{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:O3QMFMXYHLXPXHKSV4YDMJBA74","short_pith_number":"pith:O3QMFMXY","schema_version":"1.0","canonical_sha256":"76e0c2b2f83aeefb9d52af30362420ff325a2283c99d646d112ef7de9f89be66","source":{"kind":"arxiv","id":"1308.1362","version":2},"attestation_state":"computed","paper":{"title":"Nonlinear Model Reduction via an Adaptive Weighting of Snapshots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Kamran Mohseni, Liqian Peng","submitted_at":"2013-08-06T18:02:02Z","abstract_excerpt":"In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear systems characterized by parameter variations. Instead of using a global basis to construct a global reduced model, the proposed method approximates the original system by multiple lower-dimensional subspaces. Each localized reduced basis is generated by the SVD of a weighted snapshot ensemble; here, each weighting coefficient is a function of the input parameter"},"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":"1308.1362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-06T18:02:02Z","cross_cats_sorted":[],"title_canon_sha256":"20e1e54acc3072c316a9e9f818c84100d01f9fb924ac2f64e19c0e8e350aeac5","abstract_canon_sha256":"0cc392c97240c71cb076f9d93ae580bd707a4b0a036666b0a4115f436e900eff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:26.253010Z","signature_b64":"EJn3vpnd2Dbnj+1f/pODFdKBjkhtpQaTDxTemaNp7xYpNb+BHhoA64kP0RKRzcdo9pKTpehA2OHEgvCKYKTHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76e0c2b2f83aeefb9d52af30362420ff325a2283c99d646d112ef7de9f89be66","last_reissued_at":"2026-05-18T02:41:26.252585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:26.252585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Model Reduction via an Adaptive Weighting of Snapshots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Kamran Mohseni, Liqian Peng","submitted_at":"2013-08-06T18:02:02Z","abstract_excerpt":"In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear systems characterized by parameter variations. Instead of using a global basis to construct a global reduced model, the proposed method approximates the original system by multiple lower-dimensional subspaces. Each localized reduced basis is generated by the SVD of a weighted snapshot ensemble; here, each weighting coefficient is a function of the input parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1362","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":""},"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":"1308.1362","created_at":"2026-05-18T02:41:26.252650+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.1362v2","created_at":"2026-05-18T02:41:26.252650+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1362","created_at":"2026-05-18T02:41:26.252650+00:00"},{"alias_kind":"pith_short_12","alias_value":"O3QMFMXYHLXP","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"O3QMFMXYHLXPXHKS","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"O3QMFMXY","created_at":"2026-05-18T12:27:54.935989+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/O3QMFMXYHLXPXHKSV4YDMJBA74","json":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74.json","graph_json":"https://pith.science/api/pith-number/O3QMFMXYHLXPXHKSV4YDMJBA74/graph.json","events_json":"https://pith.science/api/pith-number/O3QMFMXYHLXPXHKSV4YDMJBA74/events.json","paper":"https://pith.science/paper/O3QMFMXY"},"agent_actions":{"view_html":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74","download_json":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74.json","view_paper":"https://pith.science/paper/O3QMFMXY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.1362&json=true","fetch_graph":"https://pith.science/api/pith-number/O3QMFMXYHLXPXHKSV4YDMJBA74/graph.json","fetch_events":"https://pith.science/api/pith-number/O3QMFMXYHLXPXHKSV4YDMJBA74/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74/action/storage_attestation","attest_author":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74/action/author_attestation","sign_citation":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74/action/citation_signature","submit_replication":"https://pith.science/pith/O3QMFMXYHLXPXHKSV4YDMJBA74/action/replication_record"}},"created_at":"2026-05-18T02:41:26.252650+00:00","updated_at":"2026-05-18T02:41:26.252650+00:00"}