{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OC3DUD4ISBEVQFKGLBMS5Q6DBK","short_pith_number":"pith:OC3DUD4I","schema_version":"1.0","canonical_sha256":"70b63a0f88904958154658592ec3c30a8e9a195414fc394282d929ddd104f6a8","source":{"kind":"arxiv","id":"1712.06758","version":1},"attestation_state":"computed","paper":{"title":"Scalable hierarchical PDE sampler for generating spatially correlated random fields using non-matching meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Panayot S. Vassilevski, Patrick Zulian, Rolf Krause, Sarah Osborn, Thomas Benson, Umberto Villa","submitted_at":"2017-12-19T02:52:58Z","abstract_excerpt":"This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general, unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction-diffusion PDE "},"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":"1712.06758","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-19T02:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"567029bb51fe4c01739ef4d326bff0f0831304061e35fc786753fe14bde92f6c","abstract_canon_sha256":"3ee12094e43244a87c79b70ac6e6676c8a9db83766ec7687ea0786efbdf0707e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:40.497798Z","signature_b64":"h9xfQam0CjHNEdtQrESgUxzmEa9cp3QbzovvXg5rjE4B87X25XxHN2r+gQbdiGftQcSa9J2g31pW4DEP4LLlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70b63a0f88904958154658592ec3c30a8e9a195414fc394282d929ddd104f6a8","last_reissued_at":"2026-05-18T00:27:40.497038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:40.497038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalable hierarchical PDE sampler for generating spatially correlated random fields using non-matching meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Panayot S. Vassilevski, Patrick Zulian, Rolf Krause, Sarah Osborn, Thomas Benson, Umberto Villa","submitted_at":"2017-12-19T02:52:58Z","abstract_excerpt":"This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general, unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction-diffusion PDE "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06758","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":""},"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":"1712.06758","created_at":"2026-05-18T00:27:40.497161+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.06758v1","created_at":"2026-05-18T00:27:40.497161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06758","created_at":"2026-05-18T00:27:40.497161+00:00"},{"alias_kind":"pith_short_12","alias_value":"OC3DUD4ISBEV","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OC3DUD4ISBEVQFKG","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OC3DUD4I","created_at":"2026-05-18T12:31:34.259226+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/OC3DUD4ISBEVQFKGLBMS5Q6DBK","json":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK.json","graph_json":"https://pith.science/api/pith-number/OC3DUD4ISBEVQFKGLBMS5Q6DBK/graph.json","events_json":"https://pith.science/api/pith-number/OC3DUD4ISBEVQFKGLBMS5Q6DBK/events.json","paper":"https://pith.science/paper/OC3DUD4I"},"agent_actions":{"view_html":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK","download_json":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK.json","view_paper":"https://pith.science/paper/OC3DUD4I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.06758&json=true","fetch_graph":"https://pith.science/api/pith-number/OC3DUD4ISBEVQFKGLBMS5Q6DBK/graph.json","fetch_events":"https://pith.science/api/pith-number/OC3DUD4ISBEVQFKGLBMS5Q6DBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK/action/storage_attestation","attest_author":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK/action/author_attestation","sign_citation":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK/action/citation_signature","submit_replication":"https://pith.science/pith/OC3DUD4ISBEVQFKGLBMS5Q6DBK/action/replication_record"}},"created_at":"2026-05-18T00:27:40.497161+00:00","updated_at":"2026-05-18T00:27:40.497161+00:00"}