{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WNJGER3AFFQYDYMBDZFHGM3P5Q","short_pith_number":"pith:WNJGER3A","schema_version":"1.0","canonical_sha256":"b352624760296181e1811e4a73336fec031525f6409936e91b86ff0403e9809f","source":{"kind":"arxiv","id":"2305.10784","version":2},"attestation_state":"computed","paper":{"title":"Numerical solution of the incompressible Navier-Stokes equations for chemical mixers via quantum-inspired Tensor Train Finite Element Method","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","quant-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Artem Melnikov, Egor Kornev, Karan Pinto, Markus Pflitsch, Michael Perelshtein, Sergey Dolgov","submitted_at":"2023-05-18T07:54:56Z","abstract_excerpt":"The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We propose to use Tensor Train (TT) methods, which possess logarithmic complexity in problem size and have great similarities with quantum algorithms in the structure of data representation. We develop the Tensor train Finite Element Method -- TetraFEM -- and the explicit numerical scheme for the solution of the incompressible Navier-Stokes equation via Tensor Trains. We test this approach on the simulation of liquids mixi"},"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":"2305.10784","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.flu-dyn","submitted_at":"2023-05-18T07:54:56Z","cross_cats_sorted":["cs.NA","math.NA","quant-ph"],"title_canon_sha256":"6b7e0678a32d195b262da2afec809f724e8751deb193ac635f56625f0fdebf8e","abstract_canon_sha256":"f8b302a4e3704fb7b3976beaf36a6d85d9126b4b66189b1d87d5f2d40eb230a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:12:50.845307Z","signature_b64":"BYVAdwxqHADrP6H2a4ugr8+3B98EdwPIxyYyhSCH8SU2RueKbalCl3+eM6nIWB2y1GYbPisoZicDAkiOWcyvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b352624760296181e1811e4a73336fec031525f6409936e91b86ff0403e9809f","last_reissued_at":"2026-07-05T06:12:50.844880Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:12:50.844880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical solution of the incompressible Navier-Stokes equations for chemical mixers via quantum-inspired Tensor Train Finite Element Method","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA","quant-ph"],"primary_cat":"physics.flu-dyn","authors_text":"Artem Melnikov, Egor Kornev, Karan Pinto, Markus Pflitsch, Michael Perelshtein, Sergey Dolgov","submitted_at":"2023-05-18T07:54:56Z","abstract_excerpt":"The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We propose to use Tensor Train (TT) methods, which possess logarithmic complexity in problem size and have great similarities with quantum algorithms in the structure of data representation. We develop the Tensor train Finite Element Method -- TetraFEM -- and the explicit numerical scheme for the solution of the incompressible Navier-Stokes equation via Tensor Trains. We test this approach on the simulation of liquids mixi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.10784","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.10784/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2305.10784","created_at":"2026-07-05T06:12:50.844934+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.10784v2","created_at":"2026-07-05T06:12:50.844934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.10784","created_at":"2026-07-05T06:12:50.844934+00:00"},{"alias_kind":"pith_short_12","alias_value":"WNJGER3AFFQY","created_at":"2026-07-05T06:12:50.844934+00:00"},{"alias_kind":"pith_short_16","alias_value":"WNJGER3AFFQYDYMB","created_at":"2026-07-05T06:12:50.844934+00:00"},{"alias_kind":"pith_short_8","alias_value":"WNJGER3A","created_at":"2026-07-05T06:12:50.844934+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":7,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.12833","citing_title":"A practical investigation on time integration in the quantized tensor train format","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2507.05222","citing_title":"Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates","ref_index":81,"is_internal_anchor":false},{"citing_arxiv_id":"2507.11276","citing_title":"Diagnosing phase transitions through time-scale entanglement","ref_index":33,"is_internal_anchor":false},{"citing_arxiv_id":"2510.14099","citing_title":"A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics","ref_index":46,"is_internal_anchor":false},{"citing_arxiv_id":"2604.00037","citing_title":"Fast elementwise operations on tensor trains with alternating cross interpolation","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2604.09337","citing_title":"Tailoring tensor network techniques to the quantics representation for highly inhomogeneous problems and few body problems","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2502.04425","citing_title":"Tensor-Programmable Quantum Circuits for Solving Differential Equations","ref_index":49,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q","json":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q.json","graph_json":"https://pith.science/api/pith-number/WNJGER3AFFQYDYMBDZFHGM3P5Q/graph.json","events_json":"https://pith.science/api/pith-number/WNJGER3AFFQYDYMBDZFHGM3P5Q/events.json","paper":"https://pith.science/paper/WNJGER3A"},"agent_actions":{"view_html":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q","download_json":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q.json","view_paper":"https://pith.science/paper/WNJGER3A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.10784&json=true","fetch_graph":"https://pith.science/api/pith-number/WNJGER3AFFQYDYMBDZFHGM3P5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/WNJGER3AFFQYDYMBDZFHGM3P5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q/action/storage_attestation","attest_author":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q/action/author_attestation","sign_citation":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q/action/citation_signature","submit_replication":"https://pith.science/pith/WNJGER3AFFQYDYMBDZFHGM3P5Q/action/replication_record"}},"created_at":"2026-07-05T06:12:50.844934+00:00","updated_at":"2026-07-05T06:12:50.844934+00:00"}