{"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/learning-group-invariant-calabi-yau-metrics","title":"Learning Group Invariant Calabi-Yau Metrics by Fundamental Domain Projections","arxiv_id":"2407.06914","date":"2024-07-09","proceeding":null,"authors":["Yacoub Hendi","Magdalena Larfors","Moritz Walden"],"abstract":"We present new invariant machine learning models that approximate the Ricci-flat metric on Calabi-Yau (CY) manifolds with discrete symmetries. We accomplish this by combining the $\\phi$-model of the cymetric package with non-trainable, $G$-invariant, canonicalization layers that project the $\\phi$-model's input data (i.e. points sampled from the CY geometry) to the fundamental domain of a given symmetry group $G$. These $G$-invariant layers are easy to concatenate, provided one compatibility condition is fulfilled, and combine well with spectral $\\phi$-models. Through experiments on different CY geometries, we find that, for fixed point sample size and training time, canonicalized models give slightly more accurate metric approximations than the standard $\\phi$-model. The method may also be used to compute Ricci-flat metric on smooth CY quotients. We demonstrate this aspect by experiments on a smooth $\\mathbb{Z}^2_5$ quotient of a 5-parameter quintic CY manifold.","url_abs":"https://arxiv.org/abs/2407.06914v2","url_pdf":"https://arxiv.org/pdf/2407.06914v2.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":"learning-group-invariant-calabi-yau-metrics","repo_url":"https://github.com/jake997/invariant_layers_cymetric","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","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}