FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910414527266816 |
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| author | Anandh, Thivin Ghose, Divij Jain, Himanshu Ganesan, Sashikumaar |
| author_facet | Anandh, Thivin Ghose, Divij Jain, Himanshu Ganesan, Sashikumaar |
| contents | Variational Physics-Informed Neural Networks (VPINNs) utilize a variational loss function to solve partial differential equations, mirroring Finite Element Analysis techniques. Traditional hp-VPINNs, while effective for high-frequency problems, are computationally intensive and scale poorly with increasing element counts, limiting their use in complex geometries. This work introduces FastVPINNs, a tensor-based advancement that significantly reduces computational overhead and improves scalability. Using optimized tensor operations, FastVPINNs achieve a 100-fold reduction in the median training time per epoch compared to traditional hp-VPINNs. With proper choice of hyperparameters, FastVPINNs surpass conventional PINNs in both speed and accuracy, especially in problems with high-frequency solutions. Demonstrated effectiveness in solving inverse problems on complex domains underscores FastVPINNs' potential for widespread application in scientific and engineering challenges, opening new avenues for practical implementations in scientific machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries Anandh, Thivin Ghose, Divij Jain, Himanshu Ganesan, Sashikumaar Machine Learning Computational Engineering, Finance, and Science Numerical Analysis Neural and Evolutionary Computing Variational Physics-Informed Neural Networks (VPINNs) utilize a variational loss function to solve partial differential equations, mirroring Finite Element Analysis techniques. Traditional hp-VPINNs, while effective for high-frequency problems, are computationally intensive and scale poorly with increasing element counts, limiting their use in complex geometries. This work introduces FastVPINNs, a tensor-based advancement that significantly reduces computational overhead and improves scalability. Using optimized tensor operations, FastVPINNs achieve a 100-fold reduction in the median training time per epoch compared to traditional hp-VPINNs. With proper choice of hyperparameters, FastVPINNs surpass conventional PINNs in both speed and accuracy, especially in problems with high-frequency solutions. Demonstrated effectiveness in solving inverse problems on complex domains underscores FastVPINNs' potential for widespread application in scientific and engineering challenges, opening new avenues for practical implementations in scientific machine learning. |
| title | FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries |
| topic | Machine Learning Computational Engineering, Finance, and Science Numerical Analysis Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2404.12063 |