Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910697729818624 |
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| author | Anandh, Thivin Ghose, Divij Jain, Himanshu Sunkad, Pratham Ganesan, Sashikumaar John, Volker |
| author_facet | Anandh, Thivin Ghose, Divij Jain, Himanshu Sunkad, Pratham Ganesan, Sashikumaar John, Volker |
| contents | This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems Anandh, Thivin Ghose, Divij Jain, Himanshu Sunkad, Pratham Ganesan, Sashikumaar John, Volker Numerical Analysis Computational Engineering, Finance, and Science Machine Learning This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature. |
| title | Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems |
| topic | Numerical Analysis Computational Engineering, Finance, and Science Machine Learning |
| url | https://arxiv.org/abs/2411.09329 |