{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:U46RKALLF2B2FMTBNDBPSGAHVS","short_pith_number":"pith:U46RKALL","schema_version":"1.0","canonical_sha256":"a73d15016b2e83a2b26168c2f91807acb2b0978864b1a4bc48a8c61a97e31ba2","source":{"kind":"arxiv","id":"1801.07422","version":1},"attestation_state":"computed","paper":{"title":"A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.NA","authors_text":"Florent Pled (MSME), Ludovic Chamoin (LMT), Pierre-Eric Allier (LMT), Pierre Ladev\\`eze (LMT)","submitted_at":"2018-01-23T07:56:00Z","abstract_excerpt":"We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it provides guaranteed and fully computable global/goal-oriented error estimates taking both discretization and PGD truncation errors into account. Splitting the error sources, it also leads to a natural greedy adaptive strategy which can be driven in order to optimize the accuracy of PGD approximations. The focus of the paper is on two technical points: (i) cons"},"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":"1801.07422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-23T07:56:00Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"861881060f1c014d9d9922bead29ca1a6eeb5e62b493a33a3ca392a8865ddf50","abstract_canon_sha256":"7ac998b0c41b1a753953d6d45b492c83e44e6868a181925d8e31c7375c9623f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:43.514461Z","signature_b64":"iLfaAIFvUodA2TlpGFsH2ozhH8v2jvllaH6Cw/b4Ga0JI12JGmaIj7RLhdsDaeoDvRgXpeLMJ99ciPNkIf/ICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a73d15016b2e83a2b26168c2f91807acb2b0978864b1a4bc48a8c61a97e31ba2","last_reissued_at":"2026-05-18T00:12:43.513877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:43.513877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.NA","authors_text":"Florent Pled (MSME), Ludovic Chamoin (LMT), Pierre-Eric Allier (LMT), Pierre Ladev\\`eze (LMT)","submitted_at":"2018-01-23T07:56:00Z","abstract_excerpt":"We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it provides guaranteed and fully computable global/goal-oriented error estimates taking both discretization and PGD truncation errors into account. Splitting the error sources, it also leads to a natural greedy adaptive strategy which can be driven in order to optimize the accuracy of PGD approximations. The focus of the paper is on two technical points: (i) cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07422","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":""},"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":"1801.07422","created_at":"2026-05-18T00:12:43.513969+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.07422v1","created_at":"2026-05-18T00:12:43.513969+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07422","created_at":"2026-05-18T00:12:43.513969+00:00"},{"alias_kind":"pith_short_12","alias_value":"U46RKALLF2B2","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"U46RKALLF2B2FMTB","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"U46RKALL","created_at":"2026-05-18T12:32:56.356000+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/U46RKALLF2B2FMTBNDBPSGAHVS","json":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS.json","graph_json":"https://pith.science/api/pith-number/U46RKALLF2B2FMTBNDBPSGAHVS/graph.json","events_json":"https://pith.science/api/pith-number/U46RKALLF2B2FMTBNDBPSGAHVS/events.json","paper":"https://pith.science/paper/U46RKALL"},"agent_actions":{"view_html":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS","download_json":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS.json","view_paper":"https://pith.science/paper/U46RKALL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.07422&json=true","fetch_graph":"https://pith.science/api/pith-number/U46RKALLF2B2FMTBNDBPSGAHVS/graph.json","fetch_events":"https://pith.science/api/pith-number/U46RKALLF2B2FMTBNDBPSGAHVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS/action/storage_attestation","attest_author":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS/action/author_attestation","sign_citation":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS/action/citation_signature","submit_replication":"https://pith.science/pith/U46RKALLF2B2FMTBNDBPSGAHVS/action/replication_record"}},"created_at":"2026-05-18T00:12:43.513969+00:00","updated_at":"2026-05-18T00:12:43.513969+00:00"}