{"paper":{"title":"Consistent CutPINNs for Elliptic PDEs on Curved Level-Set Domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Maneesh Kumar Singh","submitted_at":"2026-05-25T08:16:50Z","abstract_excerpt":"We propose \\emph{Consistent CutPINN}, a framework for partial differential equations posed on bounded curved domains defined implicitly by a $\\C^2$ level-set function, $\\Omega = \\{\\varphi < 0\\}$. In this paper we develop the framework for second-order elliptic problems in two dimensions. The standard PINN loss penalises the boundary mismatch in $L^2(\\partial\\Omega)$, but $L^2(\\partial\\Omega)$ does not control the $H^{1/2}(\\partial\\Omega)$ trace norm that appears in the $H^1(\\Omega)$ energy estimate. The consistent PINN framework of Bonito et al.~\\cite{bonito2025} fixes this on the unit cube $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25562","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25562/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}