{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OBESVGPDVMB5I37XQ2UQ34CZUS","short_pith_number":"pith:OBESVGPD","schema_version":"1.0","canonical_sha256":"70492a99e3ab03d46ff786a90df059a48b75ad09e53f5e614200bdf1f3c93fdb","source":{"kind":"arxiv","id":"1506.00343","version":1},"attestation_state":"computed","paper":{"title":"On Polynomial Chaos Expansion via Gradient-enhanced $\\ell_1$-minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.CO","authors_text":"Alireza Doostan, Jerrad Hampton, Ji Peng","submitted_at":"2015-06-01T04:08:56Z","abstract_excerpt":"Gradient-enhanced Uncertainty Quantification (UQ) has received recent attention, in which the derivatives of a Quantity of Interest (QoI) with respect to the uncertain parameters are utilized to improve the surrogate approximation. Polynomial chaos expansions (PCEs) are often employed in UQ, and when the QoI can be represented by a sparse PCE, $\\ell_1$-minimization can identify the PCE coefficients with a relatively small number of samples. In this work, we investigate a gradient-enhanced $\\ell_1$-minimization, where derivative information is computed to accelerate the identification of the PC"},"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":"1506.00343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-06-01T04:08:56Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"627c21aa7e7ab0f71bfe11e4517ecc36f172337c482d209c5252e17466c23adf","abstract_canon_sha256":"c472eb34899bf0906b589fb154185fa2f263ca4cd0d7310c6de12c5edd78af36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:44.802275Z","signature_b64":"f2uREL4VtJ5RzlpaOo7MUGmkSkSMraL8MqAsOth9k+wg5F4A8j6rwNzHfX5+Mml9AMO+k3c4d2wN64c2bXexCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70492a99e3ab03d46ff786a90df059a48b75ad09e53f5e614200bdf1f3c93fdb","last_reissued_at":"2026-05-18T01:18:44.801785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:44.801785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Polynomial Chaos Expansion via Gradient-enhanced $\\ell_1$-minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.CO","authors_text":"Alireza Doostan, Jerrad Hampton, Ji Peng","submitted_at":"2015-06-01T04:08:56Z","abstract_excerpt":"Gradient-enhanced Uncertainty Quantification (UQ) has received recent attention, in which the derivatives of a Quantity of Interest (QoI) with respect to the uncertain parameters are utilized to improve the surrogate approximation. Polynomial chaos expansions (PCEs) are often employed in UQ, and when the QoI can be represented by a sparse PCE, $\\ell_1$-minimization can identify the PCE coefficients with a relatively small number of samples. In this work, we investigate a gradient-enhanced $\\ell_1$-minimization, where derivative information is computed to accelerate the identification of the PC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00343","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":"1506.00343","created_at":"2026-05-18T01:18:44.801861+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00343v1","created_at":"2026-05-18T01:18:44.801861+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00343","created_at":"2026-05-18T01:18:44.801861+00:00"},{"alias_kind":"pith_short_12","alias_value":"OBESVGPDVMB5","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OBESVGPDVMB5I37X","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OBESVGPD","created_at":"2026-05-18T12:29:34.919912+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/OBESVGPDVMB5I37XQ2UQ34CZUS","json":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS.json","graph_json":"https://pith.science/api/pith-number/OBESVGPDVMB5I37XQ2UQ34CZUS/graph.json","events_json":"https://pith.science/api/pith-number/OBESVGPDVMB5I37XQ2UQ34CZUS/events.json","paper":"https://pith.science/paper/OBESVGPD"},"agent_actions":{"view_html":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS","download_json":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS.json","view_paper":"https://pith.science/paper/OBESVGPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00343&json=true","fetch_graph":"https://pith.science/api/pith-number/OBESVGPDVMB5I37XQ2UQ34CZUS/graph.json","fetch_events":"https://pith.science/api/pith-number/OBESVGPDVMB5I37XQ2UQ34CZUS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS/action/storage_attestation","attest_author":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS/action/author_attestation","sign_citation":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS/action/citation_signature","submit_replication":"https://pith.science/pith/OBESVGPDVMB5I37XQ2UQ34CZUS/action/replication_record"}},"created_at":"2026-05-18T01:18:44.801861+00:00","updated_at":"2026-05-18T01:18:44.801861+00:00"}