{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:NNDKLF53LVC6ZOR6H2L3XEOXNO","short_pith_number":"pith:NNDKLF53","schema_version":"1.0","canonical_sha256":"6b46a597bb5d45ecba3e3e97bb91d76b867c30828982ade0c03c3417022bf9c5","source":{"kind":"arxiv","id":"2111.13372","version":2},"attestation_state":"computed","paper":{"title":"A deep learning based reduced order modeling for stochastic underground flow problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Eric Chung, Shubin Fu, Yiran Wang","submitted_at":"2021-11-26T09:13:53Z","abstract_excerpt":"In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the stochastic parameter space that characterizes the possible highly heterogeneous media to the solution space of a stochastic flow problem to have fast online simulations. Dominant POD modes obtained from a well-designed spectral problem in a global snapshot space are used to represent the solution of the flow problem. Due to the small dimension of the solution, the c"},"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":"2111.13372","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2021-11-26T09:13:53Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"cd8d71bd967c5ff3b786e9760ae3d9470fecb7d546364547d0aad9b783bbdf9e","abstract_canon_sha256":"943522e6bf7e70681f0a9a9c15cfa5986be199fe078ad49152feeed4d4c6f171"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:36.915993Z","signature_b64":"T6xKVuHZZ7GKl775tp2VSE0g+6wtB8jlFJNZMa4I1+25mpxgt96HE6Mrfzsr6Q1KN2qXZS5XMvzpU/Ajb+2VCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b46a597bb5d45ecba3e3e97bb91d76b867c30828982ade0c03c3417022bf9c5","last_reissued_at":"2026-07-05T04:43:36.915473Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:36.915473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A deep learning based reduced order modeling for stochastic underground flow problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Eric Chung, Shubin Fu, Yiran Wang","submitted_at":"2021-11-26T09:13:53Z","abstract_excerpt":"In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the stochastic parameter space that characterizes the possible highly heterogeneous media to the solution space of a stochastic flow problem to have fast online simulations. Dominant POD modes obtained from a well-designed spectral problem in a global snapshot space are used to represent the solution of the flow problem. Due to the small dimension of the solution, the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.13372","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/2111.13372/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":"2111.13372","created_at":"2026-07-05T04:43:36.915528+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.13372v2","created_at":"2026-07-05T04:43:36.915528+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.13372","created_at":"2026-07-05T04:43:36.915528+00:00"},{"alias_kind":"pith_short_12","alias_value":"NNDKLF53LVC6","created_at":"2026-07-05T04:43:36.915528+00:00"},{"alias_kind":"pith_short_16","alias_value":"NNDKLF53LVC6ZOR6","created_at":"2026-07-05T04:43:36.915528+00:00"},{"alias_kind":"pith_short_8","alias_value":"NNDKLF53","created_at":"2026-07-05T04:43:36.915528+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/NNDKLF53LVC6ZOR6H2L3XEOXNO","json":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO.json","graph_json":"https://pith.science/api/pith-number/NNDKLF53LVC6ZOR6H2L3XEOXNO/graph.json","events_json":"https://pith.science/api/pith-number/NNDKLF53LVC6ZOR6H2L3XEOXNO/events.json","paper":"https://pith.science/paper/NNDKLF53"},"agent_actions":{"view_html":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO","download_json":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO.json","view_paper":"https://pith.science/paper/NNDKLF53","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.13372&json=true","fetch_graph":"https://pith.science/api/pith-number/NNDKLF53LVC6ZOR6H2L3XEOXNO/graph.json","fetch_events":"https://pith.science/api/pith-number/NNDKLF53LVC6ZOR6H2L3XEOXNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO/action/storage_attestation","attest_author":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO/action/author_attestation","sign_citation":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO/action/citation_signature","submit_replication":"https://pith.science/pith/NNDKLF53LVC6ZOR6H2L3XEOXNO/action/replication_record"}},"created_at":"2026-07-05T04:43:36.915528+00:00","updated_at":"2026-07-05T04:43:36.915528+00:00"}