{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BIIPZ6ZBEABFO6TIYKOFP72FIV","short_pith_number":"pith:BIIPZ6ZB","schema_version":"1.0","canonical_sha256":"0a10fcfb212002577a68c29c57ff45456e64acf9102b195b261c0765e1cca793","source":{"kind":"arxiv","id":"1708.06850","version":2},"attestation_state":"computed","paper":{"title":"Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.DS"],"primary_cat":"cs.LG","authors_text":"Enoch Yeung, Nathan Hodas, Soumya Kundu","submitted_at":"2017-08-22T23:32:19Z","abstract_excerpt":"The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this "},"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":"1708.06850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-22T23:32:19Z","cross_cats_sorted":["cs.AI","math.DS"],"title_canon_sha256":"af434c32aac8e3444ca609aa759118d3a19f87e20937110c15d220f77ee308ae","abstract_canon_sha256":"07c9cbb18ded4f3338ed305e717ff444dcaecf176dfa5aa555434a0f0985b327"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:29.756589Z","signature_b64":"fwQ1I1tWb6nGBuXL/GrAQnkrH4nMleoTNZ5QYgWfP/TN9bLvcwxIiPcuH1QDgEmY+jJjnnsCchGJ2QmNvPszAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a10fcfb212002577a68c29c57ff45456e64acf9102b195b261c0765e1cca793","last_reissued_at":"2026-05-18T00:28:29.755896Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:29.755896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.DS"],"primary_cat":"cs.LG","authors_text":"Enoch Yeung, Nathan Hodas, Soumya Kundu","submitted_at":"2017-08-22T23:32:19Z","abstract_excerpt":"The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06850","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":"1708.06850","created_at":"2026-05-18T00:28:29.756016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.06850v2","created_at":"2026-05-18T00:28:29.756016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06850","created_at":"2026-05-18T00:28:29.756016+00:00"},{"alias_kind":"pith_short_12","alias_value":"BIIPZ6ZBEABF","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BIIPZ6ZBEABFO6TI","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BIIPZ6ZB","created_at":"2026-05-18T12:31:08.081275+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.04164","citing_title":"Enabling Real-Time Training of a Wildfire-to-Smoke Map with Multilinear Operators","ref_index":94,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV","json":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV.json","graph_json":"https://pith.science/api/pith-number/BIIPZ6ZBEABFO6TIYKOFP72FIV/graph.json","events_json":"https://pith.science/api/pith-number/BIIPZ6ZBEABFO6TIYKOFP72FIV/events.json","paper":"https://pith.science/paper/BIIPZ6ZB"},"agent_actions":{"view_html":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV","download_json":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV.json","view_paper":"https://pith.science/paper/BIIPZ6ZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.06850&json=true","fetch_graph":"https://pith.science/api/pith-number/BIIPZ6ZBEABFO6TIYKOFP72FIV/graph.json","fetch_events":"https://pith.science/api/pith-number/BIIPZ6ZBEABFO6TIYKOFP72FIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV/action/storage_attestation","attest_author":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV/action/author_attestation","sign_citation":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV/action/citation_signature","submit_replication":"https://pith.science/pith/BIIPZ6ZBEABFO6TIYKOFP72FIV/action/replication_record"}},"created_at":"2026-05-18T00:28:29.756016+00:00","updated_at":"2026-05-18T00:28:29.756016+00:00"}