{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:DVOPYAYNGQLCXEAGMAUNTYMESK","short_pith_number":"pith:DVOPYAYN","schema_version":"1.0","canonical_sha256":"1d5cfc030d34162b90066028d9e184929bf5e3cc2c6ea29745b4c723206e362d","source":{"kind":"arxiv","id":"2203.01360","version":4},"attestation_state":"computed","paper":{"title":"Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Benjamin Peherstorfer, Eric Vanden-Eijnden, Joan Bruna","submitted_at":"2022-03-02T19:09:52Z","abstract_excerpt":"Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering applications. This work proposes Neural Galerkin schemes based on deep learning that generate training data with active learning for numerically solving high-dimensional partial differential equations. Neural Galerkin schemes build on the Dirac-Frenkel variational principle to train networks by minimizing the residual sequentially over time, which enables adapt"},"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":"2203.01360","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-03-02T19:09:52Z","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"title_canon_sha256":"fba46ee22cd90c2511fee5a81a740b4fd6593e783b3a77389f2e8df6e3ebd9b1","abstract_canon_sha256":"3ce0a629767181dc770eac9c9e0a580aaee534f128856be53479ee14f082dd41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:50:37.018599Z","signature_b64":"2fQXOddXZraiz+46GUnwDhnKz9RnbEpcapfPT0ygcgocg/dTMSL3aykZMoWAyUPmz25QQsmzA89vQ43ropypBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d5cfc030d34162b90066028d9e184929bf5e3cc2c6ea29745b4c723206e362d","last_reissued_at":"2026-07-05T07:50:37.018101Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:50:37.018101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Benjamin Peherstorfer, Eric Vanden-Eijnden, Joan Bruna","submitted_at":"2022-03-02T19:09:52Z","abstract_excerpt":"Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering applications. This work proposes Neural Galerkin schemes based on deep learning that generate training data with active learning for numerically solving high-dimensional partial differential equations. Neural Galerkin schemes build on the Dirac-Frenkel variational principle to train networks by minimizing the residual sequentially over time, which enables adapt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.01360","kind":"arxiv","version":4},"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/2203.01360/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":"2203.01360","created_at":"2026-07-05T07:50:37.018151+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.01360v4","created_at":"2026-07-05T07:50:37.018151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.01360","created_at":"2026-07-05T07:50:37.018151+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVOPYAYNGQLC","created_at":"2026-07-05T07:50:37.018151+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVOPYAYNGQLCXEAG","created_at":"2026-07-05T07:50:37.018151+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVOPYAYN","created_at":"2026-07-05T07:50:37.018151+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK","json":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK.json","graph_json":"https://pith.science/api/pith-number/DVOPYAYNGQLCXEAGMAUNTYMESK/graph.json","events_json":"https://pith.science/api/pith-number/DVOPYAYNGQLCXEAGMAUNTYMESK/events.json","paper":"https://pith.science/paper/DVOPYAYN"},"agent_actions":{"view_html":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK","download_json":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK.json","view_paper":"https://pith.science/paper/DVOPYAYN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.01360&json=true","fetch_graph":"https://pith.science/api/pith-number/DVOPYAYNGQLCXEAGMAUNTYMESK/graph.json","fetch_events":"https://pith.science/api/pith-number/DVOPYAYNGQLCXEAGMAUNTYMESK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK/action/storage_attestation","attest_author":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK/action/author_attestation","sign_citation":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK/action/citation_signature","submit_replication":"https://pith.science/pith/DVOPYAYNGQLCXEAGMAUNTYMESK/action/replication_record"}},"created_at":"2026-07-05T07:50:37.018151+00:00","updated_at":"2026-07-05T07:50:37.018151+00:00"}