{"paper":{"title":"Imposing Boundary Conditions on Neural Operators via Learned Function Extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Mapping boundary data to full-domain latent extensions lets any standard neural operator handle complex mixed-type conditions accurately.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Laura De Lorenzis, Sepehr Mousavi, Siddhartha Mishra","submitted_at":"2026-02-04T08:28:43Z","abstract_excerpt":"Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to boundary forcings. We propose a general framework for conditioning neural operators on complex non-homogeneous BCs through function extensions. Our key idea is to map boundary data to latent pseudo-extensions defined over the entire spatial domain, enabling any standard operator learning architecture t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That mapping boundary data to learned latent pseudo-extensions defined over the entire domain will allow any standard neural operator to capture rich dependencies on complex, mixed-type, and multi-segment BCs without introducing artifacts or requiring architecture-specific changes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A framework learns boundary-to-domain pseudo-extensions to condition neural operators on complex BCs, achieving SOTA accuracy on 18 challenging PDE datasets without hyperparameter tuning.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Mapping boundary data to full-domain latent extensions lets any standard neural operator handle complex mixed-type conditions accurately.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8e6b264339b92730b4510c0fdf3c7582fb1a109d7953eb412297d07ab898d416"},"source":{"id":"2602.04923","kind":"arxiv","version":2},"verdict":{"id":"0d5a5af7-8935-4b46-9c66-f74f1f583bca","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T07:08:01.575027Z","strongest_claim":"Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets.","one_line_summary":"A framework learns boundary-to-domain pseudo-extensions to condition neural operators on complex BCs, achieving SOTA accuracy on 18 challenging PDE datasets without hyperparameter tuning.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That mapping boundary data to learned latent pseudo-extensions defined over the entire domain will allow any standard neural operator to capture rich dependencies on complex, mixed-type, and multi-segment BCs without introducing artifacts or requiring architecture-specific changes.","pith_extraction_headline":"Mapping boundary data to full-domain latent extensions lets any standard neural operator handle complex mixed-type conditions accurately."},"references":{"count":37,"sample":[{"doi":"","year":2024,"title":"B. Alkin, A. Fürst, S. Schmid, L. Gruber, M. Holzleitner, and J. Brandstetter. Universal physics transformers: A framework for efficiently scaling neural operators. In A. Globerson, L. Mackey, D. Belg","work_id":"a8e3e3a8-6e52-4185-b1af-cadc815b6c26","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Layer Normalization","work_id":"20a2d720-0046-4c7c-bcd6-327ec8143f69","ref_index":3,"cited_arxiv_id":"1607.06450","is_internal_anchor":true},{"doi":"","year":2023,"title":"I. A. Baratta, J. P. Dean, J. S. Dokken, M. Habera, J. S. Hale, C. N. Richardson, M. E. Rognes, M. W. Scroggs, N. Sime, and G. N. Wells. DOLFINx: the next generation FEniCS problem solving environment","work_id":"9cd92b75-a9a3-4f01-9b47-48bafa1a2df5","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"F. Bartolucci, E. de Bezenac, B. Raonic, R. Molinaro, S. Mishra, and R. Alaifari. Representation equivalent neural operators: a framework for alias-free operator learning.Advances in Neural Informatio","work_id":"ff8963ec-b6ea-4435-8b29-af280734a412","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"J. Brandstetter, D. E. Worrall, and M. Welling. Message passing neural PDE solvers. InInternational Conference on Learning Representations, 2022","work_id":"554b1dca-2065-42b8-bd12-2888c2bfd94d","ref_index":6,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":37,"snapshot_sha256":"386f757bd718006f310df21089e7c82f59595baaa73663407e1b83bf113f8f4c","internal_anchors":3},"formal_canon":{"evidence_count":2,"snapshot_sha256":"1958d3b3a209da2a35f051c324025ff793be3f666320ba213251da90c24505e5"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}