{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2QKSUBC7XZGEDGACSSQIKJZ3EF","short_pith_number":"pith:2QKSUBC7","schema_version":"1.0","canonical_sha256":"d4152a045fbe4c41980294a085273b215ec4e9b1509fb8ce816e20d8f8c60d99","source":{"kind":"arxiv","id":"2502.00550","version":1},"attestation_state":"computed","paper":{"title":"Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Guang Lin, Haoyang Zheng","submitted_at":"2025-02-01T20:38:50Z","abstract_excerpt":"Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of high-fidelity (HF) training data, which is often prohibitively expensive to acquire. To address this, we propose multi-fidelity Laplace Neural Operators (MF-LNOs), which combine a low-fidelity (LF) base model with parallel linear/nonlinear HF correctors and dynamic inter-fidelity weighting. This allows us to exploit correlations between LF and HF datasets a"},"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":"2502.00550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-01T20:38:50Z","cross_cats_sorted":["cs.NA","math.NA","physics.comp-ph"],"title_canon_sha256":"c584fcf758066eaa0f383a53e792f7e38f153a38d6328ab4fde1c8bdffd6e14c","abstract_canon_sha256":"19472c7682e2c5146e3e1b17d37a2b8d9469e764aa3dd7f968a62254d6e5c3b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:08:35.255694Z","signature_b64":"UmzJJhqxBuGbtkRCQKmVkw+rFihT7QAjADv1DhWF0W4ry9bie6hh4SssoEepZoWmt4MHH3Ge5HLPyMbtWQmMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4152a045fbe4c41980294a085273b215ec4e9b1509fb8ce816e20d8f8c60d99","last_reissued_at":"2026-07-05T10:08:35.255234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:08:35.255234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","physics.comp-ph"],"primary_cat":"cs.LG","authors_text":"Guang Lin, Haoyang Zheng","submitted_at":"2025-02-01T20:38:50Z","abstract_excerpt":"Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of high-fidelity (HF) training data, which is often prohibitively expensive to acquire. To address this, we propose multi-fidelity Laplace Neural Operators (MF-LNOs), which combine a low-fidelity (LF) base model with parallel linear/nonlinear HF correctors and dynamic inter-fidelity weighting. This allows us to exploit correlations between LF and HF datasets a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00550","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/2502.00550/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":"2502.00550","created_at":"2026-07-05T10:08:35.255299+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.00550v1","created_at":"2026-07-05T10:08:35.255299+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00550","created_at":"2026-07-05T10:08:35.255299+00:00"},{"alias_kind":"pith_short_12","alias_value":"2QKSUBC7XZGE","created_at":"2026-07-05T10:08:35.255299+00:00"},{"alias_kind":"pith_short_16","alias_value":"2QKSUBC7XZGEDGAC","created_at":"2026-07-05T10:08:35.255299+00:00"},{"alias_kind":"pith_short_8","alias_value":"2QKSUBC7","created_at":"2026-07-05T10:08:35.255299+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2511.02481","citing_title":"NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers","ref_index":30,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF","json":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF.json","graph_json":"https://pith.science/api/pith-number/2QKSUBC7XZGEDGACSSQIKJZ3EF/graph.json","events_json":"https://pith.science/api/pith-number/2QKSUBC7XZGEDGACSSQIKJZ3EF/events.json","paper":"https://pith.science/paper/2QKSUBC7"},"agent_actions":{"view_html":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF","download_json":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF.json","view_paper":"https://pith.science/paper/2QKSUBC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.00550&json=true","fetch_graph":"https://pith.science/api/pith-number/2QKSUBC7XZGEDGACSSQIKJZ3EF/graph.json","fetch_events":"https://pith.science/api/pith-number/2QKSUBC7XZGEDGACSSQIKJZ3EF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF/action/storage_attestation","attest_author":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF/action/author_attestation","sign_citation":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF/action/citation_signature","submit_replication":"https://pith.science/pith/2QKSUBC7XZGEDGACSSQIKJZ3EF/action/replication_record"}},"created_at":"2026-07-05T10:08:35.255299+00:00","updated_at":"2026-07-05T10:08:35.255299+00:00"}