design and test a novel paradigm for nonlinear model reduction that can effectively tackle problems with parameter-dependent discontinuities. Through incorporation of a shock-capturing loss function component as well as a parameter-dependent transform layer, the TGPT-PINN overcomes the limitations of linear model reduction in the transport-dominated regime. We demonstrate this new capability for nonlinear model reduction in the PINNs framework by several nontrivial parametric partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs Chen, Yanlai Ji, Yajie Narayan, Akil Xu, Zhenli Numerical Analysis Machine Learning We introduce the Transformed Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs framework. Building on the recent development of the GPT-PINN that is a network-of-networks design achieving snapshot-based model reduction, we design and test a novel paradigm for nonlinear model reduction that can effectively tackle problems with parameter-dependent discontinuities. Through incorporation of a shock-capturing loss function component as well as a parameter-dependent transform layer, the TGPT-PINN overcomes the limitations of linear model reduction in the transport-dominated regime. We demonstrate this new capability for nonlinear model reduction in the PINNs framework by several nontrivial parametric partial differential equations. |
| title | TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2403.03459 |