{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:FQ5NPV4WGATNZZMQKJ2XCXY24Q","short_pith_number":"pith:FQ5NPV4W","schema_version":"1.0","canonical_sha256":"2c3ad7d7963026dce5905275715f1ae42e9299d3c3761394221b082885a80f89","source":{"kind":"arxiv","id":"2304.14994","version":2},"attestation_state":"computed","paper":{"title":"A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andres Potapczynski, Andrew Gordon Wilson, Marc Finzi, Matthew Choptuik","submitted_at":"2023-04-28T17:28:18Z","abstract_excerpt":"Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical solvers is difficult or impossible. While global minimization of the PDE residual over the network parameters works well for boundary value problems, catastrophic forgetting impairs the applicability of this approach to initial value problems (IVPs). In an alternative local-in-time approach, the optimization problem can be converted into an ordinary differenti"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2304.14994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-04-28T17:28:18Z","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"title_canon_sha256":"ac8693f1e1105c2a1276cfce7f67a26d21ac69474f14d0836050f4256bf99ed5","abstract_canon_sha256":"858a4167672a4ee7dcf3c1a31e7a936201cc61872f40e70128ea7d9c976315c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:46:22.223986Z","signature_b64":"Kh2nvOQ9mW/m+da2zMUKM5I6Cu/aekaFDkJ7RKZwlN1HU6Qx7Jf8BibrZTYHDC0ecCHEaLGn5IwFhAB10ZV9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c3ad7d7963026dce5905275715f1ae42e9299d3c3761394221b082885a80f89","last_reissued_at":"2026-07-05T06:46:22.223488Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:46:22.223488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andres Potapczynski, Andrew Gordon Wilson, Marc Finzi, Matthew Choptuik","submitted_at":"2023-04-28T17:28:18Z","abstract_excerpt":"Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical solvers is difficult or impossible. While global minimization of the PDE residual over the network parameters works well for boundary value problems, catastrophic forgetting impairs the applicability of this approach to initial value problems (IVPs). In an alternative local-in-time approach, the optimization problem can be converted into an ordinary differenti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.14994","kind":"arxiv","version":2},"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/2304.14994/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2304.14994","created_at":"2026-07-05T06:46:22.223538+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.14994v2","created_at":"2026-07-05T06:46:22.223538+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.14994","created_at":"2026-07-05T06:46:22.223538+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQ5NPV4WGATN","created_at":"2026-07-05T06:46:22.223538+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQ5NPV4WGATNZZMQ","created_at":"2026-07-05T06:46:22.223538+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQ5NPV4W","created_at":"2026-07-05T06:46:22.223538+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.26662","citing_title":"Zero-Shot Size Transfer for Neural ODEs on Sparse Random Graphs: Graphon Limits and Adjoint Convergence","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.00284","citing_title":"A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q","json":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q.json","graph_json":"https://pith.science/api/pith-number/FQ5NPV4WGATNZZMQKJ2XCXY24Q/graph.json","events_json":"https://pith.science/api/pith-number/FQ5NPV4WGATNZZMQKJ2XCXY24Q/events.json","paper":"https://pith.science/paper/FQ5NPV4W"},"agent_actions":{"view_html":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q","download_json":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q.json","view_paper":"https://pith.science/paper/FQ5NPV4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.14994&json=true","fetch_graph":"https://pith.science/api/pith-number/FQ5NPV4WGATNZZMQKJ2XCXY24Q/graph.json","fetch_events":"https://pith.science/api/pith-number/FQ5NPV4WGATNZZMQKJ2XCXY24Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q/action/storage_attestation","attest_author":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q/action/author_attestation","sign_citation":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q/action/citation_signature","submit_replication":"https://pith.science/pith/FQ5NPV4WGATNZZMQKJ2XCXY24Q/action/replication_record"}},"created_at":"2026-07-05T06:46:22.223538+00:00","updated_at":"2026-07-05T06:46:22.223538+00:00"}