{"paper":{"title":"Hard-constrained Physics-informed Neural Networks for Interface Problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Hard-constrained PINN formulations embed interface continuity and flux conditions directly into the neural network solution representation.","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Michael S. Penwarden, Pratanu Roy, Seung Whan Chung, Stephen T. Castonguay, Sumanta Roy, Yucheng Fu","submitted_at":"2026-04-09T16:49:55Z","abstract_excerpt":"Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challenging because continuity and flux conditions are typically imposed through soft penalty terms. The standard soft-constraint formulation leads to imperfect interface enforcement and degraded accuracy near interfaces. We introduce two ansatz-based hard-constrained PINN formulations for interface problems that embed the interface physics into the solution representation and thereby decouple interface enforcement from PD"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce two ansatz-based hard-constrained PINN formulations for interface problems that embed the interface physics into the solution representation and thereby decouple interface enforcement from PDE residual minimization.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the windowing construction remains stable for general interface geometries and that the discrete buffer correction points can be chosen without introducing new fitting parameters that affect accuracy.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Hard-constrained PINN formulations via windowing and buffer approaches enforce interface conditions by design and outperform soft-constrained baselines on 1D and 2D elliptic interface problems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hard-constrained PINN formulations embed interface continuity and flux conditions directly into the neural network solution representation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bf6c4ac925f166c902ea89ad9b28681e7472aa6068d71d8645619cf37d2718a7"},"source":{"id":"2604.08453","kind":"arxiv","version":2},"verdict":{"id":"665b6f84-fd08-4a9e-bf75-25015d7e1ba2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T17:04:06.400202Z","strongest_claim":"We introduce two ansatz-based hard-constrained PINN formulations for interface problems that embed the interface physics into the solution representation and thereby decouple interface enforcement from PDE residual minimization.","one_line_summary":"Hard-constrained PINN formulations via windowing and buffer approaches enforce interface conditions by design and outperform soft-constrained baselines on 1D and 2D elliptic interface problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the windowing construction remains stable for general interface geometries and that the discrete buffer correction points can be chosen without introducing new fitting parameters that affect accuracy.","pith_extraction_headline":"Hard-constrained PINN formulations embed interface continuity and flux conditions directly into the neural network solution representation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.08453/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"}