{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XBU65AOOXGBKXCRNSTYD6LLMJA","short_pith_number":"pith:XBU65AOO","schema_version":"1.0","canonical_sha256":"b869ee81ceb982ab8a2d94f03f2d6c48143a0789e57a5f21c6a88e89356c66a5","source":{"kind":"arxiv","id":"2505.08497","version":1},"attestation_state":"computed","paper":{"title":"A new methodology to decompose a parametric domain using reduced order data manifold in machine learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Axel TahmasebiMoradi, Chetra Mang, Mouadh Yagoubi","submitted_at":"2025-05-13T12:25:16Z","abstract_excerpt":"We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold. Moreover, two approaches are developed to reconstruct the inverse projector to project from the lower data component to the original one. Afterward, we provide a detailed strategy to decompose the parametric domain based on the low dimension manifold. Finally, numerical examples of harmonic transport problem are given to illustrate the efficiency and effectiven"},"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":"2505.08497","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-13T12:25:16Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"077a03a8a927e696b17529d2c21092b98d39d04fb039d8a5446ea7f916ef0bd5","abstract_canon_sha256":"470a7c9675223b25baa388a909d89a6ca2282b6421ceafe62a69ff445f86eef5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:31.283074Z","signature_b64":"pbP2pmj5/A2EeY4FejacNDKnCeeBnmZ5M9NgM7tWa0rgXKAoiZgDKUwsaR+x6ZaOLot8M+8PjKH0VkRTgHNXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b869ee81ceb982ab8a2d94f03f2d6c48143a0789e57a5f21c6a88e89356c66a5","last_reissued_at":"2026-07-05T11:02:31.282570Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:31.282570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new methodology to decompose a parametric domain using reduced order data manifold in machine learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Axel TahmasebiMoradi, Chetra Mang, Mouadh Yagoubi","submitted_at":"2025-05-13T12:25:16Z","abstract_excerpt":"We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold. Moreover, two approaches are developed to reconstruct the inverse projector to project from the lower data component to the original one. Afterward, we provide a detailed strategy to decompose the parametric domain based on the low dimension manifold. Finally, numerical examples of harmonic transport problem are given to illustrate the efficiency and effectiven"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08497","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/2505.08497/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":"2505.08497","created_at":"2026-07-05T11:02:31.282640+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.08497v1","created_at":"2026-07-05T11:02:31.282640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.08497","created_at":"2026-07-05T11:02:31.282640+00:00"},{"alias_kind":"pith_short_12","alias_value":"XBU65AOOXGBK","created_at":"2026-07-05T11:02:31.282640+00:00"},{"alias_kind":"pith_short_16","alias_value":"XBU65AOOXGBKXCRN","created_at":"2026-07-05T11:02:31.282640+00:00"},{"alias_kind":"pith_short_8","alias_value":"XBU65AOO","created_at":"2026-07-05T11:02:31.282640+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/XBU65AOOXGBKXCRNSTYD6LLMJA","json":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA.json","graph_json":"https://pith.science/api/pith-number/XBU65AOOXGBKXCRNSTYD6LLMJA/graph.json","events_json":"https://pith.science/api/pith-number/XBU65AOOXGBKXCRNSTYD6LLMJA/events.json","paper":"https://pith.science/paper/XBU65AOO"},"agent_actions":{"view_html":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA","download_json":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA.json","view_paper":"https://pith.science/paper/XBU65AOO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.08497&json=true","fetch_graph":"https://pith.science/api/pith-number/XBU65AOOXGBKXCRNSTYD6LLMJA/graph.json","fetch_events":"https://pith.science/api/pith-number/XBU65AOOXGBKXCRNSTYD6LLMJA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA/action/storage_attestation","attest_author":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA/action/author_attestation","sign_citation":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA/action/citation_signature","submit_replication":"https://pith.science/pith/XBU65AOOXGBKXCRNSTYD6LLMJA/action/replication_record"}},"created_at":"2026-07-05T11:02:31.282640+00:00","updated_at":"2026-07-05T11:02:31.282640+00:00"}