{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:3726U2EAGACRPIMGQ4D3N6PE63","short_pith_number":"pith:3726U2EA","schema_version":"1.0","canonical_sha256":"dff5ea6880300517a1868707b6f9e4f6c90ab92e5a22d56d43a4d544544c9db8","source":{"kind":"arxiv","id":"2402.07156","version":1},"attestation_state":"computed","paper":{"title":"A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Jun Hu, Pengzhan Jin","submitted_at":"2024-02-11T11:02:25Z","abstract_excerpt":"We propose a hybrid iterative method based on MIONet for PDEs, which combines the traditional numerical iterative solver and the recent powerful machine learning method of neural operator, and further systematically analyze its theoretical properties, including the convergence condition, the spectral behavior, as well as the convergence rate, in terms of the errors of the discretization and the model inference. We show the theoretical results for the frequently-used smoothers, i.e. Richardson (damped Jacobi) and Gauss-Seidel. We give an upper bound of the convergence rate of the hybrid method "},"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":"2402.07156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-11T11:02:25Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"ceede0c48beb7943f94229461c60bb2f6ac699484b54599c027f2707b8d16145","abstract_canon_sha256":"274e6fcd6ecb33311848a05ee35419692dc13bd222813beabddaf37d990f1e14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:44:01.953770Z","signature_b64":"zMAMW9DFzppF1BH5lk5+ThY2DblrtAnFSunXCEqmw/ItuGP6G/0zYF1VzI1oc59pR0moepLLPGGB4QSuRXJXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dff5ea6880300517a1868707b6f9e4f6c90ab92e5a22d56d43a4d544544c9db8","last_reissued_at":"2026-07-05T07:44:01.953281Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:44:01.953281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Jun Hu, Pengzhan Jin","submitted_at":"2024-02-11T11:02:25Z","abstract_excerpt":"We propose a hybrid iterative method based on MIONet for PDEs, which combines the traditional numerical iterative solver and the recent powerful machine learning method of neural operator, and further systematically analyze its theoretical properties, including the convergence condition, the spectral behavior, as well as the convergence rate, in terms of the errors of the discretization and the model inference. We show the theoretical results for the frequently-used smoothers, i.e. Richardson (damped Jacobi) and Gauss-Seidel. We give an upper bound of the convergence rate of the hybrid method "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07156","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/2402.07156/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":"2402.07156","created_at":"2026-07-05T07:44:01.953355+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.07156v1","created_at":"2026-07-05T07:44:01.953355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07156","created_at":"2026-07-05T07:44:01.953355+00:00"},{"alias_kind":"pith_short_12","alias_value":"3726U2EAGACR","created_at":"2026-07-05T07:44:01.953355+00:00"},{"alias_kind":"pith_short_16","alias_value":"3726U2EAGACRPIMG","created_at":"2026-07-05T07:44:01.953355+00:00"},{"alias_kind":"pith_short_8","alias_value":"3726U2EA","created_at":"2026-07-05T07:44:01.953355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.24876","citing_title":"IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients","ref_index":47,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07365","citing_title":"Solving Convolution-type Integral Equations using Preconditioned Neural Operators","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63","json":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63.json","graph_json":"https://pith.science/api/pith-number/3726U2EAGACRPIMGQ4D3N6PE63/graph.json","events_json":"https://pith.science/api/pith-number/3726U2EAGACRPIMGQ4D3N6PE63/events.json","paper":"https://pith.science/paper/3726U2EA"},"agent_actions":{"view_html":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63","download_json":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63.json","view_paper":"https://pith.science/paper/3726U2EA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.07156&json=true","fetch_graph":"https://pith.science/api/pith-number/3726U2EAGACRPIMGQ4D3N6PE63/graph.json","fetch_events":"https://pith.science/api/pith-number/3726U2EAGACRPIMGQ4D3N6PE63/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63/action/storage_attestation","attest_author":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63/action/author_attestation","sign_citation":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63/action/citation_signature","submit_replication":"https://pith.science/pith/3726U2EAGACRPIMGQ4D3N6PE63/action/replication_record"}},"created_at":"2026-07-05T07:44:01.953355+00:00","updated_at":"2026-07-05T07:44:01.953355+00:00"}