{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/structure-preserving-neural-networks-for-the","title":"Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system","arxiv_id":"2404.14312","date":"2024-04-22","proceeding":null,"authors":["Steffen Schotthöfer","M. Paul Laiu","Martin Frank","Cory D. Hauck"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2404.14312v3","url_pdf":"https://arxiv.org/pdf/2404.14312v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"structure-preserving-neural-networks-for-the","repo_url":"https://github.com/CSMMLab/KiT-RT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null},{"paper_slug":"structure-preserving-neural-networks-for-the","repo_url":"https://github.com/scsteffen/neuralentropyclosures","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}