{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ENGVQA2JDOVV7UMDIZA4I7KTU6","short_pith_number":"pith:ENGVQA2J","schema_version":"1.0","canonical_sha256":"234d5803491bab5fd1834641c47d53a7a218be51bec5dc127658e3a6a0dd4b38","source":{"kind":"arxiv","id":"2304.03689","version":1},"attestation_state":"computed","paper":{"title":"EPINN-NSE: Enhanced Physics-Informed Neural Networks for Solving Navier-Stokes Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"physics.comp-ph","authors_text":"Ayoub Farkane, Mohamed Boutayeb, Mounir Ghogho, Mustapha Oudani","submitted_at":"2023-04-07T15:15:51Z","abstract_excerpt":"Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult to solve, and classical numerical methods can be computationally expensive. In this paper, we present an innovative approach for solving the NSE using Physics Informed Neural Networks (PINN) and several novel techniques that improve their performance. The first model is based on an assumption that involves approximating the velocity component by employing th"},"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":"2304.03689","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2023-04-07T15:15:51Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0a9b466b29696b242fc42e6b4dfe5d5b75c2176d5cf9ea5f0517850ba906295e","abstract_canon_sha256":"e94bd706a474779180b2806d205b9a78d001546c5d83b410daf20124e2825bef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:58:59.044894Z","signature_b64":"QytPDaysYCD0x61+LZpoZGRviW+h2FlkRrKNjZgDhqDdDDQd6SmBsxzNgz8GW2E+qMd7nw9h8QMnVvvOumxbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"234d5803491bab5fd1834641c47d53a7a218be51bec5dc127658e3a6a0dd4b38","last_reissued_at":"2026-07-05T05:58:59.044473Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:58:59.044473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"EPINN-NSE: Enhanced Physics-Informed Neural Networks for Solving Navier-Stokes Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"physics.comp-ph","authors_text":"Ayoub Farkane, Mohamed Boutayeb, Mounir Ghogho, Mustapha Oudani","submitted_at":"2023-04-07T15:15:51Z","abstract_excerpt":"Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult to solve, and classical numerical methods can be computationally expensive. In this paper, we present an innovative approach for solving the NSE using Physics Informed Neural Networks (PINN) and several novel techniques that improve their performance. The first model is based on an assumption that involves approximating the velocity component by employing th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03689","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/2304.03689/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":"2304.03689","created_at":"2026-07-05T05:58:59.044530+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.03689v1","created_at":"2026-07-05T05:58:59.044530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.03689","created_at":"2026-07-05T05:58:59.044530+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENGVQA2JDOVV","created_at":"2026-07-05T05:58:59.044530+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENGVQA2JDOVV7UMD","created_at":"2026-07-05T05:58:59.044530+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENGVQA2J","created_at":"2026-07-05T05:58:59.044530+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06002","citing_title":"Solving Hamiltonian Constraint Equation with Physics-Informed Neural Networks","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6","json":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6.json","graph_json":"https://pith.science/api/pith-number/ENGVQA2JDOVV7UMDIZA4I7KTU6/graph.json","events_json":"https://pith.science/api/pith-number/ENGVQA2JDOVV7UMDIZA4I7KTU6/events.json","paper":"https://pith.science/paper/ENGVQA2J"},"agent_actions":{"view_html":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6","download_json":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6.json","view_paper":"https://pith.science/paper/ENGVQA2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.03689&json=true","fetch_graph":"https://pith.science/api/pith-number/ENGVQA2JDOVV7UMDIZA4I7KTU6/graph.json","fetch_events":"https://pith.science/api/pith-number/ENGVQA2JDOVV7UMDIZA4I7KTU6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6/action/storage_attestation","attest_author":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6/action/author_attestation","sign_citation":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6/action/citation_signature","submit_replication":"https://pith.science/pith/ENGVQA2JDOVV7UMDIZA4I7KTU6/action/replication_record"}},"created_at":"2026-07-05T05:58:59.044530+00:00","updated_at":"2026-07-05T05:58:59.044530+00:00"}