{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HUHIPKDI242LTOCMOUIUZC6G4S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"203521fae8d1d56a2afdc80f1b5f0b45fc8671605b562f9acccea78713a7ba12","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-04-29T22:32:26Z","title_canon_sha256":"3dc057fb0553d89170fc924a921286d43335bca4a8bb538eee363ca643acaabf"},"schema_version":"1.0","source":{"id":"2404.19133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.19133","created_at":"2026-07-05T08:21:53Z"},{"alias_kind":"arxiv_version","alias_value":"2404.19133v2","created_at":"2026-07-05T08:21:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19133","created_at":"2026-07-05T08:21:53Z"},{"alias_kind":"pith_short_12","alias_value":"HUHIPKDI242L","created_at":"2026-07-05T08:21:53Z"},{"alias_kind":"pith_short_16","alias_value":"HUHIPKDI242LTOCM","created_at":"2026-07-05T08:21:53Z"},{"alias_kind":"pith_short_8","alias_value":"HUHIPKDI","created_at":"2026-07-05T08:21:53Z"}],"graph_snapshots":[{"event_id":"sha256:300a9c6360cb81efe62595197fc597d756b08b5bbe12132370969e8697ebab1e","target":"graph","created_at":"2026-07-05T08:21:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.19133/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize the push-forward maps such that they can push a simple reference density to the one solving the given WGF. The new dynamical system is called parameterized WGF (PWGF), and it is defined on the finite-dimensional parameter space equipped with a pullback Wasserstein metric. Our numerical scheme can approximate the solutions of WGFs for general energy functiona","authors_text":"Haomin Zhou, Hao Wu, Shu Liu, Xiaojing Ye, Yijie Jin","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-04-29T22:32:26Z","title":"Parameterized Wasserstein Gradient Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19133","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1e07790e52033b1ea4f91abbcae2dadddd477930e84d6d04e465061a57c0d115","target":"record","created_at":"2026-07-05T08:21:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"203521fae8d1d56a2afdc80f1b5f0b45fc8671605b562f9acccea78713a7ba12","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-04-29T22:32:26Z","title_canon_sha256":"3dc057fb0553d89170fc924a921286d43335bca4a8bb538eee363ca643acaabf"},"schema_version":"1.0","source":{"id":"2404.19133","kind":"arxiv","version":2}},"canonical_sha256":"3d0e87a868d734b9b84c75114c8bc6e48d703c7339288b1087c0fdb6c73900ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d0e87a868d734b9b84c75114c8bc6e48d703c7339288b1087c0fdb6c73900ed","first_computed_at":"2026-07-05T08:21:53.464080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:21:53.464080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QL82OTv6yhOlxigsqsKFruYeVWDkBelZL6Xxw6EBPU9Bo6WTHskWiSOJnWg/DTLFamqTE9xxz/Msc7srtSQzCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:21:53.464573Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.19133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e07790e52033b1ea4f91abbcae2dadddd477930e84d6d04e465061a57c0d115","sha256:300a9c6360cb81efe62595197fc597d756b08b5bbe12132370969e8697ebab1e"],"state_sha256":"f8d2a5d632b970de6c45271cfba5e9eac6765a1e9c5f5e684734474c5fd008e9"}