{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3A52MSKGAFVHM3MY5AK2MQPD2T","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":"be0ca831f6da2c28d3fce8873b8c32f26a8c876fd2dbe1491477d12cb8ff2de1","cross_cats_sorted":["cs.MS","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-03T09:00:43Z","title_canon_sha256":"517c02378930f6b6e6d236206291216580747c374ecad79f2b5f1a6a434cc3d9"},"schema_version":"1.0","source":{"id":"2506.02647","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02647","created_at":"2026-06-23T03:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02647v2","created_at":"2026-06-23T03:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02647","created_at":"2026-06-23T03:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"3A52MSKGAFVH","created_at":"2026-06-23T03:13:45Z"},{"alias_kind":"pith_short_16","alias_value":"3A52MSKGAFVHM3MY","created_at":"2026-06-23T03:13:45Z"},{"alias_kind":"pith_short_8","alias_value":"3A52MSKG","created_at":"2026-06-23T03:13:45Z"}],"graph_snapshots":[{"event_id":"sha256:244f742598290b08a363bce43953dadd960ca2c6e8a040a20c1433a7e04353a1","target":"graph","created_at":"2026-06-23T03:13:45Z","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/2506.02647/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a parallel multilevel Monte Carlo method as stochastic gradient estimator. As a result, we achieve precise control over the stochastic gradient's bias, introduced by numerical approximation, and its sampling error, arising from the use of incomplete gradients, while optimally managing computational resources. We show that the method exhibits linear convergence i","authors_text":"David Schneiderhan, Niklas Baumgarten","cross_cats":["cs.MS","cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-03T09:00:43Z","title":"Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02647","kind":"arxiv","version":2},"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:cd84fea71088d7ec7678808c3e940f88ab4b620b429b31cd93a88de902da59a4","target":"record","created_at":"2026-06-23T03:13:45Z","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":"be0ca831f6da2c28d3fce8873b8c32f26a8c876fd2dbe1491477d12cb8ff2de1","cross_cats_sorted":["cs.MS","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-03T09:00:43Z","title_canon_sha256":"517c02378930f6b6e6d236206291216580747c374ecad79f2b5f1a6a434cc3d9"},"schema_version":"1.0","source":{"id":"2506.02647","kind":"arxiv","version":2}},"canonical_sha256":"d83ba64946016a766d98e815a641e3d4d8c7826ad0e6a115b48589750e5c87ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d83ba64946016a766d98e815a641e3d4d8c7826ad0e6a115b48589750e5c87ff","first_computed_at":"2026-06-23T03:13:45.715408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:45.715408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q+8kh1KcqZYdDyI7t5CE+KiT7NX6i4767xUHYTrWn/RFDQfZJmDnFWAd4F/gQ1Vv9YC9/PqhxwlFqymuWb2oAg==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:45.715863Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02647","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd84fea71088d7ec7678808c3e940f88ab4b620b429b31cd93a88de902da59a4","sha256:244f742598290b08a363bce43953dadd960ca2c6e8a040a20c1433a7e04353a1"],"state_sha256":"4ec0a1344158cdbbeeab7bd49aa16864a1082cb184d833ed117c76379043f1c3"}