Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911898088243200 |
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| author | Schotthöfer, Steffen Laiu, M. Paul Frank, Martin Hauck, Cory D. |
| author_facet | Schotthöfer, Steffen Laiu, M. Paul Frank, Martin Hauck, Cory D. |
| contents | The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the context of regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy closure as a two-stage approximation to the original entropy closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system Schotthöfer, Steffen Laiu, M. Paul Frank, Martin Hauck, Cory D. Numerical Analysis Machine Learning The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the context of regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy closure as a two-stage approximation to the original entropy closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. |
| title | Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2404.14312 |