Neural Parameter Regression for Explicit Representations of PDE Solution Operators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917617978048512 |
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| author | Mundinger, Konrad Zimmer, Max Pokutta, Sebastian |
| author_facet | Mundinger, Konrad Zimmer, Max Pokutta, Sebastian |
| contents | We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets (Lu et al., 2021) by employing Physics-Informed Neural Network (PINN, Raissi et al., 2019) techniques to regress Neural Network (NN) parameters. By parametrizing each solution based on specific initial conditions, it effectively approximates a mapping between function spaces. Our method enhances parameter efficiency by incorporating low-rank matrices, thereby boosting computational efficiency and scalability. The framework shows remarkable adaptability to new initial and boundary conditions, allowing for rapid fine-tuning and inference, even in cases of out-of-distribution examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural Parameter Regression for Explicit Representations of PDE Solution Operators Mundinger, Konrad Zimmer, Max Pokutta, Sebastian Machine Learning Numerical Analysis We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets (Lu et al., 2021) by employing Physics-Informed Neural Network (PINN, Raissi et al., 2019) techniques to regress Neural Network (NN) parameters. By parametrizing each solution based on specific initial conditions, it effectively approximates a mapping between function spaces. Our method enhances parameter efficiency by incorporating low-rank matrices, thereby boosting computational efficiency and scalability. The framework shows remarkable adaptability to new initial and boundary conditions, allowing for rapid fine-tuning and inference, even in cases of out-of-distribution examples. |
| title | Neural Parameter Regression for Explicit Representations of PDE Solution Operators |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2403.12764 |