{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:C4SAROFPYEXYKGETOSEQ7HJ4PN","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":"a4d3eb49f4e4d05e1fb3048999b1d389688e67e60bb15926e22a066cda9bd96b","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-01-21T00:54:50Z","title_canon_sha256":"b3a684a857f8eeb19799819c607cc7a9e79f32bc6a14b88e4252aa6a884795de"},"schema_version":"1.0","source":{"id":"2401.11354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.11354","created_at":"2026-07-05T07:35:49Z"},{"alias_kind":"arxiv_version","alias_value":"2401.11354v1","created_at":"2026-07-05T07:35:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.11354","created_at":"2026-07-05T07:35:49Z"},{"alias_kind":"pith_short_12","alias_value":"C4SAROFPYEXY","created_at":"2026-07-05T07:35:49Z"},{"alias_kind":"pith_short_16","alias_value":"C4SAROFPYEXYKGET","created_at":"2026-07-05T07:35:49Z"},{"alias_kind":"pith_short_8","alias_value":"C4SAROFP","created_at":"2026-07-05T07:35:49Z"}],"graph_snapshots":[{"event_id":"sha256:ad25e87f4f1700d52ecea101c8a8afa04ec747991e321d6ed2cf027f23986a33","target":"graph","created_at":"2026-07-05T07:35:49Z","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/2401.11354/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared $W_2$ distance-based loss functions in the \\textit{reconstruction} of SDEs from noisy data. To demonstrate the practicality of our Wasserstein distance-based loss functions, we performed numerical experiments that demonstrate the efficiency of our method in reconstructing SDEs that arise across a number of applications.","authors_text":"Mingtao Xia, Qijing Shen, Tom Chou, Xiangting Li","cross_cats":["cs.LG","stat.ME"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-01-21T00:54:50Z","title":"Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.11354","kind":"arxiv","version":1},"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:d5c25b2519aaef8ac7c551763ef87876f6ddd9375b00143eac1fec6a58cc8e60","target":"record","created_at":"2026-07-05T07:35:49Z","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":"a4d3eb49f4e4d05e1fb3048999b1d389688e67e60bb15926e22a066cda9bd96b","cross_cats_sorted":["cs.LG","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-01-21T00:54:50Z","title_canon_sha256":"b3a684a857f8eeb19799819c607cc7a9e79f32bc6a14b88e4252aa6a884795de"},"schema_version":"1.0","source":{"id":"2401.11354","kind":"arxiv","version":1}},"canonical_sha256":"172408b8afc12f85189374890f9d3c7b51d26527ff8de9b05c0d8f6b7666b64b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"172408b8afc12f85189374890f9d3c7b51d26527ff8de9b05c0d8f6b7666b64b","first_computed_at":"2026-07-05T07:35:49.474932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:35:49.474932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uMMqXmmcpCOaV5T0uHyES9mfu+1fTzkVmrSh4UGALdRWuy/sunoytArpGwgwLgylwCIli13fy49sP0+mKgElAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:35:49.475391Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.11354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5c25b2519aaef8ac7c551763ef87876f6ddd9375b00143eac1fec6a58cc8e60","sha256:ad25e87f4f1700d52ecea101c8a8afa04ec747991e321d6ed2cf027f23986a33"],"state_sha256":"6f4768eef76407529aa22fdf41458d40b222a46b55cb7e4dd9f162211d517ee0"}