Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Koumpanakis, Michail Vilalta, Ricardo |
| author_facet | Koumpanakis, Michail Vilalta, Ricardo |
| contents | This paper proposes a new way to learn Physics-Informed Neural Network loss functions using Generalized Additive Models. We apply our method by meta-learning parametric partial differential equations, PDEs, on Burger's and 2D Heat Equations. The goal is to learn a new loss function for each parametric PDE using meta-learning. The derived loss function replaces the traditional data loss, allowing us to learn each parametric PDE more efficiently, improving the meta-learner's performance and convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks Koumpanakis, Michail Vilalta, Ricardo Machine Learning Analysis of PDEs Computational Physics This paper proposes a new way to learn Physics-Informed Neural Network loss functions using Generalized Additive Models. We apply our method by meta-learning parametric partial differential equations, PDEs, on Burger's and 2D Heat Equations. The goal is to learn a new loss function for each parametric PDE using meta-learning. The derived loss function replaces the traditional data loss, allowing us to learn each parametric PDE more efficiently, improving the meta-learner's performance and convergence. |
| title | Meta-learning Loss Functions of Parametric Partial Differential Equations Using Physics-Informed Neural Networks |
| topic | Machine Learning Analysis of PDEs Computational Physics |
| url | https://arxiv.org/abs/2412.00225 |