{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PD2KI2K6KEPLLJBXFPOBDHI7TA","short_pith_number":"pith:PD2KI2K6","schema_version":"1.0","canonical_sha256":"78f4a4695e511eb5a4372bdc119d1f983dcce417b0b9aeb579ed8d31faca07d4","source":{"kind":"arxiv","id":"2401.17172","version":1},"attestation_state":"computed","paper":{"title":"Learning Domain-Independent Green's Function For Elliptic Partial Differential Equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Maggie Cheng, Mahesh Krishnamurthy, Pawan Negi, Shuwang Li, Wenjun Ying","submitted_at":"2024-01-30T17:00:22Z","abstract_excerpt":"Green's function characterizes a partial differential equation (PDE) and maps its solution in the entire domain as integrals. Finding the analytical form of Green's function is a non-trivial exercise, especially for a PDE defined on a complex domain or a PDE with variable coefficients. In this paper, we propose a novel boundary integral network to learn the domain-independent Green's function, referred to as BIN-G. We evaluate the Green's function in the BIN-G using a radial basis function (RBF) kernel-based neural network. We train the BIN-G by minimizing the residual of the PDE and the mean "},"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":"2401.17172","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2024-01-30T17:00:22Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"9cf4063c80599de46b17610335bea25aa24c2a7cec6b5d492751aae56854a392","abstract_canon_sha256":"e295d5391dd481de01aa2b0f0b050a0de3cbdf2ceb3a6fc721ad9af3f19d2e33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:39:20.998249Z","signature_b64":"eRX3OXm3ZffySUqx0NfmHGirql2k6ONqy9lNmQxPlgkM9IyWXPdhJkiGc+so3zOiWQdbauhLjnN3hChsmqj7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78f4a4695e511eb5a4372bdc119d1f983dcce417b0b9aeb579ed8d31faca07d4","last_reissued_at":"2026-07-05T07:39:20.997803Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:39:20.997803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning Domain-Independent Green's Function For Elliptic Partial Differential Equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"physics.comp-ph","authors_text":"Maggie Cheng, Mahesh Krishnamurthy, Pawan Negi, Shuwang Li, Wenjun Ying","submitted_at":"2024-01-30T17:00:22Z","abstract_excerpt":"Green's function characterizes a partial differential equation (PDE) and maps its solution in the entire domain as integrals. Finding the analytical form of Green's function is a non-trivial exercise, especially for a PDE defined on a complex domain or a PDE with variable coefficients. In this paper, we propose a novel boundary integral network to learn the domain-independent Green's function, referred to as BIN-G. We evaluate the Green's function in the BIN-G using a radial basis function (RBF) kernel-based neural network. We train the BIN-G by minimizing the residual of the PDE and the mean "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.17172","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/2401.17172/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":"2401.17172","created_at":"2026-07-05T07:39:20.997860+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.17172v1","created_at":"2026-07-05T07:39:20.997860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.17172","created_at":"2026-07-05T07:39:20.997860+00:00"},{"alias_kind":"pith_short_12","alias_value":"PD2KI2K6KEPL","created_at":"2026-07-05T07:39:20.997860+00:00"},{"alias_kind":"pith_short_16","alias_value":"PD2KI2K6KEPLLJBX","created_at":"2026-07-05T07:39:20.997860+00:00"},{"alias_kind":"pith_short_8","alias_value":"PD2KI2K6","created_at":"2026-07-05T07:39:20.997860+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/PD2KI2K6KEPLLJBXFPOBDHI7TA","json":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA.json","graph_json":"https://pith.science/api/pith-number/PD2KI2K6KEPLLJBXFPOBDHI7TA/graph.json","events_json":"https://pith.science/api/pith-number/PD2KI2K6KEPLLJBXFPOBDHI7TA/events.json","paper":"https://pith.science/paper/PD2KI2K6"},"agent_actions":{"view_html":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA","download_json":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA.json","view_paper":"https://pith.science/paper/PD2KI2K6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.17172&json=true","fetch_graph":"https://pith.science/api/pith-number/PD2KI2K6KEPLLJBXFPOBDHI7TA/graph.json","fetch_events":"https://pith.science/api/pith-number/PD2KI2K6KEPLLJBXFPOBDHI7TA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA/action/storage_attestation","attest_author":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA/action/author_attestation","sign_citation":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA/action/citation_signature","submit_replication":"https://pith.science/pith/PD2KI2K6KEPLLJBXFPOBDHI7TA/action/replication_record"}},"created_at":"2026-07-05T07:39:20.997860+00:00","updated_at":"2026-07-05T07:39:20.997860+00:00"}