{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KGF5GOOH5K6BGF2A23ZJK25JNZ","short_pith_number":"pith:KGF5GOOH","schema_version":"1.0","canonical_sha256":"518bd339c7eabc131740d6f2956ba96e71a091b98ec8e65333fe373a3ad15492","source":{"kind":"arxiv","id":"2412.01379","version":2},"attestation_state":"computed","paper":{"title":"A deformation-based framework for learning solution mappings of PDEs defined on varying domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Pengzhan Jin, Shanshan Xiao, Yifa Tang","submitted_at":"2024-12-02T11:07:01Z","abstract_excerpt":"In this work, we establish a deformation-based framework for learning solution mappings of PDEs defined on varying domains. The union of functions defined on varying domains can be identified as a metric space according to the deformation, then the solution mapping is regarded as a continuous metric-to-metric mapping, and subsequently can be represented by another continuous metric-to-Banach mapping using two different strategies, referred to as the D2D subframework and the D2E subframework, respectively. We point out that such a metric-to-Banach mapping can be learned by neural networks, henc"},"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":"2412.01379","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-12-02T11:07:01Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"1c0adba4b720a45c0ebc4e8b63f1e86b2e5c19825c2713217a493d89f79239ff","abstract_canon_sha256":"4c4fc27e1ae231a7e97f989bc278f4ab439182fbf0f286b3199eb8eb0804d1a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:57:33.075005Z","signature_b64":"QjrYmsnyjIGnna5B42t57T033R7x1dYk4C1yYnTvVMVzTRt9YqqYGHBM0eVWCmXs/Q/qGcPz5vsqMUcLtadRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"518bd339c7eabc131740d6f2956ba96e71a091b98ec8e65333fe373a3ad15492","last_reissued_at":"2026-07-05T11:57:33.074612Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:57:33.074612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A deformation-based framework for learning solution mappings of PDEs defined on varying domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Pengzhan Jin, Shanshan Xiao, Yifa Tang","submitted_at":"2024-12-02T11:07:01Z","abstract_excerpt":"In this work, we establish a deformation-based framework for learning solution mappings of PDEs defined on varying domains. The union of functions defined on varying domains can be identified as a metric space according to the deformation, then the solution mapping is regarded as a continuous metric-to-metric mapping, and subsequently can be represented by another continuous metric-to-Banach mapping using two different strategies, referred to as the D2D subframework and the D2E subframework, respectively. We point out that such a metric-to-Banach mapping can be learned by neural networks, henc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.01379","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/2412.01379/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":"2412.01379","created_at":"2026-07-05T11:57:33.074666+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.01379v2","created_at":"2026-07-05T11:57:33.074666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.01379","created_at":"2026-07-05T11:57:33.074666+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGF5GOOH5K6B","created_at":"2026-07-05T11:57:33.074666+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGF5GOOH5K6BGF2A","created_at":"2026-07-05T11:57:33.074666+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGF5GOOH","created_at":"2026-07-05T11:57:33.074666+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/KGF5GOOH5K6BGF2A23ZJK25JNZ","json":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ.json","graph_json":"https://pith.science/api/pith-number/KGF5GOOH5K6BGF2A23ZJK25JNZ/graph.json","events_json":"https://pith.science/api/pith-number/KGF5GOOH5K6BGF2A23ZJK25JNZ/events.json","paper":"https://pith.science/paper/KGF5GOOH"},"agent_actions":{"view_html":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ","download_json":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ.json","view_paper":"https://pith.science/paper/KGF5GOOH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.01379&json=true","fetch_graph":"https://pith.science/api/pith-number/KGF5GOOH5K6BGF2A23ZJK25JNZ/graph.json","fetch_events":"https://pith.science/api/pith-number/KGF5GOOH5K6BGF2A23ZJK25JNZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ/action/storage_attestation","attest_author":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ/action/author_attestation","sign_citation":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ/action/citation_signature","submit_replication":"https://pith.science/pith/KGF5GOOH5K6BGF2A23ZJK25JNZ/action/replication_record"}},"created_at":"2026-07-05T11:57:33.074666+00:00","updated_at":"2026-07-05T11:57:33.074666+00:00"}