{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:PNGUXRBC33BWN46ABWK65IAXGA","short_pith_number":"pith:PNGUXRBC","schema_version":"1.0","canonical_sha256":"7b4d4bc422dec366f3c00d95eea0173023807eff312fa6c5dc1c7dc2cc2e23a7","source":{"kind":"arxiv","id":"2302.03358","version":2},"attestation_state":"computed","paper":{"title":"Deep-OSG: Deep Learning of Operators in Semigroup","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA","physics.comp-ph","stat.ML"],"primary_cat":"cs.LG","authors_text":"Junfeng Chen, Kailiang Wu","submitted_at":"2023-02-07T10:04:52Z","abstract_excerpt":"This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data collected at varied time lags. It is a sequel to the previous flow map learning (FML) works [T. Qin, K. Wu, and D. Xiu, J. Comput. Phys., 395:620--635, 2019], [K. Wu and D. Xiu, J. Comput. Phys., 408:109307, 2020], and [Z. Chen, V. Churchill, K. Wu, and D. Xiu, J. Comput. Phys., 449:110782, 2022], which focused on learning single evolution operator with a fixed time step. This paper aims to learn a family of evolution "},"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":"2302.03358","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2023-02-07T10:04:52Z","cross_cats_sorted":["cs.NA","math.DS","math.NA","physics.comp-ph","stat.ML"],"title_canon_sha256":"31cec89e67a6434089302e6fbcc5fd74598fa60d7a6f13e4f9eaa2d9af1257d5","abstract_canon_sha256":"34ce904068d4d9b3809d9a058a1d83b7f890f7b9eec463eed3d9c3124fb8c1a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:49:41.383422Z","signature_b64":"LA8Q3nIf1nret6RkKloBAf/nbtFt1KuLEgGzlbSlhxLnZr7p6ASnkoNVEWyq5QAu9+L3y1eElYsuTUgZceb8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b4d4bc422dec366f3c00d95eea0173023807eff312fa6c5dc1c7dc2cc2e23a7","last_reissued_at":"2026-07-05T06:49:41.382925Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:49:41.382925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deep-OSG: Deep Learning of Operators in Semigroup","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA","physics.comp-ph","stat.ML"],"primary_cat":"cs.LG","authors_text":"Junfeng Chen, Kailiang Wu","submitted_at":"2023-02-07T10:04:52Z","abstract_excerpt":"This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data collected at varied time lags. It is a sequel to the previous flow map learning (FML) works [T. Qin, K. Wu, and D. Xiu, J. Comput. Phys., 395:620--635, 2019], [K. Wu and D. Xiu, J. Comput. Phys., 408:109307, 2020], and [Z. Chen, V. Churchill, K. Wu, and D. Xiu, J. Comput. Phys., 449:110782, 2022], which focused on learning single evolution operator with a fixed time step. This paper aims to learn a family of evolution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.03358","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/2302.03358/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":"2302.03358","created_at":"2026-07-05T06:49:41.382985+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.03358v2","created_at":"2026-07-05T06:49:41.382985+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.03358","created_at":"2026-07-05T06:49:41.382985+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNGUXRBC33BW","created_at":"2026-07-05T06:49:41.382985+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNGUXRBC33BWN46A","created_at":"2026-07-05T06:49:41.382985+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNGUXRBC","created_at":"2026-07-05T06:49:41.382985+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.31438","citing_title":"Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA","json":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA.json","graph_json":"https://pith.science/api/pith-number/PNGUXRBC33BWN46ABWK65IAXGA/graph.json","events_json":"https://pith.science/api/pith-number/PNGUXRBC33BWN46ABWK65IAXGA/events.json","paper":"https://pith.science/paper/PNGUXRBC"},"agent_actions":{"view_html":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA","download_json":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA.json","view_paper":"https://pith.science/paper/PNGUXRBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.03358&json=true","fetch_graph":"https://pith.science/api/pith-number/PNGUXRBC33BWN46ABWK65IAXGA/graph.json","fetch_events":"https://pith.science/api/pith-number/PNGUXRBC33BWN46ABWK65IAXGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA/action/storage_attestation","attest_author":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA/action/author_attestation","sign_citation":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA/action/citation_signature","submit_replication":"https://pith.science/pith/PNGUXRBC33BWN46ABWK65IAXGA/action/replication_record"}},"created_at":"2026-07-05T06:49:41.382985+00:00","updated_at":"2026-07-05T06:49:41.382985+00:00"}