Entropy stable conservative flux form neural networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912470099034112 |
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| author | Liu, Lizuo Li, Tongtong Gelb, Anne Lee, Yoonsang |
| author_facet | Liu, Lizuo Li, Tongtong Gelb, Anne Lee, Yoonsang |
| contents | We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Numerical experiments demonstrate that the entropy-stable CFN achieves both stability and conservation while maintaining accuracy over extended time domains. Furthermore, it successfully predicts shock propagation speeds in long-term simulations, {\it without} oracle knowledge of later-time profiles in the training data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01746 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropy stable conservative flux form neural networks Liu, Lizuo Li, Tongtong Gelb, Anne Lee, Yoonsang Numerical Analysis Machine Learning 65M08, 68T07, 65M22, 65M32, 65D25 We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Numerical experiments demonstrate that the entropy-stable CFN achieves both stability and conservation while maintaining accuracy over extended time domains. Furthermore, it successfully predicts shock propagation speeds in long-term simulations, {\it without} oracle knowledge of later-time profiles in the training data. |
| title | Entropy stable conservative flux form neural networks |
| topic | Numerical Analysis Machine Learning 65M08, 68T07, 65M22, 65M32, 65D25 |
| url | https://arxiv.org/abs/2411.01746 |