{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:CDTQXSBEQVFP4FVXBNDCP3WY6A","short_pith_number":"pith:CDTQXSBE","schema_version":"1.0","canonical_sha256":"10e70bc824854afe16b70b4627eed8f01e9c405e6a7e92f2f10a8db7ba781642","source":{"kind":"arxiv","id":"2201.02217","version":1},"attestation_state":"computed","paper":{"title":"Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Huaiqian You, Marta D'Elia, Stewart Silling, Tian Gao, Yue Yu","submitted_at":"2022-01-06T19:19:35Z","abstract_excerpt":"Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel "},"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":"2201.02217","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2022-01-06T19:19:35Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"9247abd1b992d300c29ce40d1265ef9af6ba3a72e3910301985f32b179aace24","abstract_canon_sha256":"463e671ebcfaa6f449e032065452f5cb483589a38e151606e86e288650d286c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:54:50.109111Z","signature_b64":"lMmGp8jzQW8IKSkv2mOEiwsxwh5aM6B4WZqcMWoBX04rimhvTw8NbzmBrWhwTCf/8wyAA8+SgqnevfojZCRRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10e70bc824854afe16b70b4627eed8f01e9c405e6a7e92f2f10a8db7ba781642","last_reissued_at":"2026-07-05T04:54:50.108679Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:54:50.108679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Huaiqian You, Marta D'Elia, Stewart Silling, Tian Gao, Yue Yu","submitted_at":"2022-01-06T19:19:35Z","abstract_excerpt":"Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.02217","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/2201.02217/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":"2201.02217","created_at":"2026-07-05T04:54:50.108744+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.02217v1","created_at":"2026-07-05T04:54:50.108744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.02217","created_at":"2026-07-05T04:54:50.108744+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDTQXSBEQVFP","created_at":"2026-07-05T04:54:50.108744+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDTQXSBEQVFP4FVX","created_at":"2026-07-05T04:54:50.108744+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDTQXSBE","created_at":"2026-07-05T04:54:50.108744+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.23106","citing_title":"Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery","ref_index":2001,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A","json":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A.json","graph_json":"https://pith.science/api/pith-number/CDTQXSBEQVFP4FVXBNDCP3WY6A/graph.json","events_json":"https://pith.science/api/pith-number/CDTQXSBEQVFP4FVXBNDCP3WY6A/events.json","paper":"https://pith.science/paper/CDTQXSBE"},"agent_actions":{"view_html":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A","download_json":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A.json","view_paper":"https://pith.science/paper/CDTQXSBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.02217&json=true","fetch_graph":"https://pith.science/api/pith-number/CDTQXSBEQVFP4FVXBNDCP3WY6A/graph.json","fetch_events":"https://pith.science/api/pith-number/CDTQXSBEQVFP4FVXBNDCP3WY6A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A/action/storage_attestation","attest_author":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A/action/author_attestation","sign_citation":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A/action/citation_signature","submit_replication":"https://pith.science/pith/CDTQXSBEQVFP4FVXBNDCP3WY6A/action/replication_record"}},"created_at":"2026-07-05T04:54:50.108744+00:00","updated_at":"2026-07-05T04:54:50.108744+00:00"}