{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:J6C2OSXMURNY3XCSSYJIYARJUW","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":"be5748ea9cc03d9295dd1aeafa5a7e9b08850f88826d226a49d1e96cbbb9b516","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-04-01T14:45:16Z","title_canon_sha256":"a13e88c2bde142524a5d8f70e8a97a9c8044e6ac692d178f06fe1a8c43f8c4b0"},"schema_version":"1.0","source":{"id":"2404.01145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.01145","created_at":"2026-07-05T08:03:01Z"},{"alias_kind":"arxiv_version","alias_value":"2404.01145v1","created_at":"2026-07-05T08:03:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.01145","created_at":"2026-07-05T08:03:01Z"},{"alias_kind":"pith_short_12","alias_value":"J6C2OSXMURNY","created_at":"2026-07-05T08:03:01Z"},{"alias_kind":"pith_short_16","alias_value":"J6C2OSXMURNY3XCS","created_at":"2026-07-05T08:03:01Z"},{"alias_kind":"pith_short_8","alias_value":"J6C2OSXM","created_at":"2026-07-05T08:03:01Z"}],"graph_snapshots":[{"event_id":"sha256:2751d7689eb7f7c0460d414f292207cbbf6171a864ab68e8177891a8ce1718bb","target":"graph","created_at":"2026-07-05T08:03:01Z","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/2404.01145/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that sequential-in-time training methods can be understood broadly as either optimize-then-discretize (OtD) or discretize-then-optimize (DtO) schemes, which are well known concepts in numerical analysis. The unifying perspective leads to novel stability and a posteriori error analysis results that provide insights into theoretical and numerical aspects that are inherent to eit","authors_text":"Benjamin Peherstorfer, Eric Vanden-Eijnden, Huan Zhang, Yifan Chen","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-04-01T14:45:16Z","title":"Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.01145","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":"sha256:8ddff0bcff7f6991ee42051b5e02cf3db4ca0dc922a07a212e8e0631a83f3b5e","target":"record","created_at":"2026-07-05T08:03:01Z","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":"be5748ea9cc03d9295dd1aeafa5a7e9b08850f88826d226a49d1e96cbbb9b516","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-04-01T14:45:16Z","title_canon_sha256":"a13e88c2bde142524a5d8f70e8a97a9c8044e6ac692d178f06fe1a8c43f8c4b0"},"schema_version":"1.0","source":{"id":"2404.01145","kind":"arxiv","version":1}},"canonical_sha256":"4f85a74aeca45b8ddc5296128c0229a5924a52ad122707ca0b83045f28529941","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f85a74aeca45b8ddc5296128c0229a5924a52ad122707ca0b83045f28529941","first_computed_at":"2026-07-05T08:03:01.485366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:03:01.485366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDBslIbAAEP5O+oPnR9jDSl2Opq4U+ryif27palOPReI60C2BN/OlixUXvCKMGKzo/AzH0/yZCv50wAZ+BblDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:03:01.485813Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.01145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ddff0bcff7f6991ee42051b5e02cf3db4ca0dc922a07a212e8e0631a83f3b5e","sha256:2751d7689eb7f7c0460d414f292207cbbf6171a864ab68e8177891a8ce1718bb"],"state_sha256":"63be87902bfe960605e0da5327070ab38f93b2d2257d044fee84efd55e3173d8"}