{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:CXGFPM4ULJVOAKZGTBQJ3XMSAM","short_pith_number":"pith:CXGFPM4U","schema_version":"1.0","canonical_sha256":"15cc57b3945a6ae02b2698609ddd920303ea85a8bf8a686c6514b854e0012a31","source":{"kind":"arxiv","id":"2407.03801","version":1},"attestation_state":"computed","paper":{"title":"Solving the inverse source problem of the fractional Poisson equation by MC-fPINNs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Cheng Yuan, Jerry Zhijian Yang, Peiying Wu, Rui Sheng","submitted_at":"2024-07-04T10:11:37Z","abstract_excerpt":"In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks $ u_{NN}(x;\\theta )$ and $f_{NN}(x;\\psi)$ to approximate the solution $u^{*}(x)$ and the forcing term $f^{*}(x)$ of the fractional Poisson equation. To optimize these two neural networks, we use the Monte Carlo sampling method mentioned in MC-fPINNs and define a new loss function combining measurement data and the underlying physical model. Meanwhile, we present a comprehensive error analysis for this method, along with a prior rule to select the a"},"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":"2407.03801","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2024-07-04T10:11:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"25e224cb4bb4b07b8b3edc2de473309ecd5c8d210e830ecd5b6016170228a390","abstract_canon_sha256":"e101dc5753d0cfadf281705ba7f973e0a3e66d371cd436ece0d145d750d12e57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:40:24.294477Z","signature_b64":"IIh0KNC6xEohu6pJvTp6k9PrHRpBuwEk1EUZWTBRomZkJu9y5TDm9wlAbKB4q6fSQJ2PLf9/mtlWOWA1MlsyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15cc57b3945a6ae02b2698609ddd920303ea85a8bf8a686c6514b854e0012a31","last_reissued_at":"2026-07-05T08:40:24.293998Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:40:24.293998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving the inverse source problem of the fractional Poisson equation by MC-fPINNs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Cheng Yuan, Jerry Zhijian Yang, Peiying Wu, Rui Sheng","submitted_at":"2024-07-04T10:11:37Z","abstract_excerpt":"In this paper, we effectively solve the inverse source problem of the fractional Poisson equation using MC-fPINNs. We construct two neural networks $ u_{NN}(x;\\theta )$ and $f_{NN}(x;\\psi)$ to approximate the solution $u^{*}(x)$ and the forcing term $f^{*}(x)$ of the fractional Poisson equation. To optimize these two neural networks, we use the Monte Carlo sampling method mentioned in MC-fPINNs and define a new loss function combining measurement data and the underlying physical model. Meanwhile, we present a comprehensive error analysis for this method, along with a prior rule to select the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03801","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/2407.03801/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":"2407.03801","created_at":"2026-07-05T08:40:24.294054+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.03801v1","created_at":"2026-07-05T08:40:24.294054+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.03801","created_at":"2026-07-05T08:40:24.294054+00:00"},{"alias_kind":"pith_short_12","alias_value":"CXGFPM4ULJVO","created_at":"2026-07-05T08:40:24.294054+00:00"},{"alias_kind":"pith_short_16","alias_value":"CXGFPM4ULJVOAKZG","created_at":"2026-07-05T08:40:24.294054+00:00"},{"alias_kind":"pith_short_8","alias_value":"CXGFPM4U","created_at":"2026-07-05T08:40:24.294054+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/CXGFPM4ULJVOAKZGTBQJ3XMSAM","json":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM.json","graph_json":"https://pith.science/api/pith-number/CXGFPM4ULJVOAKZGTBQJ3XMSAM/graph.json","events_json":"https://pith.science/api/pith-number/CXGFPM4ULJVOAKZGTBQJ3XMSAM/events.json","paper":"https://pith.science/paper/CXGFPM4U"},"agent_actions":{"view_html":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM","download_json":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM.json","view_paper":"https://pith.science/paper/CXGFPM4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.03801&json=true","fetch_graph":"https://pith.science/api/pith-number/CXGFPM4ULJVOAKZGTBQJ3XMSAM/graph.json","fetch_events":"https://pith.science/api/pith-number/CXGFPM4ULJVOAKZGTBQJ3XMSAM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM/action/storage_attestation","attest_author":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM/action/author_attestation","sign_citation":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM/action/citation_signature","submit_replication":"https://pith.science/pith/CXGFPM4ULJVOAKZGTBQJ3XMSAM/action/replication_record"}},"created_at":"2026-07-05T08:40:24.294054+00:00","updated_at":"2026-07-05T08:40:24.294054+00:00"}