{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JS3BH6SK5KKNAPQIAHVLNJAL32","short_pith_number":"pith:JS3BH6SK","schema_version":"1.0","canonical_sha256":"4cb613fa4aea94d03e0801eab6a40bde8b93d86fac3930ba5a1b38d743217849","source":{"kind":"arxiv","id":"1812.08373","version":3},"attestation_state":"computed","paper":{"title":"Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Kevin Carlberg, Kookjin Lee","submitted_at":"2018-12-20T06:23:55Z","abstract_excerpt":"Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) POD. Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov $n$-wid"},"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":"1812.08373","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-12-20T06:23:55Z","cross_cats_sorted":[],"title_canon_sha256":"153d45b04c1b5f61ed294a060ae70a0460ef81180ad6789a362225a88c6ddcca","abstract_canon_sha256":"92c4170789e6694e7f7054168242ea343b0fcf6580da00a79e0c69b6fb71b34a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:02.577747Z","signature_b64":"rF5wdpHUQsss99f1j+LXO2l/2f/vqp4JKVvwutj+FEYNcmXExrvf5GwToAu4IFU/ToREmgE9QC3YIUAw3TfuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cb613fa4aea94d03e0801eab6a40bde8b93d86fac3930ba5a1b38d743217849","last_reissued_at":"2026-05-17T23:44:02.577366Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:02.577366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NA","authors_text":"Kevin Carlberg, Kookjin Lee","submitted_at":"2018-12-20T06:23:55Z","abstract_excerpt":"Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) POD. Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov $n$-wid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08373","kind":"arxiv","version":3},"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":"1812.08373","created_at":"2026-05-17T23:44:02.577426+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.08373v3","created_at":"2026-05-17T23:44:02.577426+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08373","created_at":"2026-05-17T23:44:02.577426+00:00"},{"alias_kind":"pith_short_12","alias_value":"JS3BH6SK5KKN","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JS3BH6SK5KKNAPQI","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JS3BH6SK","created_at":"2026-05-18T12:32:31.084164+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/JS3BH6SK5KKNAPQIAHVLNJAL32","json":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32.json","graph_json":"https://pith.science/api/pith-number/JS3BH6SK5KKNAPQIAHVLNJAL32/graph.json","events_json":"https://pith.science/api/pith-number/JS3BH6SK5KKNAPQIAHVLNJAL32/events.json","paper":"https://pith.science/paper/JS3BH6SK"},"agent_actions":{"view_html":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32","download_json":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32.json","view_paper":"https://pith.science/paper/JS3BH6SK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.08373&json=true","fetch_graph":"https://pith.science/api/pith-number/JS3BH6SK5KKNAPQIAHVLNJAL32/graph.json","fetch_events":"https://pith.science/api/pith-number/JS3BH6SK5KKNAPQIAHVLNJAL32/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32/action/storage_attestation","attest_author":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32/action/author_attestation","sign_citation":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32/action/citation_signature","submit_replication":"https://pith.science/pith/JS3BH6SK5KKNAPQIAHVLNJAL32/action/replication_record"}},"created_at":"2026-05-17T23:44:02.577426+00:00","updated_at":"2026-05-17T23:44:02.577426+00:00"}