{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ZRQP6LPWL3BF5NQMDU3JES6JD7","short_pith_number":"pith:ZRQP6LPW","schema_version":"1.0","canonical_sha256":"cc60ff2df65ec25eb60c1d36924bc91fc9f9bdc13e8f8e65e25f2c8f490ddf4a","source":{"kind":"arxiv","id":"2206.03551","version":1},"attestation_state":"computed","paper":{"title":"NOMAD: Nonlinear Manifold Decoders for Operator Learning","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"George J. Pappas, Georgios Kissas, Jacob H. Seidman, Paris Perdikaris","submitted_at":"2022-06-07T19:52:44Z","abstract_excerpt":"Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensio"},"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":"2206.03551","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-07T19:52:44Z","cross_cats_sorted":[],"title_canon_sha256":"cc22c5d74d6b84f54c6eeecca3c2a932201213b1c57e0db6a170994f7219d5b2","abstract_canon_sha256":"942a192ee3a738368a02aa00cf103c31b77734132e22a4c777926622ba9665c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:30:10.586012Z","signature_b64":"WKxj1xDbX4SGRtx88lyJmtqE1VmjElo6U77pzkE0CXIgs8WiQIuCk5B5n+yPhIOhHTqhz7oGbSrmWp4XWwY3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc60ff2df65ec25eb60c1d36924bc91fc9f9bdc13e8f8e65e25f2c8f490ddf4a","last_reissued_at":"2026-07-05T04:30:10.585490Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:30:10.585490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"NOMAD: Nonlinear Manifold Decoders for Operator Learning","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"George J. Pappas, Georgios Kissas, Jacob H. Seidman, Paris Perdikaris","submitted_at":"2022-06-07T19:52:44Z","abstract_excerpt":"Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.03551","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/2206.03551/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":"2206.03551","created_at":"2026-07-05T04:30:10.585557+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.03551v1","created_at":"2026-07-05T04:30:10.585557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.03551","created_at":"2026-07-05T04:30:10.585557+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZRQP6LPWL3BF","created_at":"2026-07-05T04:30:10.585557+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZRQP6LPWL3BF5NQM","created_at":"2026-07-05T04:30:10.585557+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZRQP6LPW","created_at":"2026-07-05T04:30:10.585557+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.08956","citing_title":"From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.19823","citing_title":"Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7","json":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7.json","graph_json":"https://pith.science/api/pith-number/ZRQP6LPWL3BF5NQMDU3JES6JD7/graph.json","events_json":"https://pith.science/api/pith-number/ZRQP6LPWL3BF5NQMDU3JES6JD7/events.json","paper":"https://pith.science/paper/ZRQP6LPW"},"agent_actions":{"view_html":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7","download_json":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7.json","view_paper":"https://pith.science/paper/ZRQP6LPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.03551&json=true","fetch_graph":"https://pith.science/api/pith-number/ZRQP6LPWL3BF5NQMDU3JES6JD7/graph.json","fetch_events":"https://pith.science/api/pith-number/ZRQP6LPWL3BF5NQMDU3JES6JD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7/action/storage_attestation","attest_author":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7/action/author_attestation","sign_citation":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7/action/citation_signature","submit_replication":"https://pith.science/pith/ZRQP6LPWL3BF5NQMDU3JES6JD7/action/replication_record"}},"created_at":"2026-07-05T04:30:10.585557+00:00","updated_at":"2026-07-05T04:30:10.585557+00:00"}