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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2506.01453 |
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| _version_ | 1866916949481488384 |
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| author | Ciril, Igor Haddaoui, Khalil Tendero, Yohann |
| author_facet | Ciril, Igor Haddaoui, Khalil Tendero, Yohann |
| contents | We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and reliable learning algorithms, combining fast convergence during training with accurate predictions. The methodology that relies on solving a certain relaxed related problem is assessed through a series of one-dimensional scalar test cases. These numerical experiments demonstrate the potential of the methodology developed in this paper and its applicability to more complex industrial scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Initial Data to Boundary Layers: Neural Networks for Nonlinear Hyperbolic Conservation Laws Ciril, Igor Haddaoui, Khalil Tendero, Yohann Analysis of PDEs Artificial Intelligence We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and reliable learning algorithms, combining fast convergence during training with accurate predictions. The methodology that relies on solving a certain relaxed related problem is assessed through a series of one-dimensional scalar test cases. These numerical experiments demonstrate the potential of the methodology developed in this paper and its applicability to more complex industrial scenarios. |
| title | From Initial Data to Boundary Layers: Neural Networks for Nonlinear Hyperbolic Conservation Laws |
| topic | Analysis of PDEs Artificial Intelligence |
| url | https://arxiv.org/abs/2506.01453 |