{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BFLWJKH7PTPDW4VAKMUL34UGGE","short_pith_number":"pith:BFLWJKH7","schema_version":"1.0","canonical_sha256":"095764a8ff7cde3b72a05328bdf286313c1faab146135ae14734eb6e9f86a49f","source":{"kind":"arxiv","id":"2507.20463","version":1},"attestation_state":"computed","paper":{"title":"Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"math.DS","authors_text":"Benjamin Peherstorfer, Julie Bessac, Marc T. Henry de Frahan, Paul Schwerdtner, Prakash Mohan","submitted_at":"2025-07-28T01:45:55Z","abstract_excerpt":"Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to the embedded data in downstream learning steps is ignored. In contrast, we propose a greedy training procedure that takes into account both the reconstruction error on the snapshot data and the prediction error of reduced models fitted to the data. Because our procedure learns quadratic manifolds with the objective of achieving accurate reduced models, it avoids oscillatory and other non-smooth embeddings that can hind"},"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":"2507.20463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-07-28T01:45:55Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"1a6d59c0c7eade072daf98f1cd8fbad734e0d0a9c4b385e781215610e170c286","abstract_canon_sha256":"89bcbf609694d338c42ce8578ad0ea68c2e017e5abc07c5785b268c5e1af6cfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:19.740133Z","signature_b64":"B3TLSys54Kqhn5a3FFsR6zfv/gJFGUW3t4rnKQko6ikvCUr6NFYnj6BIWqehpWpsnyGvBRSWER9n1GfnugC8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"095764a8ff7cde3b72a05328bdf286313c1faab146135ae14734eb6e9f86a49f","last_reissued_at":"2026-07-05T11:44:19.739681Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:19.739681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"math.DS","authors_text":"Benjamin Peherstorfer, Julie Bessac, Marc T. Henry de Frahan, Paul Schwerdtner, Prakash Mohan","submitted_at":"2025-07-28T01:45:55Z","abstract_excerpt":"Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to the embedded data in downstream learning steps is ignored. In contrast, we propose a greedy training procedure that takes into account both the reconstruction error on the snapshot data and the prediction error of reduced models fitted to the data. Because our procedure learns quadratic manifolds with the objective of achieving accurate reduced models, it avoids oscillatory and other non-smooth embeddings that can hind"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20463","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/2507.20463/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":"2507.20463","created_at":"2026-07-05T11:44:19.739739+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.20463v1","created_at":"2026-07-05T11:44:19.739739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20463","created_at":"2026-07-05T11:44:19.739739+00:00"},{"alias_kind":"pith_short_12","alias_value":"BFLWJKH7PTPD","created_at":"2026-07-05T11:44:19.739739+00:00"},{"alias_kind":"pith_short_16","alias_value":"BFLWJKH7PTPDW4VA","created_at":"2026-07-05T11:44:19.739739+00:00"},{"alias_kind":"pith_short_8","alias_value":"BFLWJKH7","created_at":"2026-07-05T11:44:19.739739+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/BFLWJKH7PTPDW4VAKMUL34UGGE","json":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE.json","graph_json":"https://pith.science/api/pith-number/BFLWJKH7PTPDW4VAKMUL34UGGE/graph.json","events_json":"https://pith.science/api/pith-number/BFLWJKH7PTPDW4VAKMUL34UGGE/events.json","paper":"https://pith.science/paper/BFLWJKH7"},"agent_actions":{"view_html":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE","download_json":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE.json","view_paper":"https://pith.science/paper/BFLWJKH7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.20463&json=true","fetch_graph":"https://pith.science/api/pith-number/BFLWJKH7PTPDW4VAKMUL34UGGE/graph.json","fetch_events":"https://pith.science/api/pith-number/BFLWJKH7PTPDW4VAKMUL34UGGE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE/action/storage_attestation","attest_author":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE/action/author_attestation","sign_citation":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE/action/citation_signature","submit_replication":"https://pith.science/pith/BFLWJKH7PTPDW4VAKMUL34UGGE/action/replication_record"}},"created_at":"2026-07-05T11:44:19.739739+00:00","updated_at":"2026-07-05T11:44:19.739739+00:00"}