{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RNYSUTEGGBRZKUXXKWTFL7LW4Y","short_pith_number":"pith:RNYSUTEG","schema_version":"1.0","canonical_sha256":"8b712a4c8630639552f755a655fd76e603096251afa84e86eaa91e4f750e69c9","source":{"kind":"arxiv","id":"1506.06178","version":1},"attestation_state":"computed","paper":{"title":"Robust Model Reduction by $L^1$-norm Minimization and Approximation via Dictionaries: Application to Linear and Nonlinear Hyperbolic Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David Amsallem, Remi Abgrall","submitted_at":"2015-06-19T23:05:58Z","abstract_excerpt":"We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online $L^1$-norm minimization of the residual. It is shown why this is a natural framework for hyperbolic problems and tested on nonlinear problems such as Burgers' equation and the one-dimensional Euler equations involving shocks and discontinuities. Efficient algorithms are presented for the computation of the $L^1$-norm minimizer, both in the cases of linear and no"},"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":"1506.06178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-06-19T23:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"caae38f6e0a7a2c1168cbeb9cc00a77dd625db97de116f74de6fe6b9737dc74b","abstract_canon_sha256":"da8f536f542843fc4b59fa39b1e69f617c3f5dde866a668496c6dcb4621fa398"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:58.527504Z","signature_b64":"1OBLIFu+YO0IUYJ89jCku+ec8GLZ9q0IhpyR5gN49Lem6ktKPgVJKzctu8q4AI+ob6x2dfb/IgczIuCobjdJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b712a4c8630639552f755a655fd76e603096251afa84e86eaa91e4f750e69c9","last_reissued_at":"2026-05-18T01:41:58.527063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:58.527063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust Model Reduction by $L^1$-norm Minimization and Approximation via Dictionaries: Application to Linear and Nonlinear Hyperbolic Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David Amsallem, Remi Abgrall","submitted_at":"2015-06-19T23:05:58Z","abstract_excerpt":"We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online $L^1$-norm minimization of the residual. It is shown why this is a natural framework for hyperbolic problems and tested on nonlinear problems such as Burgers' equation and the one-dimensional Euler equations involving shocks and discontinuities. Efficient algorithms are presented for the computation of the $L^1$-norm minimizer, both in the cases of linear and no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06178","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":"1506.06178","created_at":"2026-05-18T01:41:58.527134+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.06178v1","created_at":"2026-05-18T01:41:58.527134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06178","created_at":"2026-05-18T01:41:58.527134+00:00"},{"alias_kind":"pith_short_12","alias_value":"RNYSUTEGGBRZ","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RNYSUTEGGBRZKUXX","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RNYSUTEG","created_at":"2026-05-18T12:29:39.896362+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/RNYSUTEGGBRZKUXXKWTFL7LW4Y","json":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y.json","graph_json":"https://pith.science/api/pith-number/RNYSUTEGGBRZKUXXKWTFL7LW4Y/graph.json","events_json":"https://pith.science/api/pith-number/RNYSUTEGGBRZKUXXKWTFL7LW4Y/events.json","paper":"https://pith.science/paper/RNYSUTEG"},"agent_actions":{"view_html":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y","download_json":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y.json","view_paper":"https://pith.science/paper/RNYSUTEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.06178&json=true","fetch_graph":"https://pith.science/api/pith-number/RNYSUTEGGBRZKUXXKWTFL7LW4Y/graph.json","fetch_events":"https://pith.science/api/pith-number/RNYSUTEGGBRZKUXXKWTFL7LW4Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y/action/storage_attestation","attest_author":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y/action/author_attestation","sign_citation":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y/action/citation_signature","submit_replication":"https://pith.science/pith/RNYSUTEGGBRZKUXXKWTFL7LW4Y/action/replication_record"}},"created_at":"2026-05-18T01:41:58.527134+00:00","updated_at":"2026-05-18T01:41:58.527134+00:00"}