{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BON625D56QX24CUGLE2EP67IXN","short_pith_number":"pith:BON625D5","schema_version":"1.0","canonical_sha256":"0b9bed747df42fae0a86593447fbe8bb552c68d27ba18595689f35be0be35030","source":{"kind":"arxiv","id":"2507.20929","version":1},"attestation_state":"computed","paper":{"title":"Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Chi Kiu Althina Chau, Kam Ian Leong, Kei Chon Sio, Wei Shan Lee","submitted_at":"2025-07-28T15:41:51Z","abstract_excerpt":"Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We break through this barrier with a hybrid Fourier-neural architecture for the Euler-Bernoulli beam equation, achieving unprecedented L2 error of $1.94 \\times 10^{-7}$-a 17-fold improvement over standard PINNs and \\(15-500\\times\\) better than traditional numerical methods. Our approach synergistically combines a truncated Fourier series capturing dominant modal be"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.20929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-07-28T15:41:51Z","cross_cats_sorted":["cond-mat.mtrl-sci","physics.comp-ph"],"title_canon_sha256":"6b9e2162b4e31f56dc48f53df680b26229d44f16818d9fa3e1f1c33bab248628","abstract_canon_sha256":"b69bb92d56d82ea03e1b2c4a85bee92e2a19012a173a5ec037edd9972060db71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:28.360038Z","signature_b64":"75rIMNOYxS+Mftrs3rjdzauwezA3RecfCqyAFyLpjGX8w5GDRsPFubT0S79147HZ4i3kITr0P0/rV6T3ppePDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b9bed747df42fae0a86593447fbe8bb552c68d27ba18595689f35be0be35030","last_reissued_at":"2026-07-05T11:44:28.359528Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:28.359528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Chi Kiu Althina Chau, Kam Ian Leong, Kei Chon Sio, Wei Shan Lee","submitted_at":"2025-07-28T15:41:51Z","abstract_excerpt":"Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We break through this barrier with a hybrid Fourier-neural architecture for the Euler-Bernoulli beam equation, achieving unprecedented L2 error of $1.94 \\times 10^{-7}$-a 17-fold improvement over standard PINNs and \\(15-500\\times\\) better than traditional numerical methods. Our approach synergistically combines a truncated Fourier series capturing dominant modal be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20929","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/2507.20929/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.20929","created_at":"2026-07-05T11:44:28.359596+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.20929v1","created_at":"2026-07-05T11:44:28.359596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20929","created_at":"2026-07-05T11:44:28.359596+00:00"},{"alias_kind":"pith_short_12","alias_value":"BON625D56QX2","created_at":"2026-07-05T11:44:28.359596+00:00"},{"alias_kind":"pith_short_16","alias_value":"BON625D56QX24CUG","created_at":"2026-07-05T11:44:28.359596+00:00"},{"alias_kind":"pith_short_8","alias_value":"BON625D5","created_at":"2026-07-05T11:44:28.359596+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN","json":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN.json","graph_json":"https://pith.science/api/pith-number/BON625D56QX24CUGLE2EP67IXN/graph.json","events_json":"https://pith.science/api/pith-number/BON625D56QX24CUGLE2EP67IXN/events.json","paper":"https://pith.science/paper/BON625D5"},"agent_actions":{"view_html":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN","download_json":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN.json","view_paper":"https://pith.science/paper/BON625D5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.20929&json=true","fetch_graph":"https://pith.science/api/pith-number/BON625D56QX24CUGLE2EP67IXN/graph.json","fetch_events":"https://pith.science/api/pith-number/BON625D56QX24CUGLE2EP67IXN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN/action/storage_attestation","attest_author":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN/action/author_attestation","sign_citation":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN/action/citation_signature","submit_replication":"https://pith.science/pith/BON625D56QX24CUGLE2EP67IXN/action/replication_record"}},"created_at":"2026-07-05T11:44:28.359596+00:00","updated_at":"2026-07-05T11:44:28.359596+00:00"}