{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GFYZJBZKIP4OLZQA5D7HWBUEZY","short_pith_number":"pith:GFYZJBZK","schema_version":"1.0","canonical_sha256":"317194872a43f8e5e600e8fe7b0684ce1f8bd56eb4b3c31eb6dcc52b188bfc45","source":{"kind":"arxiv","id":"2410.18153","version":1},"attestation_state":"computed","paper":{"title":"Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"primary_cat":"math.NA","authors_text":"Taiki Miyagawa, Takeru Yokota","submitted_at":"2024-10-23T06:16:35Z","abstract_excerpt":"We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its unrealistic computational costs and has been a long standing problem over decades. Thus, numerical approximations of FDEs have been developed, but they often oversimplify the solutions. To tackle these two issues, we propose a hybrid approach combining physics-informed neural networks (PINNs) with the \\textit{cylindrical approximation}. The cylindrical approximation e"},"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":"2410.18153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-23T06:16:35Z","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"title_canon_sha256":"38f8226edeab32add525d0c2f3dd6d57da9c105aefca14aacd128c32017df29a","abstract_canon_sha256":"554f3a476404fcebd5cc002ca233583a0e663953de0e02f12a1f652c8d32831b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:25:04.297402Z","signature_b64":"+ibFg9zo09hwLawyjc4u+N91Ld0jtBFdBisI3vxYFLBbr/lXQ1iNQjDA/UIc29H7ksbdQy7Px7KN5J6JjXgxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"317194872a43f8e5e600e8fe7b0684ce1f8bd56eb4b3c31eb6dcc52b188bfc45","last_reissued_at":"2026-07-05T09:25:04.296999Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:25:04.296999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Physics-informed Neural Networks for Functional Differential Equations: Cylindrical Approximation and Its Convergence Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.AI","cs.NA","hep-th","stat.ML"],"primary_cat":"math.NA","authors_text":"Taiki Miyagawa, Takeru Yokota","submitted_at":"2024-10-23T06:16:35Z","abstract_excerpt":"We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its unrealistic computational costs and has been a long standing problem over decades. Thus, numerical approximations of FDEs have been developed, but they often oversimplify the solutions. To tackle these two issues, we propose a hybrid approach combining physics-informed neural networks (PINNs) with the \\textit{cylindrical approximation}. The cylindrical approximation e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18153","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/2410.18153/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":"2410.18153","created_at":"2026-07-05T09:25:04.297055+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.18153v1","created_at":"2026-07-05T09:25:04.297055+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18153","created_at":"2026-07-05T09:25:04.297055+00:00"},{"alias_kind":"pith_short_12","alias_value":"GFYZJBZKIP4O","created_at":"2026-07-05T09:25:04.297055+00:00"},{"alias_kind":"pith_short_16","alias_value":"GFYZJBZKIP4OLZQA","created_at":"2026-07-05T09:25:04.297055+00:00"},{"alias_kind":"pith_short_8","alias_value":"GFYZJBZK","created_at":"2026-07-05T09:25:04.297055+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/GFYZJBZKIP4OLZQA5D7HWBUEZY","json":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY.json","graph_json":"https://pith.science/api/pith-number/GFYZJBZKIP4OLZQA5D7HWBUEZY/graph.json","events_json":"https://pith.science/api/pith-number/GFYZJBZKIP4OLZQA5D7HWBUEZY/events.json","paper":"https://pith.science/paper/GFYZJBZK"},"agent_actions":{"view_html":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY","download_json":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY.json","view_paper":"https://pith.science/paper/GFYZJBZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.18153&json=true","fetch_graph":"https://pith.science/api/pith-number/GFYZJBZKIP4OLZQA5D7HWBUEZY/graph.json","fetch_events":"https://pith.science/api/pith-number/GFYZJBZKIP4OLZQA5D7HWBUEZY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/action/storage_attestation","attest_author":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/action/author_attestation","sign_citation":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/action/citation_signature","submit_replication":"https://pith.science/pith/GFYZJBZKIP4OLZQA5D7HWBUEZY/action/replication_record"}},"created_at":"2026-07-05T09:25:04.297055+00:00","updated_at":"2026-07-05T09:25:04.297055+00:00"}