{"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/model-reduction-of-a-parametrized-scalar","title":"Model reduction of a parametrized scalar hyperbolic conservation law using displacement interpolation","arxiv_id":"1805.05938","date":"2018-05-15","proceeding":null,"authors":["Donsub Rim","Kyle T. Mandli"],"abstract":"We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to construct basis functions that are local in parameter and time space via displacement interpolation. The construction is motivated by the observation that the derivative of solutions to hyperbolic conservation laws satisfy a contractive property with respect to the Wasserstein metric [Bolley et al. J. Hyperbolic Differ. Equ. 02 (2005), pp. 91-107]. We will discuss the approximation properties of the displacement interpolation, and show that it can naturally complement linear interpolation. Numerical experiments illustrate that we can successfully achieve the model reduction of a parametrized Burgers' equation, and that the reduced order model is suitable for performing typical tasks in uncertainty quantification.","url_abs":"http://arxiv.org/abs/1805.05938v1","url_pdf":"http://arxiv.org/pdf/1805.05938v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"model-reduction-of-a-parametrized-scalar","repo_url":"https://github.com/dsrim/mr_burgers1d","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}