{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Z2RWZNX2C7TI7YNTJUEYFKFSIG","short_pith_number":"pith:Z2RWZNX2","schema_version":"1.0","canonical_sha256":"cea36cb6fa17e68fe1b34d0982a8b241ad552f5be1be2c4c5a2731941c5184e6","source":{"kind":"arxiv","id":"2503.17797","version":2},"attestation_state":"computed","paper":{"title":"Enhancing Fourier Neural Operators with Local Spatial Features","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["eess.IV"],"primary_cat":"cs.LG","authors_text":"Carola-Bibiane Sch\\\"onlieb, Chaoyu Liu, Chris Budd, Davide Murari, Lihao Liu, Yangming Li","submitted_at":"2025-03-22T15:11:56Z","abstract_excerpt":"Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as an efficient approach for solving these PDE problems. By using parametrization in the frequency domain, FNOs can efficiently capture global patterns. However, this approach inherently overlooks the critical role of local spatial features, as frequency-domain parameterized convolutions primarily emphasize global interactions without encoding comprehensive lo"},"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":"2503.17797","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-22T15:11:56Z","cross_cats_sorted":["eess.IV"],"title_canon_sha256":"fabad52a9bf583d159be7a8d3ab44755454494c667835415996861ed151f1f71","abstract_canon_sha256":"6ddce400877a86fb3cc22c1fd9a94c1796cd1fc25860de5a4122f55a2ce2ccd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:20.156370Z","signature_b64":"OOyvz1/mNpPrG8ZKoW4q+3VoML/zL73Ea1V/jY5JYA2Vk9qMc6XlsB+LYJcCnxp1f9HX/9xM1jLCK2EDkrkDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea36cb6fa17e68fe1b34d0982a8b241ad552f5be1be2c4c5a2731941c5184e6","last_reissued_at":"2026-07-05T11:15:20.155890Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:20.155890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enhancing Fourier Neural Operators with Local Spatial Features","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["eess.IV"],"primary_cat":"cs.LG","authors_text":"Carola-Bibiane Sch\\\"onlieb, Chaoyu Liu, Chris Budd, Davide Murari, Lihao Liu, Yangming Li","submitted_at":"2025-03-22T15:11:56Z","abstract_excerpt":"Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as an efficient approach for solving these PDE problems. By using parametrization in the frequency domain, FNOs can efficiently capture global patterns. However, this approach inherently overlooks the critical role of local spatial features, as frequency-domain parameterized convolutions primarily emphasize global interactions without encoding comprehensive lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.17797","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/2503.17797/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":"2503.17797","created_at":"2026-07-05T11:15:20.155950+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.17797v2","created_at":"2026-07-05T11:15:20.155950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.17797","created_at":"2026-07-05T11:15:20.155950+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2RWZNX2C7TI","created_at":"2026-07-05T11:15:20.155950+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2RWZNX2C7TI7YNT","created_at":"2026-07-05T11:15:20.155950+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2RWZNX2","created_at":"2026-07-05T11:15:20.155950+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2512.10723","citing_title":"Generalized Spherical Neural Operators: Green's Function Formulation","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12965","citing_title":"U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26745","citing_title":"Robust Model-Based Iteration for Passive Gamma Emission Tomography","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04198","citing_title":"Deep Wave Network for Modeling Multi-Scale Physical Dynamics","ref_index":48,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20372","citing_title":"AI models of unstable flow exhibit hallucination","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG","json":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG.json","graph_json":"https://pith.science/api/pith-number/Z2RWZNX2C7TI7YNTJUEYFKFSIG/graph.json","events_json":"https://pith.science/api/pith-number/Z2RWZNX2C7TI7YNTJUEYFKFSIG/events.json","paper":"https://pith.science/paper/Z2RWZNX2"},"agent_actions":{"view_html":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG","download_json":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG.json","view_paper":"https://pith.science/paper/Z2RWZNX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.17797&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2RWZNX2C7TI7YNTJUEYFKFSIG/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2RWZNX2C7TI7YNTJUEYFKFSIG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG/action/storage_attestation","attest_author":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG/action/author_attestation","sign_citation":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG/action/citation_signature","submit_replication":"https://pith.science/pith/Z2RWZNX2C7TI7YNTJUEYFKFSIG/action/replication_record"}},"created_at":"2026-07-05T11:15:20.155950+00:00","updated_at":"2026-07-05T11:15:20.155950+00:00"}