{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:USNL3OAX5DDRYVQWZB4KI776HI","short_pith_number":"pith:USNL3OAX","schema_version":"1.0","canonical_sha256":"a49abdb817e8c71c5616c878a47ffe3a128e37b0f7848dc88428380393a59045","source":{"kind":"arxiv","id":"2307.15256","version":2},"attestation_state":"computed","paper":{"title":"Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hao Dong, Jiale Linghu, JunZhi Cui, Yufeng Nie","submitted_at":"2023-07-28T01:44:10Z","abstract_excerpt":"The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials with highly oscillatory and discontinuous coefficients. In this novel HOMS-DRM, higher-order multi-scale analysis and modeling are first employed to overcome limitations of prohibitive computation and Frequency Principle when direct deep learning simulation. Then, improved deep Ritz method are designed to high-accuracy and mesh-free simulation for macroscop"},"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":"2307.15256","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-28T01:44:10Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"193dbce1552366e95df5bc9be41506ce9cbafb63354dd02d0d2394914dcb98d6","abstract_canon_sha256":"b9eb74cb958944782da1edf00a2206aa014887a1c8d315b16a25c3a5fb9c3785"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:40:16.029609Z","signature_b64":"rrxvA96JoqUPEGbpHHHUiLL21DpmXgc46LOQ9NNr3pJ85SKn93/P+1qJt4/HJPl/EuvMyQFxgRtaBHVXWQ9OAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a49abdb817e8c71c5616c878a47ffe3a128e37b0f7848dc88428380393a59045","last_reissued_at":"2026-07-05T06:40:16.029120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:40:16.029120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-order multi-scale deep Ritz method for multi-scale problems of authentic composite materials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hao Dong, Jiale Linghu, JunZhi Cui, Yufeng Nie","submitted_at":"2023-07-28T01:44:10Z","abstract_excerpt":"The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials with highly oscillatory and discontinuous coefficients. In this novel HOMS-DRM, higher-order multi-scale analysis and modeling are first employed to overcome limitations of prohibitive computation and Frequency Principle when direct deep learning simulation. Then, improved deep Ritz method are designed to high-accuracy and mesh-free simulation for macroscop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15256","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/2307.15256/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":"2307.15256","created_at":"2026-07-05T06:40:16.029179+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.15256v2","created_at":"2026-07-05T06:40:16.029179+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.15256","created_at":"2026-07-05T06:40:16.029179+00:00"},{"alias_kind":"pith_short_12","alias_value":"USNL3OAX5DDR","created_at":"2026-07-05T06:40:16.029179+00:00"},{"alias_kind":"pith_short_16","alias_value":"USNL3OAX5DDRYVQW","created_at":"2026-07-05T06:40:16.029179+00:00"},{"alias_kind":"pith_short_8","alias_value":"USNL3OAX","created_at":"2026-07-05T06:40:16.029179+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/USNL3OAX5DDRYVQWZB4KI776HI","json":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI.json","graph_json":"https://pith.science/api/pith-number/USNL3OAX5DDRYVQWZB4KI776HI/graph.json","events_json":"https://pith.science/api/pith-number/USNL3OAX5DDRYVQWZB4KI776HI/events.json","paper":"https://pith.science/paper/USNL3OAX"},"agent_actions":{"view_html":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI","download_json":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI.json","view_paper":"https://pith.science/paper/USNL3OAX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.15256&json=true","fetch_graph":"https://pith.science/api/pith-number/USNL3OAX5DDRYVQWZB4KI776HI/graph.json","fetch_events":"https://pith.science/api/pith-number/USNL3OAX5DDRYVQWZB4KI776HI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI/action/storage_attestation","attest_author":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI/action/author_attestation","sign_citation":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI/action/citation_signature","submit_replication":"https://pith.science/pith/USNL3OAX5DDRYVQWZB4KI776HI/action/replication_record"}},"created_at":"2026-07-05T06:40:16.029179+00:00","updated_at":"2026-07-05T06:40:16.029179+00:00"}