{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:NJWVT4QU7ZNEQ3MTNBJ2LTNXK7","short_pith_number":"pith:NJWVT4QU","schema_version":"1.0","canonical_sha256":"6a6d59f214fe5a486d936853a5cdb757e63297bfc9bb7a815495f178824f3ec0","source":{"kind":"arxiv","id":"2110.11812","version":1},"attestation_state":"computed","paper":{"title":"Probabilistic ODE Solutions in Millions of Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"stat.ML","authors_text":"Jonathan Schmidt, Nathanael Bosch, Nicholas Kr\\\"amer, Philipp Hennig","submitted_at":"2021-10-22T14:35:45Z","abstract_excerpt":"Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed implementation schemes behind solving {high-dimensional} ODEs with a probabilistic numerical algorithm. This has not been possible before due to matrix-matrix operations in each solver step, but is crucial for scientifically relevant problems -- most importantly, the solution of discretised {partial} differential equations. In a nutshell, efficient high-dimens"},"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":"2110.11812","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-10-22T14:35:45Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"38a223481f1c5fd44f09aefbb59926dd0e1adefdd8008a2bd33ca5353be704ba","abstract_canon_sha256":"4085c97d7d3ce62219d74b857549a93f59372da393168e0b5e63d29b5be6af58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:24:51.920790Z","signature_b64":"Zf9xSy8Amhbps0JjigeCCAG2O9X11SC44MQVzpVwIXgXZ3QvMQL57s1aMfOKvYDnizaAwJyJvI/H3G7GcI2TBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a6d59f214fe5a486d936853a5cdb757e63297bfc9bb7a815495f178824f3ec0","last_reissued_at":"2026-07-05T03:24:51.920376Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:24:51.920376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probabilistic ODE Solutions in Millions of Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"stat.ML","authors_text":"Jonathan Schmidt, Nathanael Bosch, Nicholas Kr\\\"amer, Philipp Hennig","submitted_at":"2021-10-22T14:35:45Z","abstract_excerpt":"Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed implementation schemes behind solving {high-dimensional} ODEs with a probabilistic numerical algorithm. This has not been possible before due to matrix-matrix operations in each solver step, but is crucial for scientifically relevant problems -- most importantly, the solution of discretised {partial} differential equations. In a nutshell, efficient high-dimens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.11812","kind":"arxiv","version":1},"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/2110.11812/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":"2110.11812","created_at":"2026-07-05T03:24:51.920435+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.11812v1","created_at":"2026-07-05T03:24:51.920435+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.11812","created_at":"2026-07-05T03:24:51.920435+00:00"},{"alias_kind":"pith_short_12","alias_value":"NJWVT4QU7ZNE","created_at":"2026-07-05T03:24:51.920435+00:00"},{"alias_kind":"pith_short_16","alias_value":"NJWVT4QU7ZNEQ3MT","created_at":"2026-07-05T03:24:51.920435+00:00"},{"alias_kind":"pith_short_8","alias_value":"NJWVT4QU","created_at":"2026-07-05T03:24:51.920435+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/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7","json":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7.json","graph_json":"https://pith.science/api/pith-number/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/graph.json","events_json":"https://pith.science/api/pith-number/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/events.json","paper":"https://pith.science/paper/NJWVT4QU"},"agent_actions":{"view_html":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7","download_json":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7.json","view_paper":"https://pith.science/paper/NJWVT4QU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.11812&json=true","fetch_graph":"https://pith.science/api/pith-number/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/graph.json","fetch_events":"https://pith.science/api/pith-number/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/action/storage_attestation","attest_author":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/action/author_attestation","sign_citation":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/action/citation_signature","submit_replication":"https://pith.science/pith/NJWVT4QU7ZNEQ3MTNBJ2LTNXK7/action/replication_record"}},"created_at":"2026-07-05T03:24:51.920435+00:00","updated_at":"2026-07-05T03:24:51.920435+00:00"}