{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:LCIN2E4HMKQSKEOYU5TYV6JMHX","short_pith_number":"pith:LCIN2E4H","schema_version":"1.0","canonical_sha256":"5890dd138762a12511d8a7678af92c3dfd5269acb7da141ad53e6714d04a16c8","source":{"kind":"arxiv","id":"2408.14734","version":1},"attestation_state":"computed","paper":{"title":"General-Kindred Physics-Informed Neural Network to the Solutions of Singularly Perturbed Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"primary_cat":"cs.LG","authors_text":"Peizhi Zhao, Qinglong Ma, Sen Wang, Tao Song","submitted_at":"2024-08-27T02:03:22Z","abstract_excerpt":"Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the field of PINN. The solution of singular perturbation problems often exhibits sharp boundary layers and steep gradients, and traditional PINN cannot achieve approximation of boundary layers. In this manuscript, we propose the General-Kindred Physics-Informed Neural Network (GKPINN) for solving Singular Perturbation Differential Equations (SPDEs). This approach ut"},"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":"2408.14734","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-08-27T02:03:22Z","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"title_canon_sha256":"c19e06c6dffee0a47699e61c497cb80ab7f3843f076b228806c62916c8c93709","abstract_canon_sha256":"5e6e6be4cc0bed31704e57282413256649ad4695f7b7d79060e9ba7649a551d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:59:38.185289Z","signature_b64":"17Jjq1SvvP4twbPNkzMPy5Cf4rvH3DpHJkxLZg2V/etFYAT5W1ACqK0kvuJ6igwZzgy/Szcia3m9cxrd3D/QCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5890dd138762a12511d8a7678af92c3dfd5269acb7da141ad53e6714d04a16c8","last_reissued_at":"2026-07-05T08:59:38.184853Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:59:38.184853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General-Kindred Physics-Informed Neural Network to the Solutions of Singularly Perturbed Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"primary_cat":"cs.LG","authors_text":"Peizhi Zhao, Qinglong Ma, Sen Wang, Tao Song","submitted_at":"2024-08-27T02:03:22Z","abstract_excerpt":"Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the field of PINN. The solution of singular perturbation problems often exhibits sharp boundary layers and steep gradients, and traditional PINN cannot achieve approximation of boundary layers. In this manuscript, we propose the General-Kindred Physics-Informed Neural Network (GKPINN) for solving Singular Perturbation Differential Equations (SPDEs). This approach ut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.14734","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/2408.14734/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":"2408.14734","created_at":"2026-07-05T08:59:38.184912+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.14734v1","created_at":"2026-07-05T08:59:38.184912+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.14734","created_at":"2026-07-05T08:59:38.184912+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCIN2E4HMKQS","created_at":"2026-07-05T08:59:38.184912+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCIN2E4HMKQSKEOY","created_at":"2026-07-05T08:59:38.184912+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCIN2E4H","created_at":"2026-07-05T08:59:38.184912+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/LCIN2E4HMKQSKEOYU5TYV6JMHX","json":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX.json","graph_json":"https://pith.science/api/pith-number/LCIN2E4HMKQSKEOYU5TYV6JMHX/graph.json","events_json":"https://pith.science/api/pith-number/LCIN2E4HMKQSKEOYU5TYV6JMHX/events.json","paper":"https://pith.science/paper/LCIN2E4H"},"agent_actions":{"view_html":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX","download_json":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX.json","view_paper":"https://pith.science/paper/LCIN2E4H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.14734&json=true","fetch_graph":"https://pith.science/api/pith-number/LCIN2E4HMKQSKEOYU5TYV6JMHX/graph.json","fetch_events":"https://pith.science/api/pith-number/LCIN2E4HMKQSKEOYU5TYV6JMHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX/action/storage_attestation","attest_author":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX/action/author_attestation","sign_citation":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX/action/citation_signature","submit_replication":"https://pith.science/pith/LCIN2E4HMKQSKEOYU5TYV6JMHX/action/replication_record"}},"created_at":"2026-07-05T08:59:38.184912+00:00","updated_at":"2026-07-05T08:59:38.184912+00:00"}