{"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/geometric-clifford-algebra-networks","title":"Geometric Clifford Algebra Networks","arxiv_id":"2302.06594","date":"2023-02-13","proceeding":null,"authors":["David Ruhe","Jayesh K. Gupta","Steven de Keninck","Max Welling","Johannes Brandstetter"],"abstract":"We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\\mathrm{Pin}(p,q,r)$ group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable $\\textit{geometric templates}$ that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.","url_abs":"https://arxiv.org/abs/2302.06594v2","url_pdf":"https://arxiv.org/pdf/2302.06594v2.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":"geometric-clifford-algebra-networks","repo_url":"https://github.com/microsoft/pdearena","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"geometric-clifford-algebra-networks","repo_url":"https://github.com/pdearena/pdearena","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"gcans","method_name":"gCANS"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2302.06594","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}