{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EE2OPMRWYFUW7PTXKZ3HQ6BWEY","short_pith_number":"pith:EE2OPMRW","canonical_record":{"source":{"id":"2506.05245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2025-06-05T17:03:42Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"c141988326660ff7d2e0daa0536a96c1fcfd73ee3ee1ad8addd6248f37fa50e9","abstract_canon_sha256":"c5668bbbe60b08fcf113904064ee82af44027a3e2ef9974ebbff13c4247b7d70"},"schema_version":"1.0"},"canonical_sha256":"2134e7b236c1696fbe7756767878362624fc507764596713b05b776201177464","source":{"kind":"arxiv","id":"2506.05245","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05245","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05245v1","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05245","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"EE2OPMRWYFUW","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_16","alias_value":"EE2OPMRWYFUW7PTX","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_8","alias_value":"EE2OPMRW","created_at":"2026-07-05T11:16:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EE2OPMRWYFUW7PTXKZ3HQ6BWEY","target":"record","payload":{"canonical_record":{"source":{"id":"2506.05245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2025-06-05T17:03:42Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"c141988326660ff7d2e0daa0536a96c1fcfd73ee3ee1ad8addd6248f37fa50e9","abstract_canon_sha256":"c5668bbbe60b08fcf113904064ee82af44027a3e2ef9974ebbff13c4247b7d70"},"schema_version":"1.0"},"canonical_sha256":"2134e7b236c1696fbe7756767878362624fc507764596713b05b776201177464","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:44.681298Z","signature_b64":"RKxHq9TqWBmFRnfaWKwCLrWqSGshuF8eZK+Yfu7cYTzZ3zB1NaRiFPmayCTZLHSo/CzxGiko87jk0WiGGBhYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2134e7b236c1696fbe7756767878362624fc507764596713b05b776201177464","last_reissued_at":"2026-07-05T11:16:44.680692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:44.680692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.05245","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jww7PQsceMyyRsHiPr/IxK7P2BmHDXUctzY+SVEgQAxOim9+AUmzvzlMURxxPV8WDp4BgN+k8/NBqJTaPB54Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:13:52.984641Z"},"content_sha256":"556f053886dc68da92ecb0f102af41662ade1c1e801d14da1bf7ac317ff11b51","schema_version":"1.0","event_id":"sha256:556f053886dc68da92ecb0f102af41662ade1c1e801d14da1bf7ac317ff11b51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EE2OPMRWYFUW7PTXKZ3HQ6BWEY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"nlin.PS","authors_text":"Panayotis G. Kevrekidis, Shaoxuan Chen, Su Yang, Wei Zhu","submitted_at":"2025-06-05T17:03:42Z","abstract_excerpt":"We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to noise, our approach based on Neural ODEs directly models moment trajectories, enabling robust learning from sparse and potentially irregular time series. Using as an application platform the nonlinear Schr\\\"{o}dinger equation, the framework accurately recovers governing moment dynamics when closure is available, even with limited and irregular observations. For s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05245","kind":"arxiv","version":1},"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/2506.05245/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oIF5FY5iLUQ3lX1k9Mv16++NwWsF8v3KPI1Bc1o+/MzemeswoitYKxBFAmPCEEdfigB+6oGjlSg3Eff8tU+jDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:13:52.985187Z"},"content_sha256":"63d2d40cb4111dbb3e03b6675d07b18f6aee006d017c2d50e56fe511ef484b90","schema_version":"1.0","event_id":"sha256:63d2d40cb4111dbb3e03b6675d07b18f6aee006d017c2d50e56fe511ef484b90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EE2OPMRWYFUW7PTXKZ3HQ6BWEY/bundle.json","state_url":"https://pith.science/pith/EE2OPMRWYFUW7PTXKZ3HQ6BWEY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EE2OPMRWYFUW7PTXKZ3HQ6BWEY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T12:13:52Z","links":{"resolver":"https://pith.science/pith/EE2OPMRWYFUW7PTXKZ3HQ6BWEY","bundle":"https://pith.science/pith/EE2OPMRWYFUW7PTXKZ3HQ6BWEY/bundle.json","state":"https://pith.science/pith/EE2OPMRWYFUW7PTXKZ3HQ6BWEY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EE2OPMRWYFUW7PTXKZ3HQ6BWEY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EE2OPMRWYFUW7PTXKZ3HQ6BWEY","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":"c5668bbbe60b08fcf113904064ee82af44027a3e2ef9974ebbff13c4247b7d70","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2025-06-05T17:03:42Z","title_canon_sha256":"c141988326660ff7d2e0daa0536a96c1fcfd73ee3ee1ad8addd6248f37fa50e9"},"schema_version":"1.0","source":{"id":"2506.05245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05245","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05245v1","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05245","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"EE2OPMRWYFUW","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_16","alias_value":"EE2OPMRWYFUW7PTX","created_at":"2026-07-05T11:16:44Z"},{"alias_kind":"pith_short_8","alias_value":"EE2OPMRW","created_at":"2026-07-05T11:16:44Z"}],"graph_snapshots":[{"event_id":"sha256:63d2d40cb4111dbb3e03b6675d07b18f6aee006d017c2d50e56fe511ef484b90","target":"graph","created_at":"2026-07-05T11:16:44Z","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/2506.05245/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to noise, our approach based on Neural ODEs directly models moment trajectories, enabling robust learning from sparse and potentially irregular time series. Using as an application platform the nonlinear Schr\\\"{o}dinger equation, the framework accurately recovers governing moment dynamics when closure is available, even with limited and irregular observations. For s","authors_text":"Panayotis G. Kevrekidis, Shaoxuan Chen, Su Yang, Wei Zhu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2025-06-05T17:03:42Z","title":"Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05245","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":"sha256:556f053886dc68da92ecb0f102af41662ade1c1e801d14da1bf7ac317ff11b51","target":"record","created_at":"2026-07-05T11:16:44Z","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":"c5668bbbe60b08fcf113904064ee82af44027a3e2ef9974ebbff13c4247b7d70","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2025-06-05T17:03:42Z","title_canon_sha256":"c141988326660ff7d2e0daa0536a96c1fcfd73ee3ee1ad8addd6248f37fa50e9"},"schema_version":"1.0","source":{"id":"2506.05245","kind":"arxiv","version":1}},"canonical_sha256":"2134e7b236c1696fbe7756767878362624fc507764596713b05b776201177464","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2134e7b236c1696fbe7756767878362624fc507764596713b05b776201177464","first_computed_at":"2026-07-05T11:16:44.680692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:44.680692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RKxHq9TqWBmFRnfaWKwCLrWqSGshuF8eZK+Yfu7cYTzZ3zB1NaRiFPmayCTZLHSo/CzxGiko87jk0WiGGBhYDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:44.681298Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:556f053886dc68da92ecb0f102af41662ade1c1e801d14da1bf7ac317ff11b51","sha256:63d2d40cb4111dbb3e03b6675d07b18f6aee006d017c2d50e56fe511ef484b90"],"state_sha256":"2666655c96455ecf92e5ec761bf4db3956dd0e8420942b35064064846e678d9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jCTmWOa1tVvjWPwe3l2moTxg3kHGgCwCoaSmFA6nDHFKWCePlNi5dzFqHVO/41DwGOyvx9LFHIg2JzlYgmsJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T12:13:52.989652Z","bundle_sha256":"d094ad80e593fe1a2d92e3d119667706c22305222d5cf1cc18079ef28832e22b"}}