{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HSKVL3F32PVPRG3A7C4WVM65OY","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":"b7dcb7653341ac8bef464103e3797095f8bf2e01ec9d401a7c2535d68b0bb8cb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-02-26T05:21:06Z","title_canon_sha256":"2e83111e51643b5e7066537cae2caf7e390886e46ecde05ddafa770a1b31a9b1"},"schema_version":"1.0","source":{"id":"2002.11309","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.11309","created_at":"2026-07-05T04:32:47Z"},{"alias_kind":"arxiv_version","alias_value":"2002.11309v4","created_at":"2026-07-05T04:32:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.11309","created_at":"2026-07-05T04:32:47Z"},{"alias_kind":"pith_short_12","alias_value":"HSKVL3F32PVP","created_at":"2026-07-05T04:32:47Z"},{"alias_kind":"pith_short_16","alias_value":"HSKVL3F32PVPRG3A","created_at":"2026-07-05T04:32:47Z"},{"alias_kind":"pith_short_8","alias_value":"HSKVL3F3","created_at":"2026-07-05T04:32:47Z"}],"graph_snapshots":[{"event_id":"sha256:40528d83272419b4bab73a38c018e4c568101facf29a9894bc204d369278a4b2","target":"graph","created_at":"2026-07-05T04:32:47Z","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/2002.11309/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the Fokker-Planck equation as a system of ordinary differential equations (ODEs) on finite-dimensional parameter space with the parameters inherited from generative models such as normalizing flows. We call such ODEs neural parametric Fokker-Planck equations. The fact that the Fokker-Planck equation can be viewed as the $L^2$-Wasserstein gradient flow of Kullback-Leibler (KL) divergence allows us to deriv","authors_text":"Haomin Zhou, Hongyuan Zha, Shu Liu, Wuchen Li","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-02-26T05:21:06Z","title":"Neural Parametric Fokker-Planck Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.11309","kind":"arxiv","version":4},"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":"sha256:747c05f8c30073e3c4517bf6ac63695c5ca80b1259e3cf999266a33178313e81","target":"record","created_at":"2026-07-05T04:32:47Z","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":"b7dcb7653341ac8bef464103e3797095f8bf2e01ec9d401a7c2535d68b0bb8cb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-02-26T05:21:06Z","title_canon_sha256":"2e83111e51643b5e7066537cae2caf7e390886e46ecde05ddafa770a1b31a9b1"},"schema_version":"1.0","source":{"id":"2002.11309","kind":"arxiv","version":4}},"canonical_sha256":"3c9555ecbbd3eaf89b60f8b96ab3dd763c5e6f2b8c91bba347a658246a936c04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c9555ecbbd3eaf89b60f8b96ab3dd763c5e6f2b8c91bba347a658246a936c04","first_computed_at":"2026-07-05T04:32:47.103810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:32:47.103810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBLr3NOAn5nHMAkkgNlvG8hgtRJZLleHjYZoUv0ygegYpNdEbseTiZbU9FSDUWua29YBy6eOgeckLAgEnnhYCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:32:47.104251Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.11309","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:747c05f8c30073e3c4517bf6ac63695c5ca80b1259e3cf999266a33178313e81","sha256:40528d83272419b4bab73a38c018e4c568101facf29a9894bc204d369278a4b2"],"state_sha256":"d0e89fe870f233dfd555b04d02e367ca69be493361a2e8945f05106b4f6be7d6"}