{"paper":{"title":"Flexible SE(2) graph neural networks with applications to PDE surrogates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.NA","math.NA","physics.flu-dyn"],"primary_cat":"cs.LG","authors_text":"Aleksis Pirinen, Maria B{\\aa}nkestad, Olof Mogren","submitted_at":"2024-05-30T17:39:15Z","abstract_excerpt":"This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.20287","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/2405.20287/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"}