PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915121379409920 |
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| author | Ye, Zhanhong Huang, Xiang Chen, Leheng Liu, Hongsheng Wang, Zidong Dong, Bin |
| author_facet | Ye, Zhanhong Huang, Xiang Chen, Leheng Liu, Hongsheng Wang, Zidong Dong, Bin |
| contents | This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the seamless integration of both symbolic and numerical information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed to generate mesh-free predicted solutions. Following pretraining on data exhibiting a certain level of diversity, our model achieves zero-shot accuracies on benchmark datasets that is comparable to those of specifically trained expert models. Additionally, PDEformer demonstrates promising results in the inverse problem of PDE coefficient recovery. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations Ye, Zhanhong Huang, Xiang Chen, Leheng Liu, Hongsheng Wang, Zidong Dong, Bin Numerical Analysis This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the seamless integration of both symbolic and numerical information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed to generate mesh-free predicted solutions. Following pretraining on data exhibiting a certain level of diversity, our model achieves zero-shot accuracies on benchmark datasets that is comparable to those of specifically trained expert models. Additionally, PDEformer demonstrates promising results in the inverse problem of PDE coefficient recovery. |
| title | PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.12652 |