{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NOQLYURXSEQUBQA5BHIPYGSUOP","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":"23e2fa79e0dca0f013d0fcd3e2ada07eed0b985c3481a1c9c1dd735657425960","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-16T16:23:54Z","title_canon_sha256":"1dc89dc5129a4a85ab9ebc11689051f199c6d094dc1fbed432bb62bd82cf94b3"},"schema_version":"1.0","source":{"id":"2104.09625","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.09625","created_at":"2026-07-05T02:33:35Z"},{"alias_kind":"arxiv_version","alias_value":"2104.09625v1","created_at":"2026-07-05T02:33:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.09625","created_at":"2026-07-05T02:33:35Z"},{"alias_kind":"pith_short_12","alias_value":"NOQLYURXSEQU","created_at":"2026-07-05T02:33:35Z"},{"alias_kind":"pith_short_16","alias_value":"NOQLYURXSEQUBQA5","created_at":"2026-07-05T02:33:35Z"},{"alias_kind":"pith_short_8","alias_value":"NOQLYURX","created_at":"2026-07-05T02:33:35Z"}],"graph_snapshots":[{"event_id":"sha256:721efd68bfdc3242dff2a8757055327af4e778ebb9b42aa0350be049892278b4","target":"graph","created_at":"2026-07-05T02:33:35Z","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/2104.09625/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data sets. We provide a new perspective, that is, a different type of architecture through exploring the possible connections between traditional numerical methods (such as finite difference schemes) and deep neural networks, particularly convolutional and fully-connected neural networks. Our proposed approach will show its effectiveness and efficiency in solving PD","authors_text":"Cheng Chang, Liu Liu, Tieyong Zeng","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-16T16:23:54Z","title":"Finite Difference Nets: A Deep Recurrent Framework for Solving Evolution PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.09625","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":"sha256:16fd0478ac0da38bbad26da4590ddd5cdb45ec0e7f7c5e235618bb642ab9f7f8","target":"record","created_at":"2026-07-05T02:33:35Z","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":"23e2fa79e0dca0f013d0fcd3e2ada07eed0b985c3481a1c9c1dd735657425960","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.NA","submitted_at":"2021-04-16T16:23:54Z","title_canon_sha256":"1dc89dc5129a4a85ab9ebc11689051f199c6d094dc1fbed432bb62bd82cf94b3"},"schema_version":"1.0","source":{"id":"2104.09625","kind":"arxiv","version":1}},"canonical_sha256":"6ba0bc5237912140c01d09d0fc1a5473c4c8b72b4317b1c25dfaaf4d899bf661","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ba0bc5237912140c01d09d0fc1a5473c4c8b72b4317b1c25dfaaf4d899bf661","first_computed_at":"2026-07-05T02:33:35.430579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:33:35.430579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oIx9bK0JjPmyuMUjBT6kMaEgxa0UaXHtP8mt8nf4WbNKmHlOuZwm/8HxhGvodpYBTmVGL1+Jj1XvfPES8XzVDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:33:35.430976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.09625","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16fd0478ac0da38bbad26da4590ddd5cdb45ec0e7f7c5e235618bb642ab9f7f8","sha256:721efd68bfdc3242dff2a8757055327af4e778ebb9b42aa0350be049892278b4"],"state_sha256":"8add1b20284f40b21e09c9d08ab2e6aa87b51279e756d789a2ec43b43e09a05e"}