SGM-PINN: Sampling Graphical Models for Faster Training of Physics-Informed Neural Networks
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929415952269312 |
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| author | Anticev, John Aghdaei, Ali Cheng, Wuxinlin Feng, Zhuo |
| author_facet | Anticev, John Aghdaei, Ali Cheng, Wuxinlin Feng, Zhuo |
| contents | SGM-PINN is a graph-based importance sampling framework to improve the training efficacy of Physics-Informed Neural Networks (PINNs) on parameterized problems. By applying a graph decomposition scheme to an undirected Probabilistic Graphical Model (PGM) built from the training dataset, our method generates node clusters encoding conditional dependence between training samples. Biasing sampling towards more important clusters allows smaller mini-batches and training datasets, improving training speed and accuracy. We additionally fuse an efficient robustness metric with residual losses to determine regions requiring additional sampling. Experiments demonstrate the advantages of the proposed framework, achieving $3\times$ faster convergence compared to prior state-of-the-art sampling methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SGM-PINN: Sampling Graphical Models for Faster Training of Physics-Informed Neural Networks Anticev, John Aghdaei, Ali Cheng, Wuxinlin Feng, Zhuo Machine Learning SGM-PINN is a graph-based importance sampling framework to improve the training efficacy of Physics-Informed Neural Networks (PINNs) on parameterized problems. By applying a graph decomposition scheme to an undirected Probabilistic Graphical Model (PGM) built from the training dataset, our method generates node clusters encoding conditional dependence between training samples. Biasing sampling towards more important clusters allows smaller mini-batches and training datasets, improving training speed and accuracy. We additionally fuse an efficient robustness metric with residual losses to determine regions requiring additional sampling. Experiments demonstrate the advantages of the proposed framework, achieving $3\times$ faster convergence compared to prior state-of-the-art sampling methods. |
| title | SGM-PINN: Sampling Graphical Models for Faster Training of Physics-Informed Neural Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2407.07358 |