{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JSHEB65LJILGW3FFVBND2QBBR5","short_pith_number":"pith:JSHEB65L","schema_version":"1.0","canonical_sha256":"4c8e40fbab4a166b6ca5a85a3d40218f65cdf9f7972a0d228abeca2dce3a45be","source":{"kind":"arxiv","id":"2502.19392","version":2},"attestation_state":"computed","paper":{"title":"Error estimates for viscous Burgers' equation using deep learning method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Deepanshu Verma, Manil T. Mohan, Sagar Gautam, Wasim Akram","submitted_at":"2025-02-26T18:36:43Z","abstract_excerpt":"The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value problem for non-stationary viscous Burgers equation is established by using semigroup techniques and fixed point arguments. By considering a suitable approximate problem and deriving appropriate energy estimates, we prove the existence of a unique strong solution. Additionally, we extend our analysis to the global well-posedness of the non-homogeneous problem. "},"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":"2502.19392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-02-26T18:36:43Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8c165df9c71862b03fa5ba59c6c37398ee330b18cf837fdfb5c562bb433bd5ef","abstract_canon_sha256":"1685b6f824dd0d9fb6fdc77fcb1eb5e19c2366bd510cc5f3d8bd918d6e56a509"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:54:44.585809Z","signature_b64":"tOM4N0MkBctoEwtrKwSDmM7qaw1yuf656IWWzlWtQ0GVHWf86SQcZwcVfoMhLHUWS7e5QTyeQOo6DyKSyNiJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c8e40fbab4a166b6ca5a85a3d40218f65cdf9f7972a0d228abeca2dce3a45be","last_reissued_at":"2026-07-05T11:54:44.585352Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:54:44.585352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Error estimates for viscous Burgers' equation using deep learning method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Deepanshu Verma, Manil T. Mohan, Sagar Gautam, Wasim Akram","submitted_at":"2025-02-26T18:36:43Z","abstract_excerpt":"The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value problem for non-stationary viscous Burgers equation is established by using semigroup techniques and fixed point arguments. By considering a suitable approximate problem and deriving appropriate energy estimates, we prove the existence of a unique strong solution. Additionally, we extend our analysis to the global well-posedness of the non-homogeneous problem. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19392","kind":"arxiv","version":2},"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/2502.19392/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":"2502.19392","created_at":"2026-07-05T11:54:44.585410+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.19392v2","created_at":"2026-07-05T11:54:44.585410+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19392","created_at":"2026-07-05T11:54:44.585410+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSHEB65LJILG","created_at":"2026-07-05T11:54:44.585410+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSHEB65LJILGW3FF","created_at":"2026-07-05T11:54:44.585410+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSHEB65L","created_at":"2026-07-05T11:54:44.585410+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.17614","citing_title":"A priori error analysis of consistent PINNs for parabolic PDEs","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5","json":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5.json","graph_json":"https://pith.science/api/pith-number/JSHEB65LJILGW3FFVBND2QBBR5/graph.json","events_json":"https://pith.science/api/pith-number/JSHEB65LJILGW3FFVBND2QBBR5/events.json","paper":"https://pith.science/paper/JSHEB65L"},"agent_actions":{"view_html":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5","download_json":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5.json","view_paper":"https://pith.science/paper/JSHEB65L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.19392&json=true","fetch_graph":"https://pith.science/api/pith-number/JSHEB65LJILGW3FFVBND2QBBR5/graph.json","fetch_events":"https://pith.science/api/pith-number/JSHEB65LJILGW3FFVBND2QBBR5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5/action/storage_attestation","attest_author":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5/action/author_attestation","sign_citation":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5/action/citation_signature","submit_replication":"https://pith.science/pith/JSHEB65LJILGW3FFVBND2QBBR5/action/replication_record"}},"created_at":"2026-07-05T11:54:44.585410+00:00","updated_at":"2026-07-05T11:54:44.585410+00:00"}