{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CKOQF7ZK27ZYO5RVQZHTHDRP4M","short_pith_number":"pith:CKOQF7ZK","schema_version":"1.0","canonical_sha256":"129d02ff2ad7f3877635864f338e2fe322faf6c2f19148b495db5cda33de6f26","source":{"kind":"arxiv","id":"2606.03936","version":1},"attestation_state":"computed","paper":{"title":"Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.geo-ph"],"primary_cat":"cs.LG","authors_text":"Fanny Lehmann, Filippo Gatti, Niccol\\`o Perrone, Stefania Fresca","submitted_at":"2026-06-02T17:26:15Z","abstract_excerpt":"Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain. We address this by treating NO predictions as auxiliary observations in a diffusion posterior sampling framework. Our method, FreqNO-DPS (https://github.com/niccoloperrone/FreqNO-"},"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":"2606.03936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-02T17:26:15Z","cross_cats_sorted":["physics.geo-ph"],"title_canon_sha256":"20d13f969b74240de57e8e24b1102e114d4edaa76d65253f3cec4ad8d53ebfdf","abstract_canon_sha256":"a6c9bd8d79912b4ab89f86fa4124b8e1e2d7b650370b7fea9bfdcf4a776e1e8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T02:06:07.358497Z","signature_b64":"RaRQTGbbuiUL10XhggZZizEHDRGsm3X6WSjUSZ/0JQ/9gYhDx+NlIX66My2x/ubgkPtX0x8DTdPBWWTOxlPRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"129d02ff2ad7f3877635864f338e2fe322faf6c2f19148b495db5cda33de6f26","last_reissued_at":"2026-06-03T02:06:07.358091Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T02:06:07.358091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.geo-ph"],"primary_cat":"cs.LG","authors_text":"Fanny Lehmann, Filippo Gatti, Niccol\\`o Perrone, Stefania Fresca","submitted_at":"2026-06-02T17:26:15Z","abstract_excerpt":"Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain. We address this by treating NO predictions as auxiliary observations in a diffusion posterior sampling framework. Our method, FreqNO-DPS (https://github.com/niccoloperrone/FreqNO-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03936","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/2606.03936/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":"2606.03936","created_at":"2026-06-03T02:06:07.358150+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.03936v1","created_at":"2026-06-03T02:06:07.358150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03936","created_at":"2026-06-03T02:06:07.358150+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKOQF7ZK27ZY","created_at":"2026-06-03T02:06:07.358150+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKOQF7ZK27ZYO5RV","created_at":"2026-06-03T02:06:07.358150+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKOQF7ZK","created_at":"2026-06-03T02:06:07.358150+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M","json":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M.json","graph_json":"https://pith.science/api/pith-number/CKOQF7ZK27ZYO5RVQZHTHDRP4M/graph.json","events_json":"https://pith.science/api/pith-number/CKOQF7ZK27ZYO5RVQZHTHDRP4M/events.json","paper":"https://pith.science/paper/CKOQF7ZK"},"agent_actions":{"view_html":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M","download_json":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M.json","view_paper":"https://pith.science/paper/CKOQF7ZK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.03936&json=true","fetch_graph":"https://pith.science/api/pith-number/CKOQF7ZK27ZYO5RVQZHTHDRP4M/graph.json","fetch_events":"https://pith.science/api/pith-number/CKOQF7ZK27ZYO5RVQZHTHDRP4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M/action/storage_attestation","attest_author":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M/action/author_attestation","sign_citation":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M/action/citation_signature","submit_replication":"https://pith.science/pith/CKOQF7ZK27ZYO5RVQZHTHDRP4M/action/replication_record"}},"created_at":"2026-06-03T02:06:07.358150+00:00","updated_at":"2026-06-03T02:06:07.358150+00:00"}