{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:TXIKAAOISIR55OFVZ3JWH4LQHM","short_pith_number":"pith:TXIKAAOI","schema_version":"1.0","canonical_sha256":"9dd0a001c89223deb8b5ced363f1703b1cf613711b44b51b958e09c1801df61c","source":{"kind":"arxiv","id":"2101.08932","version":2},"attestation_state":"computed","paper":{"title":"Sobolev Training for Physics Informed Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hwijae Son, Hyung Ju Hwang, Jin Woo Jang, Woo Jin Han","submitted_at":"2021-01-22T03:35:42Z","abstract_excerpt":"Physics Informed Neural Networks (PINNs) is a promising application of deep learning. The smooth architecture of a fully connected neural network is appropriate for finding the solutions of PDEs; the corresponding loss function can also be intuitively designed and guarantees the convergence for various kinds of PDEs. However, the rate of convergence has been considered as a weakness of this approach. This paper proposes Sobolev-PINNs, a novel loss function for the training of PINNs, making the training substantially efficient. Inspired by the recent studies that incorporate derivative informat"},"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":"2101.08932","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-01-22T03:35:42Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"46d12daf09d7d56fc2e725908e3e4919358a13bb430ff84fd90b8b40673a6d72","abstract_canon_sha256":"3f607b6bc3c5e436343363b881d5e7e6f451e6bf8aeb154c0d6c392accab263d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:38:59.118236Z","signature_b64":"Q/NSavRq3sOUvtkV/ZuIQJZ/rZ/E7DS3HokdHLElQAi1EOeF52JwLtjYbC8LpFEzjv4twgQnFZ58DX5OPwqADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dd0a001c89223deb8b5ced363f1703b1cf613711b44b51b958e09c1801df61c","last_reissued_at":"2026-07-05T03:38:59.117859Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:38:59.117859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sobolev Training for Physics Informed Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hwijae Son, Hyung Ju Hwang, Jin Woo Jang, Woo Jin Han","submitted_at":"2021-01-22T03:35:42Z","abstract_excerpt":"Physics Informed Neural Networks (PINNs) is a promising application of deep learning. The smooth architecture of a fully connected neural network is appropriate for finding the solutions of PDEs; the corresponding loss function can also be intuitively designed and guarantees the convergence for various kinds of PDEs. However, the rate of convergence has been considered as a weakness of this approach. This paper proposes Sobolev-PINNs, a novel loss function for the training of PINNs, making the training substantially efficient. Inspired by the recent studies that incorporate derivative informat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.08932","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/2101.08932/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":"2101.08932","created_at":"2026-07-05T03:38:59.117919+00:00"},{"alias_kind":"arxiv_version","alias_value":"2101.08932v2","created_at":"2026-07-05T03:38:59.117919+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.08932","created_at":"2026-07-05T03:38:59.117919+00:00"},{"alias_kind":"pith_short_12","alias_value":"TXIKAAOISIR5","created_at":"2026-07-05T03:38:59.117919+00:00"},{"alias_kind":"pith_short_16","alias_value":"TXIKAAOISIR55OFV","created_at":"2026-07-05T03:38:59.117919+00:00"},{"alias_kind":"pith_short_8","alias_value":"TXIKAAOI","created_at":"2026-07-05T03:38:59.117919+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.06047","citing_title":"Neural Shortest Path for Surface Reconstruction from Point Clouds","ref_index":50,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM","json":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM.json","graph_json":"https://pith.science/api/pith-number/TXIKAAOISIR55OFVZ3JWH4LQHM/graph.json","events_json":"https://pith.science/api/pith-number/TXIKAAOISIR55OFVZ3JWH4LQHM/events.json","paper":"https://pith.science/paper/TXIKAAOI"},"agent_actions":{"view_html":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM","download_json":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM.json","view_paper":"https://pith.science/paper/TXIKAAOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2101.08932&json=true","fetch_graph":"https://pith.science/api/pith-number/TXIKAAOISIR55OFVZ3JWH4LQHM/graph.json","fetch_events":"https://pith.science/api/pith-number/TXIKAAOISIR55OFVZ3JWH4LQHM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM/action/storage_attestation","attest_author":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM/action/author_attestation","sign_citation":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM/action/citation_signature","submit_replication":"https://pith.science/pith/TXIKAAOISIR55OFVZ3JWH4LQHM/action/replication_record"}},"created_at":"2026-07-05T03:38:59.117919+00:00","updated_at":"2026-07-05T03:38:59.117919+00:00"}